File size: 97,900 Bytes
323a418
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
WEBVTT

00:00.000 --> 00:03.440
 The following is a conversation with Thomas Sanholm.

00:03.440 --> 00:06.880
 He's a professor at CMU and co creator of Labratus,

00:06.880 --> 00:09.880
 which is the first AI system to beat top human players

00:09.880 --> 00:13.000
 in the game of Heads Up No Limit Texas Holdem.

00:13.000 --> 00:15.600
 He has published over 450 papers

00:15.600 --> 00:17.320
 on game theory and machine learning,

00:17.320 --> 00:21.120
 including a best paper in 2017 at NIPS,

00:21.120 --> 00:23.560
 now renamed to Newrips,

00:23.560 --> 00:27.040
 which is where I caught up with him for this conversation.

00:27.040 --> 00:30.680
 His research and companies have had wide reaching impact

00:30.680 --> 00:32.160
 in the real world,

00:32.160 --> 00:34.400
 especially because he and his group

00:34.400 --> 00:36.640
 not only propose new ideas,

00:36.640 --> 00:40.440
 but also build systems to prove that these ideas work

00:40.440 --> 00:42.120
 in the real world.

00:42.120 --> 00:44.640
 This conversation is part of the MIT course

00:44.640 --> 00:46.440
 on artificial general intelligence

00:46.440 --> 00:49.040
 and the artificial intelligence podcast.

00:49.040 --> 00:52.400
 If you enjoy it, subscribe on YouTube, iTunes,

00:52.400 --> 00:54.320
 or simply connect with me on Twitter

00:54.320 --> 00:58.080
 at Lex Friedman, spelled F R I D.

00:58.080 --> 01:02.120
 And now here's my conversation with Thomas Sanholm.

01:03.080 --> 01:06.120
 Can you describe at the high level

01:06.120 --> 01:09.320
 the game of poker, Texas Holdem, Heads Up Texas Holdem

01:09.320 --> 01:13.280
 for people who might not be familiar with this card game?

01:13.280 --> 01:14.440
 Yeah, happy to.

01:14.440 --> 01:16.520
 So Heads Up No Limit Texas Holdem

01:16.520 --> 01:18.840
 has really emerged in the AI community

01:18.840 --> 01:21.360
 as a main benchmark for testing these

01:21.360 --> 01:23.560
 application independent algorithms

01:23.560 --> 01:26.440
 for imperfect information game solving.

01:26.440 --> 01:30.960
 And this is a game that's actually played by humans.

01:30.960 --> 01:33.960
 You don't see that much on TV or casinos

01:33.960 --> 01:36.160
 because well, for various reasons,

01:36.160 --> 01:40.240
 but you do see it in some expert level casinos

01:40.240 --> 01:43.080
 and you see it in the best poker movies of all time.

01:43.080 --> 01:45.720
 It's actually an event in the World Series of Poker,

01:45.720 --> 01:48.200
 but mostly it's played online

01:48.200 --> 01:50.880
 and typically for pretty big sums of money.

01:50.880 --> 01:54.560
 And this is a game that usually only experts play.

01:54.560 --> 01:58.720
 So if you go to your home game on a Friday night,

01:58.720 --> 02:01.280
 it probably is not gonna be Heads Up No Limit Texas Holdem.

02:01.280 --> 02:04.640
 It might be No Limit Texas Holdem in some cases,

02:04.640 --> 02:08.720
 but typically for a big group and it's not as competitive.

02:08.720 --> 02:10.520
 While Heads Up means it's two players.

02:10.520 --> 02:13.360
 So it's really like me against you.

02:13.360 --> 02:14.680
 Am I better or are you better?

02:14.680 --> 02:17.520
 Much like chess or go in that sense,

02:17.520 --> 02:19.520
 but an imperfect information game,

02:19.520 --> 02:21.520
 which makes it much harder because I have to deal

02:21.520 --> 02:25.560
 with issues of you knowing things that I don't know

02:25.560 --> 02:27.200
 and I know things that you don't know

02:27.200 --> 02:29.720
 instead of pieces being nicely laid on the board

02:29.720 --> 02:31.120
 for both of us to see.

02:31.120 --> 02:34.840
 So in Texas Holdem, there's two cards

02:34.840 --> 02:37.440
 that you only see that belong to you.

02:37.440 --> 02:38.520
 Yeah. And there is,

02:38.520 --> 02:40.400
 they gradually lay out some cards

02:40.400 --> 02:44.080
 that add up overall to five cards that everybody can see.

02:44.080 --> 02:45.720
 Yeah. So the imperfect nature

02:45.720 --> 02:47.560
 of the information is the two cards

02:47.560 --> 02:48.400
 that you're holding in your hand.

02:48.400 --> 02:49.380
 Up front, yeah.

02:49.380 --> 02:51.840
 So as you said, you first get two cards

02:51.840 --> 02:55.200
 in private each and then there's a betting round.

02:55.200 --> 02:58.320
 Then you get three cards in public on the table.

02:58.320 --> 02:59.240
 Then there's a betting round.

02:59.240 --> 03:01.680
 Then you get the fourth card in public on the table.

03:01.680 --> 03:02.580
 There's a betting round.

03:02.580 --> 03:04.920
 Then you get the 5th card on the table.

03:04.920 --> 03:05.760
 There's a betting round.

03:05.760 --> 03:07.480
 So there's a total of four betting rounds

03:07.480 --> 03:11.140
 and four tranches of information revelation if you will.

03:11.140 --> 03:14.120
 The only the first tranche is private

03:14.120 --> 03:16.520
 and then it's public from there.

03:16.520 --> 03:21.520
 And this is probably by far the most popular game in AI

03:24.040 --> 03:26.380
 and just the general public

03:26.380 --> 03:28.400
 in terms of imperfect information.

03:28.400 --> 03:32.520
 So that's probably the most popular spectator game

03:32.520 --> 03:33.400
 to watch, right?

03:33.400 --> 03:37.260
 So, which is why it's a super exciting game to tackle.

03:37.260 --> 03:40.480
 So it's on the order of chess, I would say,

03:40.480 --> 03:43.680
 in terms of popularity, in terms of AI setting it

03:43.680 --> 03:46.360
 as the bar of what is intelligence.

03:46.360 --> 03:50.400
 So in 2017, Labratus, how do you pronounce it?

03:50.400 --> 03:51.220
 Labratus.

03:51.220 --> 03:52.060
 Labratus.

03:52.060 --> 03:52.900
 Labratus beats.

03:52.900 --> 03:54.080
 A little Latin there.

03:54.080 --> 03:55.520
 A little bit of Latin.

03:55.520 --> 04:00.520
 Labratus beats a few, four expert human players.

04:01.040 --> 04:03.080
 Can you describe that event?

04:03.080 --> 04:04.060
 What you learned from it?

04:04.060 --> 04:04.900
 What was it like?

04:04.900 --> 04:06.860
 What was the process in general

04:06.860 --> 04:09.960
 for people who have not read the papers and the study?

04:09.960 --> 04:12.920
 Yeah, so the event was that we invited

04:12.920 --> 04:14.840
 four of the top 10 players,

04:14.840 --> 04:17.080
 with these specialist players in Heads Up No Limit,

04:17.080 --> 04:19.080
 Texas Holden, which is very important

04:19.080 --> 04:21.400
 because this game is actually quite different

04:21.400 --> 04:23.900
 than the multiplayer version.

04:23.900 --> 04:25.680
 We brought them in to Pittsburgh

04:25.680 --> 04:28.920
 to play at the Reverse Casino for 20 days.

04:28.920 --> 04:31.840
 We wanted to get 120,000 hands in

04:31.840 --> 04:36.160
 because we wanted to get statistical significance.

04:36.160 --> 04:39.040
 So it's a lot of hands for humans to play,

04:39.040 --> 04:42.840
 even for these top pros who play fairly quickly normally.

04:42.840 --> 04:46.400
 So we couldn't just have one of them play so many hands.

04:46.400 --> 04:50.400
 20 days, they were playing basically morning to evening.

04:50.400 --> 04:55.400
 And I raised 200,000 as a little incentive for them to play.

04:55.660 --> 05:00.060
 And the setting was so that they didn't all get 50,000.

05:01.080 --> 05:02.640
 We actually paid them out

05:02.640 --> 05:05.480
 based on how they did against the AI each.

05:05.480 --> 05:09.440
 So they had an incentive to play as hard as they could,

05:09.440 --> 05:11.160
 whether they're way ahead or way behind

05:11.160 --> 05:13.760
 or right at the mark of beating the AI.

05:13.760 --> 05:16.000
 And you don't make any money, unfortunately.

05:16.000 --> 05:17.920
 Right, no, we can't make any money.

05:17.920 --> 05:20.320
 So originally, a couple of years earlier,

05:20.320 --> 05:24.080
 I actually explored whether we could actually play for money

05:24.080 --> 05:28.000
 because that would be, of course, interesting as well,

05:28.000 --> 05:29.520
 to play against the top people for money.

05:29.520 --> 05:33.040
 But the Pennsylvania Gaming Board said no, so we couldn't.

05:33.040 --> 05:35.520
 So this is much like an exhibit,

05:36.400 --> 05:39.760
 like for a musician or a boxer or something like that.

05:39.760 --> 05:41.600
 Nevertheless, they were keeping track of the money

05:41.600 --> 05:46.600
 and brought us close to $2 million, I think.

05:48.200 --> 05:51.840
 So if it was for real money, if you were able to earn money,

05:51.840 --> 05:55.360
 that was a quite impressive and inspiring achievement.

05:55.360 --> 05:59.280
 Just a few details, what were the players looking at?

05:59.280 --> 06:00.460
 Were they behind a computer?

06:00.460 --> 06:02.080
 What was the interface like?

06:02.080 --> 06:05.240
 Yes, they were playing much like they normally do.

06:05.240 --> 06:07.200
 These top players, when they play this game,

06:07.200 --> 06:08.680
 they play mostly online.

06:08.680 --> 06:11.640
 So they're used to playing through a UI.

06:11.640 --> 06:13.280
 And they did the same thing here.

06:13.280 --> 06:14.520
 So there was this layout.

06:14.520 --> 06:17.920
 You could imagine there's a table on a screen.

06:17.920 --> 06:20.080
 There's the human sitting there,

06:20.080 --> 06:21.720
 and then there's the AI sitting there.

06:21.720 --> 06:24.560
 And the screen shows everything that's happening.

06:24.560 --> 06:27.480
 The cards coming out and shows the bets being made.

06:27.480 --> 06:29.940
 And we also had the betting history for the human.

06:29.940 --> 06:33.320
 So if the human forgot what had happened in the hand so far,

06:33.320 --> 06:37.240
 they could actually reference back and so forth.

06:37.240 --> 06:39.480
 Is there a reason they were given access

06:39.480 --> 06:41.200
 to the betting history for?

06:41.200 --> 06:45.860
 Well, we just, it didn't really matter.

06:45.860 --> 06:47.360
 They wouldn't have forgotten anyway.

06:47.360 --> 06:48.800
 These are top quality people.

06:48.800 --> 06:51.300
 But we just wanted to put out there

06:51.300 --> 06:53.460
 so it's not a question of the human forgetting

06:53.460 --> 06:55.320
 and the AI somehow trying to get advantage

06:55.320 --> 06:56.760
 of better memory.

06:56.760 --> 06:57.640
 So what was that like?

06:57.640 --> 06:59.720
 I mean, that was an incredible accomplishment.

06:59.720 --> 07:02.760
 So what did it feel like before the event?

07:02.760 --> 07:05.640
 Did you have doubt, hope?

07:05.640 --> 07:08.160
 Where was your confidence at?

07:08.160 --> 07:09.240
 Yeah, that's great.

07:09.240 --> 07:10.160
 So great question.

07:10.160 --> 07:14.200
 So 18 months earlier, I had organized a similar brains

07:14.200 --> 07:17.840
 versus AI competition with a previous AI called Cloudyco

07:17.840 --> 07:20.560
 and we couldn't beat the humans.

07:20.560 --> 07:23.800
 So this time around, it was only 18 months later.

07:23.800 --> 07:27.820
 And I knew that this new AI, Libratus, was way stronger,

07:27.820 --> 07:31.360
 but it's hard to say how you'll do against the top humans

07:31.360 --> 07:32.440
 before you try.

07:32.440 --> 07:35.160
 So I thought we had about a 50, 50 shot.

07:35.160 --> 07:38.880
 And the international betting sites put us

07:38.880 --> 07:41.800
 as a four to one or five to one underdog.

07:41.800 --> 07:44.700
 So it's kind of interesting that people really believe

07:44.700 --> 07:48.440
 in people and over AI, not just people.

07:48.440 --> 07:50.720
 People don't just over believe in themselves,

07:50.720 --> 07:53.280
 but they have overconfidence in other people as well

07:53.280 --> 07:55.440
 compared to the performance of AI.

07:55.440 --> 07:59.120
 And yeah, so we were a four to one or five to one underdog.

07:59.120 --> 08:02.880
 And even after three days of beating the humans in a row,

08:02.880 --> 08:06.520
 we were still 50, 50 on the international betting sites.

08:06.520 --> 08:09.040
 Do you think there's something special and magical

08:09.040 --> 08:12.160
 about poker and the way people think about it,

08:12.160 --> 08:14.600
 in the sense you have,

08:14.600 --> 08:17.320
 I mean, even in chess, there's no Hollywood movies.

08:17.320 --> 08:21.200
 Poker is the star of many movies.

08:21.200 --> 08:26.200
 And there's this feeling that certain human facial

08:26.640 --> 08:30.760
 expressions and body language, eye movement,

08:30.760 --> 08:33.360
 all these tells are critical to poker.

08:33.360 --> 08:35.000
 Like you can look into somebody's soul

08:35.000 --> 08:37.880
 and understand their betting strategy and so on.

08:37.880 --> 08:41.520
 So that's probably why, possibly,

08:41.520 --> 08:43.640
 do you think that is why people have a confidence

08:43.640 --> 08:45.640
 that humans will outperform?

08:45.640 --> 08:48.920
 Because AI systems cannot, in this construct,

08:48.920 --> 08:51.040
 perceive these kinds of tells.

08:51.040 --> 08:53.200
 They're only looking at betting patterns

08:53.200 --> 08:58.200
 and nothing else, betting patterns and statistics.

08:58.200 --> 09:02.200
 So what's more important to you

09:02.200 --> 09:06.120
 if you step back on human players, human versus human?

09:06.120 --> 09:08.600
 What's the role of these tells,

09:08.600 --> 09:11.880
 of these ideas that we romanticize?

09:11.880 --> 09:15.480
 Yeah, so I'll split it into two parts.

09:15.480 --> 09:20.480
 So one is why do humans trust humans more than AI

09:20.480 --> 09:22.600
 and have overconfidence in humans?

09:22.600 --> 09:25.920
 I think that's not really related to the tell question.

09:25.920 --> 09:28.600
 It's just that they've seen these top players,

09:28.600 --> 09:31.040
 how good they are, and they're really fantastic.

09:31.040 --> 09:36.040
 So it's just hard to believe that an AI could beat them.

09:36.040 --> 09:37.680
 So I think that's where that comes from.

09:37.680 --> 09:40.600
 And that's actually maybe a more general lesson about AI.

09:40.600 --> 09:43.200
 That until you've seen it overperform a human,

09:43.200 --> 09:45.080
 it's hard to believe that it could.

09:45.080 --> 09:50.080
 But then the tells, a lot of these top players,

09:50.560 --> 09:52.760
 they're so good at hiding tells

09:52.760 --> 09:56.240
 that among the top players,

09:56.240 --> 09:59.480
 it's actually not really worth it

09:59.480 --> 10:01.200
 for them to invest a lot of effort

10:01.200 --> 10:03.160
 trying to find tells in each other

10:03.160 --> 10:05.640
 because they're so good at hiding them.

10:05.640 --> 10:09.840
 So yes, at the kind of Friday evening game,

10:09.840 --> 10:11.800
 tells are gonna be a huge thing.

10:11.800 --> 10:13.160
 You can read other people.

10:13.160 --> 10:14.120
 And if you're a good reader,

10:14.120 --> 10:16.440
 you'll read them like an open book.

10:16.440 --> 10:18.280
 But at the top levels of poker now,

10:18.280 --> 10:21.960
 the tells become a much smaller and smaller aspect

10:21.960 --> 10:24.480
 of the game as you go to the top levels.

10:24.480 --> 10:28.120
 The amount of strategies, the amount of possible actions

10:28.120 --> 10:33.120
 is very large, 10 to the power of 100 plus.

10:35.400 --> 10:37.880
 So there has to be some, I've read a few of the papers

10:37.880 --> 10:42.080
 related, it has to form some abstractions

10:42.080 --> 10:44.040
 of various hands and actions.

10:44.040 --> 10:47.560
 So what kind of abstractions are effective

10:47.560 --> 10:49.200
 for the game of poker?

10:49.200 --> 10:50.880
 Yeah, so you're exactly right.

10:50.880 --> 10:55.360
 So when you go from a game tree that's 10 to the 161,

10:55.360 --> 10:58.000
 especially in an imperfect information game,

10:58.000 --> 11:00.200
 it's way too large to solve directly,

11:00.200 --> 11:03.280
 even with our fastest equilibrium finding algorithms.

11:03.280 --> 11:07.200
 So you wanna abstract it first.

11:07.200 --> 11:10.920
 And abstraction in games is much trickier

11:10.920 --> 11:15.440
 than abstraction in MDPs or other single agent settings.

11:15.440 --> 11:17.760
 Because you have these abstraction pathologies

11:17.760 --> 11:19.880
 that if I have a finer grained abstraction,

11:19.880 --> 11:23.240
 the strategy that I can get from that for the real game

11:23.240 --> 11:25.240
 might actually be worse than the strategy

11:25.240 --> 11:27.160
 I can get from the coarse grained abstraction.

11:27.160 --> 11:28.760
 So you have to be very careful.

11:28.760 --> 11:31.080
 Now the kinds of abstractions, just to zoom out,

11:31.080 --> 11:34.480
 we're talking about, there's the hands abstractions

11:34.480 --> 11:37.280
 and then there's betting strategies.

11:37.280 --> 11:38.600
 Yeah, betting actions, yeah.

11:38.600 --> 11:39.440
 Baiting actions.

11:39.440 --> 11:41.640
 So there's information abstraction,

11:41.640 --> 11:44.720
 don't talk about general games, information abstraction,

11:44.720 --> 11:47.560
 which is the abstraction of what chance does.

11:47.560 --> 11:50.080
 And this would be the cards in the case of poker.

11:50.080 --> 11:52.480
 And then there's action abstraction,

11:52.480 --> 11:57.000
 which is abstracting the actions of the actual players,

11:57.000 --> 11:59.560
 which would be bets in the case of poker.

11:59.560 --> 12:01.320
 Yourself and the other players?

12:01.320 --> 12:03.680
 Yes, yourself and other players.

12:03.680 --> 12:08.280
 And for information abstraction,

12:08.280 --> 12:11.160
 we were completely automated.

12:11.160 --> 12:13.840
 So these are algorithms,

12:13.840 --> 12:16.760
 but they do what we call potential aware abstraction,

12:16.760 --> 12:19.000
 where we don't just look at the value of the hand,

12:19.000 --> 12:20.840
 but also how it might materialize

12:20.840 --> 12:22.560
 into good or bad hands over time.

12:22.560 --> 12:25.280
 And it's a certain kind of bottom up process

12:25.280 --> 12:27.640
 with integer programming there and clustering

12:27.640 --> 12:31.480
 and various aspects, how do you build this abstraction?

12:31.480 --> 12:34.400
 And then in the action abstraction,

12:34.400 --> 12:39.400
 there it's largely based on how humans and other AIs

12:40.520 --> 12:42.320
 have played this game in the past.

12:42.320 --> 12:43.880
 But in the beginning,

12:43.880 --> 12:47.680
 we actually used an automated action abstraction technology,

12:47.680 --> 12:50.240
 which is provably convergent

12:51.240 --> 12:54.040
 that it finds the optimal combination of bet sizes,

12:54.040 --> 12:55.480
 but it's not very scalable.

12:55.480 --> 12:57.280
 So we couldn't use it for the whole game,

12:57.280 --> 12:59.880
 but we use it for the first couple of betting actions.

12:59.880 --> 13:03.080
 So what's more important, the strength of the hand,

13:03.080 --> 13:08.080
 so the information abstraction or the how you play them,

13:09.320 --> 13:11.640
 the actions, does it, you know,

13:11.640 --> 13:13.200
 the romanticized notion again,

13:13.200 --> 13:15.600
 is that it doesn't matter what hands you have,

13:15.600 --> 13:19.240
 that the actions, the betting may be the way you win

13:19.240 --> 13:20.320
 no matter what hands you have.

13:20.320 --> 13:23.280
 Yeah, so that's why you have to play a lot of hands

13:23.280 --> 13:26.800
 so that the role of luck gets smaller.

13:26.800 --> 13:29.920
 So you could otherwise get lucky and get some good hands

13:29.920 --> 13:31.480
 and then you're gonna win the match.

13:31.480 --> 13:34.400
 Even with thousands of hands, you can get lucky

13:35.280 --> 13:36.720
 because there's so much variance

13:36.720 --> 13:40.880
 in No Limit Texas Holden because if we both go all in,

13:40.880 --> 13:43.640
 it's a huge stack of variance, so there are these

13:43.640 --> 13:47.800
 massive swings in No Limit Texas Holden.

13:47.800 --> 13:50.240
 So that's why you have to play not just thousands,

13:50.240 --> 13:55.000
 but over 100,000 hands to get statistical significance.

13:55.000 --> 13:57.880
 So let me ask another way this question.

13:57.880 --> 14:00.880
 If you didn't even look at your hands,

14:02.000 --> 14:04.560
 but they didn't know that, the opponents didn't know that,

14:04.560 --> 14:06.680
 how well would you be able to do?

14:06.680 --> 14:07.760
 Oh, that's a good question.

14:07.760 --> 14:09.600
 There's actually, I heard this story

14:09.600 --> 14:11.800
 that there's this Norwegian female poker player

14:11.800 --> 14:15.240
 called Annette Oberstad who's actually won a tournament

14:15.240 --> 14:18.640
 by doing exactly that, but that would be extremely rare.

14:18.640 --> 14:23.440
 So you cannot really play well that way.

14:23.440 --> 14:27.840
 Okay, so the hands do have some role to play, okay.

14:27.840 --> 14:32.840
 So Labradus does not use, as far as I understand,

14:33.120 --> 14:35.320
 they use learning methods, deep learning.

14:35.320 --> 14:40.320
 Is there room for learning in,

14:40.600 --> 14:44.120
 there's no reason why Labradus doesn't combine

14:44.120 --> 14:46.400
 with an AlphaGo type approach for estimating

14:46.400 --> 14:49.200
 the quality for function estimator.

14:49.200 --> 14:52.040
 What are your thoughts on this,

14:52.040 --> 14:54.760
 maybe as compared to another algorithm

14:54.760 --> 14:56.720
 which I'm not that familiar with, DeepStack,

14:56.720 --> 14:59.280
 the engine that does use deep learning,

14:59.280 --> 15:01.560
 that it's unclear how well it does,

15:01.560 --> 15:03.480
 but nevertheless uses deep learning.

15:03.480 --> 15:05.400
 So what are your thoughts about learning methods

15:05.400 --> 15:09.280
 to aid in the way that Labradus plays in the game of poker?

15:09.280 --> 15:10.640
 Yeah, so as you said,

15:10.640 --> 15:13.080
 Labradus did not use learning methods

15:13.080 --> 15:15.680
 and played very well without them.

15:15.680 --> 15:17.840
 Since then, we have actually, actually here,

15:17.840 --> 15:20.000
 we have a couple of papers on things

15:20.000 --> 15:22.360
 that do use learning techniques.

15:22.360 --> 15:23.200
 Excellent.

15:24.440 --> 15:26.360
 And deep learning in particular.

15:26.360 --> 15:29.920
 And sort of the way you're talking about

15:29.920 --> 15:33.360
 where it's learning an evaluation function,

15:33.360 --> 15:37.400
 but in imperfect information games,

15:37.400 --> 15:42.400
 unlike let's say in Go or now also in chess and shogi,

15:42.440 --> 15:47.400
 it's not sufficient to learn an evaluation for a state

15:47.400 --> 15:52.400
 because the value of an information set

15:52.920 --> 15:55.400
 depends not only on the exact state,

15:55.400 --> 15:59.200
 but it also depends on both players beliefs.

15:59.200 --> 16:01.240
 Like if I have a bad hand,

16:01.240 --> 16:04.720
 I'm much better off if the opponent thinks I have a good hand

16:04.720 --> 16:05.560
 and vice versa.

16:05.560 --> 16:06.480
 If I have a good hand,

16:06.480 --> 16:09.360
 I'm much better off if the opponent believes

16:09.360 --> 16:10.280
 I have a bad hand.

16:11.360 --> 16:15.640
 So the value of a state is not just a function of the cards.

16:15.640 --> 16:19.600
 It depends on, if you will, the path of play,

16:19.600 --> 16:22.040
 but only to the extent that it's captured

16:22.040 --> 16:23.720
 in the belief distributions.

16:23.720 --> 16:26.240
 So that's why it's not as simple

16:26.240 --> 16:29.320
 as it is in perfect information games.

16:29.320 --> 16:31.080
 And I don't wanna say it's simple there either.

16:31.080 --> 16:34.200
 It's of course very complicated computationally there too,

16:34.200 --> 16:36.520
 but at least conceptually, it's very straightforward.

16:36.520 --> 16:38.760
 There's a state, there's an evaluation function.

16:38.760 --> 16:39.800
 You can try to learn it.

16:39.800 --> 16:43.280
 Here, you have to do something more.

16:43.280 --> 16:47.160
 And what we do is in one of these papers,

16:47.160 --> 16:50.800
 we're looking at where we allow the opponent

16:50.800 --> 16:53.000
 to actually take different strategies

16:53.000 --> 16:56.440
 at the leaf of the search tree, if you will.

16:56.440 --> 16:59.840
 And that is a different way of doing it.

16:59.840 --> 17:02.560
 And it doesn't assume therefore a particular way

17:02.560 --> 17:04.040
 that the opponent plays,

17:04.040 --> 17:05.840
 but it allows the opponent to choose

17:05.840 --> 17:09.800
 from a set of different continuation strategies.

17:09.800 --> 17:13.400
 And that forces us to not be too optimistic

17:13.400 --> 17:15.520
 in a look ahead search.

17:15.520 --> 17:19.040
 And that's one way you can do sound look ahead search

17:19.040 --> 17:21.480
 in imperfect information games,

17:21.480 --> 17:23.360
 which is very difficult.

17:23.360 --> 17:26.080
 And you were asking about DeepStack.

17:26.080 --> 17:29.280
 What they did, it was very different than what we do,

17:29.280 --> 17:32.000
 either in Libratus or in this new work.

17:32.000 --> 17:35.440
 They were randomly generating various situations

17:35.440 --> 17:36.440
 in the game.

17:36.440 --> 17:38.080
 Then they were doing the look ahead

17:38.080 --> 17:39.840
 from there to the end of the game,

17:39.840 --> 17:42.960
 as if that was the start of a different game.

17:42.960 --> 17:44.920
 And then they were using deep learning

17:44.920 --> 17:47.960
 to learn those values of those states,

17:47.960 --> 17:50.280
 but the states were not just the physical states.

17:50.280 --> 17:52.560
 They include belief distributions.

17:52.560 --> 17:56.800
 When you talk about look ahead for DeepStack

17:56.800 --> 17:59.480
 or with Libratus, does it mean,

17:59.480 --> 18:02.680
 considering every possibility that the game can evolve,

18:02.680 --> 18:04.280
 are we talking about extremely,

18:04.280 --> 18:06.880
 sort of this exponentially growth of a tree?

18:06.880 --> 18:09.720
 Yes, so we're talking about exactly that.

18:11.280 --> 18:14.280
 Much like you do in alpha beta search

18:14.280 --> 18:17.480
 or Monte Carlo tree search, but with different techniques.

18:17.480 --> 18:19.280
 So there's a different search algorithm.

18:19.280 --> 18:21.920
 And then we have to deal with the leaves differently.

18:21.920 --> 18:24.000
 So if you think about what Libratus did,

18:24.000 --> 18:25.520
 we didn't have to worry about this

18:25.520 --> 18:28.560
 because we only did it at the end of the game.

18:28.560 --> 18:32.280
 So we would always terminate into a real situation

18:32.280 --> 18:34.000
 and we would know what the payout is.

18:34.000 --> 18:36.880
 It didn't do these depth limited lookaheads,

18:36.880 --> 18:40.680
 but now in this new paper, which is called depth limited,

18:40.680 --> 18:42.120
 I think it's called depth limited search

18:42.120 --> 18:43.880
 for imperfect information games,

18:43.880 --> 18:47.040
 we can actually do sound depth limited lookahead.

18:47.040 --> 18:49.240
 So we can actually start to do the look ahead

18:49.240 --> 18:51.080
 from the beginning of the game on,

18:51.080 --> 18:53.400
 because that's too complicated to do

18:53.400 --> 18:54.920
 for this whole long game.

18:54.920 --> 18:57.680
 So in Libratus, we were just doing it for the end.

18:57.680 --> 19:00.720
 So, and then the other side, this belief distribution,

19:00.720 --> 19:05.320
 so is it explicitly modeled what kind of beliefs

19:05.320 --> 19:07.400
 that the opponent might have?

19:07.400 --> 19:11.840
 Yeah, it is explicitly modeled, but it's not assumed.

19:11.840 --> 19:15.400
 The beliefs are actually output, not input.

19:15.400 --> 19:18.840
 Of course, the starting beliefs are input,

19:18.840 --> 19:20.640
 but they just fall from the rules of the game

19:20.640 --> 19:23.520
 because we know that the dealer deals uniformly

19:23.520 --> 19:27.720
 from the deck, so I know that every pair of cards

19:27.720 --> 19:30.440
 that you might have is equally likely.

19:30.440 --> 19:32.200
 I know that for a fact, that just follows

19:32.200 --> 19:33.160
 from the rules of the game.

19:33.160 --> 19:35.200
 Of course, except the two cards that I have,

19:35.200 --> 19:36.560
 I know you don't have those.

19:36.560 --> 19:37.560
 Yeah.

19:37.560 --> 19:38.720
 You have to take that into account.

19:38.720 --> 19:40.920
 That's called card removal and that's very important.

19:40.920 --> 19:43.760
 Is the dealing always coming from a single deck

19:43.760 --> 19:45.880
 in Heads Up, so you can assume.

19:45.880 --> 19:50.880
 Single deck, so you know that if I have the ace of spades,

19:50.880 --> 19:53.560
 I know you don't have an ace of spades.

19:53.560 --> 19:56.880
 Great, so in the beginning, your belief is basically

19:56.880 --> 19:59.320
 the fact that it's a fair dealing of hands,

19:59.320 --> 20:02.800
 but how do you start to adjust that belief?

20:02.800 --> 20:06.800
 Well, that's where this beauty of game theory comes.

20:06.800 --> 20:10.920
 So Nash equilibrium, which John Nash introduced in 1950,

20:10.920 --> 20:13.800
 introduces what rational play is

20:13.800 --> 20:16.040
 when you have more than one player.

20:16.040 --> 20:18.440
 And these are pairs of strategies

20:18.440 --> 20:20.360
 where strategies are contingency plans,

20:20.360 --> 20:21.600
 one for each player.

20:22.880 --> 20:25.720
 So that neither player wants to deviate

20:25.720 --> 20:26.960
 to a different strategy,

20:26.960 --> 20:29.160
 given that the other doesn't deviate.

20:29.160 --> 20:33.840
 But as a side effect, you get the beliefs from base roll.

20:33.840 --> 20:36.440
 So Nash equilibrium really isn't just deriving

20:36.440 --> 20:38.360
 in these imperfect information games,

20:38.360 --> 20:41.920
 Nash equilibrium, it doesn't just define strategies.

20:41.920 --> 20:44.960
 It also defines beliefs for both of us

20:44.960 --> 20:48.840
 and defines beliefs for each state.

20:48.840 --> 20:53.280
 So at each state, it's called information sets.

20:53.280 --> 20:55.560
 At each information set in the game,

20:55.560 --> 20:59.000
 there's a set of different states that we might be in,

20:59.000 --> 21:00.880
 but I don't know which one we're in.

21:01.760 --> 21:03.400
 Nash equilibrium tells me exactly

21:03.400 --> 21:05.000
 what is the probability distribution

21:05.000 --> 21:08.280
 over those real world states in my mind.

21:08.280 --> 21:11.440
 How does Nash equilibrium give you that distribution?

21:11.440 --> 21:12.280
 So why?

21:12.280 --> 21:13.320
 I'll do a simple example.

21:13.320 --> 21:16.760
 So you know the game Rock, Paper, Scissors?

21:16.760 --> 21:20.000
 So we can draw it as player one moves first

21:20.000 --> 21:21.600
 and then player two moves.

21:21.600 --> 21:24.520
 But of course, it's important that player two

21:24.520 --> 21:26.400
 doesn't know what player one moved,

21:26.400 --> 21:28.600
 otherwise player two would win every time.

21:28.600 --> 21:30.480
 So we can draw that as an information set

21:30.480 --> 21:33.280
 where player one makes one of three moves first,

21:33.280 --> 21:36.200
 and then there's an information set for player two.

21:36.200 --> 21:39.920
 So player two doesn't know which of those nodes

21:39.920 --> 21:41.800
 the world is in.

21:41.800 --> 21:44.920
 But once we know the strategy for player one,

21:44.920 --> 21:47.320
 Nash equilibrium will say that you play 1 3rd Rock,

21:47.320 --> 21:49.400
 1 3rd Paper, 1 3rd Scissors.

21:49.400 --> 21:52.600
 From that, I can derive my beliefs on the information set

21:52.600 --> 21:54.480
 that they're 1 3rd, 1 3rd, 1 3rd.

21:54.480 --> 21:56.280
 So Bayes gives you that.

21:56.280 --> 21:57.560
 Bayes gives you.

21:57.560 --> 21:59.760
 But is that specific to a particular player,

21:59.760 --> 22:03.960
 or is it something you quickly update

22:03.960 --> 22:05.040
 with the specific player?

22:05.040 --> 22:08.800
 No, the game theory isn't really player specific.

22:08.800 --> 22:11.720
 So that's also why we don't need any data.

22:11.720 --> 22:12.760
 We don't need any history

22:12.760 --> 22:14.800
 how these particular humans played in the past

22:14.800 --> 22:17.400
 or how any AI or human had played before.

22:17.400 --> 22:20.240
 It's all about rationality.

22:20.240 --> 22:22.720
 So the AI just thinks about

22:22.720 --> 22:24.880
 what would a rational opponent do?

22:24.880 --> 22:28.000
 And what would I do if I am rational?

22:28.000 --> 22:31.080
 And that's the idea of game theory.

22:31.080 --> 22:35.560
 So it's really a data free, opponent free approach.

22:35.560 --> 22:37.680
 So it comes from the design of the game

22:37.680 --> 22:40.040
 as opposed to the design of the player.

22:40.040 --> 22:43.080
 Exactly, there's no opponent modeling per se.

22:43.080 --> 22:45.600
 I mean, we've done some work on combining opponent modeling

22:45.600 --> 22:48.840
 with game theory so you can exploit weak players even more,

22:48.840 --> 22:50.280
 but that's another strand.

22:50.280 --> 22:52.320
 And in Librarus, we didn't turn that on.

22:52.320 --> 22:55.000
 So I decided that these players are too good.

22:55.000 --> 22:58.080
 And when you start to exploit an opponent,

22:58.080 --> 23:01.800
 you typically open yourself up to exploitation.

23:01.800 --> 23:04.000
 And these guys have so few holes to exploit

23:04.000 --> 23:06.760
 and they're world's leading experts in counter exploitation.

23:06.760 --> 23:09.200
 So I decided that we're not gonna turn that stuff on.

23:09.200 --> 23:12.160
 Actually, I saw a few of your papers exploiting opponents.

23:12.160 --> 23:14.800
 It sounded very interesting to explore.

23:15.720 --> 23:17.880
 Do you think there's room for exploitation

23:17.880 --> 23:19.920
 generally outside of Librarus?

23:19.920 --> 23:24.080
 Is there a subject or people differences

23:24.080 --> 23:27.920
 that could be exploited, maybe not just in poker,

23:27.920 --> 23:30.440
 but in general interactions and negotiations,

23:30.440 --> 23:33.480
 all these other domains that you're considering?

23:33.480 --> 23:34.680
 Yeah, definitely.

23:34.680 --> 23:35.920
 We've done some work on that.

23:35.920 --> 23:39.880
 And I really like the work at hybrid digested too.

23:39.880 --> 23:43.440
 So you figure out what would a rational opponent do.

23:43.440 --> 23:46.280
 And by the way, that's safe in these zero sum games,

23:46.280 --> 23:47.480
 two player zero sum games,

23:47.480 --> 23:49.560
 because if the opponent does something irrational,

23:49.560 --> 23:52.200
 yes, it might throw off my beliefs,

23:53.080 --> 23:55.760
 but the amount that the player can gain

23:55.760 --> 23:59.160
 by throwing off my belief is always less

23:59.160 --> 24:01.800
 than they lose by playing poorly.

24:01.800 --> 24:03.080
 So it's safe.

24:03.080 --> 24:06.720
 But still, if somebody's weak as a player,

24:06.720 --> 24:10.240
 you might wanna play differently to exploit them more.

24:10.240 --> 24:12.040
 So you can think about it this way,

24:12.040 --> 24:15.600
 a game theoretic strategy is unbeatable,

24:15.600 --> 24:19.600
 but it doesn't maximally beat the other opponent.

24:19.600 --> 24:22.800
 So the winnings per hand might be better

24:22.800 --> 24:24.240
 with a different strategy.

24:24.240 --> 24:25.720
 And the hybrid is that you start

24:25.720 --> 24:27.080
 from a game theoretic approach.

24:27.080 --> 24:30.840
 And then as you gain data about the opponent

24:30.840 --> 24:32.600
 in certain parts of the game tree,

24:32.600 --> 24:34.360
 then in those parts of the game tree,

24:34.360 --> 24:37.800
 you start to tweak your strategy more and more

24:37.800 --> 24:40.960
 towards exploitation while still staying fairly close

24:40.960 --> 24:42.160
 to the game theoretic strategy

24:42.160 --> 24:46.840
 so as to not open yourself up to exploitation too much.

24:46.840 --> 24:48.320
 How do you do that?

24:48.320 --> 24:53.320
 Do you try to vary up strategies, make it unpredictable?

24:53.640 --> 24:57.520
 It's like, what is it, tit for tat strategies

24:57.520 --> 25:00.720
 in Prisoner's Dilemma or?

25:00.720 --> 25:03.240
 Well, that's a repeated game.

25:03.240 --> 25:04.080
 Repeated games.

25:04.080 --> 25:06.520
 Simple Prisoner's Dilemma, repeated games.

25:06.520 --> 25:08.760
 But even there, there's no proof that says

25:08.760 --> 25:10.080
 that that's the best thing.

25:10.080 --> 25:13.280
 But experimentally, it actually does well.

25:13.280 --> 25:15.320
 So what kind of games are there, first of all?

25:15.320 --> 25:17.040
 I don't know if this is something

25:17.040 --> 25:18.600
 that you could just summarize.

25:18.600 --> 25:20.360
 There's perfect information games

25:20.360 --> 25:22.400
 where all the information's on the table.

25:22.400 --> 25:25.480
 There is imperfect information games.

25:25.480 --> 25:28.560
 There's repeated games that you play over and over.

25:28.560 --> 25:31.320
 There's zero sum games.

25:31.320 --> 25:34.440
 There's non zero sum games.

25:34.440 --> 25:37.520
 And then there's a really important distinction

25:37.520 --> 25:40.720
 you're making, two player versus more players.

25:40.720 --> 25:44.760
 So what are, what other games are there?

25:44.760 --> 25:46.160
 And what's the difference, for example,

25:46.160 --> 25:50.040
 with this two player game versus more players?

25:50.040 --> 25:51.680
 What are the key differences in your view?

25:51.680 --> 25:54.600
 So let me start from the basics.

25:54.600 --> 25:59.600
 So a repeated game is a game where the same exact game

25:59.600 --> 26:01.800
 is played over and over.

26:01.800 --> 26:05.800
 In these extensive form games, where it's,

26:05.800 --> 26:08.480
 think about three form, maybe with these information sets

26:08.480 --> 26:11.400
 to represent incomplete information,

26:11.400 --> 26:14.840
 you can have kind of repetitive interactions.

26:14.840 --> 26:17.760
 Even repeated games are a special case of that, by the way.

26:17.760 --> 26:21.520
 But the game doesn't have to be exactly the same.

26:21.520 --> 26:23.040
 It's like in sourcing auctions.

26:23.040 --> 26:26.320
 Yes, we're gonna see the same supply base year to year,

26:26.320 --> 26:28.800
 but what I'm buying is a little different every time.

26:28.800 --> 26:31.000
 And the supply base is a little different every time

26:31.000 --> 26:31.840
 and so on.

26:31.840 --> 26:33.400
 So it's not really repeated.

26:33.400 --> 26:35.680
 So to find a purely repeated game

26:35.680 --> 26:37.840
 is actually very rare in the world.

26:37.840 --> 26:42.840
 So they're really a very course model of what's going on.

26:42.840 --> 26:46.360
 Then if you move up from just repeated,

26:46.360 --> 26:49.040
 simple repeated matrix games,

26:49.040 --> 26:50.800
 not all the way to extensive form games,

26:50.800 --> 26:53.600
 but in between, they're stochastic games,

26:53.600 --> 26:57.000
 where, you know, there's these,

26:57.000 --> 27:00.520
 you think about it like these little matrix games.

27:00.520 --> 27:04.200
 And when you take an action and your opponent takes an action,

27:04.200 --> 27:07.680
 they determine not which next state I'm going to,

27:07.680 --> 27:09.120
 next game I'm going to,

27:09.120 --> 27:11.440
 but the distribution over next games

27:11.440 --> 27:13.360
 where I might be going to.

27:13.360 --> 27:15.360
 So that's the stochastic game.

27:15.360 --> 27:19.000
 But it's like matrix games, repeated stochastic games,

27:19.000 --> 27:20.400
 extensive form games.

27:20.400 --> 27:23.040
 That is from less to more general.

27:23.040 --> 27:26.280
 And poker is an example of the last one.

27:26.280 --> 27:28.400
 So it's really in the most general setting.

27:29.560 --> 27:30.640
 Extensive form games.

27:30.640 --> 27:34.520
 And that's kind of what the AI community has been working on

27:34.520 --> 27:36.280
 and being benchmarked on

27:36.280 --> 27:38.040
 with this Heads Up No Limit Texas Holdem.

27:38.040 --> 27:39.760
 Can you describe extensive form games?

27:39.760 --> 27:41.560
 What's the model here?

27:41.560 --> 27:44.320
 Yeah, so if you're familiar with the tree form,

27:44.320 --> 27:45.760
 so it's really the tree form.

27:45.760 --> 27:47.560
 Like in chess, there's a search tree.

27:47.560 --> 27:48.720
 Versus a matrix.

27:48.720 --> 27:50.080
 Versus a matrix, yeah.

27:50.080 --> 27:53.000
 And the matrix is called the matrix form

27:53.000 --> 27:55.320
 or bi matrix form or normal form game.

27:55.320 --> 27:57.080
 And here you have the tree form.

27:57.080 --> 28:00.000
 So you can actually do certain types of reasoning there

28:00.000 --> 28:04.680
 that you lose the information when you go to normal form.

28:04.680 --> 28:07.000
 There's a certain form of equivalence.

28:07.000 --> 28:08.880
 Like if you go from tree form and you say it,

28:08.880 --> 28:12.720
 every possible contingency plan is a strategy.

28:12.720 --> 28:15.080
 Then I can actually go back to the normal form,

28:15.080 --> 28:18.600
 but I lose some information from the lack of sequentiality.

28:18.600 --> 28:21.280
 Then the multiplayer versus two player distinction

28:21.280 --> 28:22.880
 is an important one.

28:22.880 --> 28:27.320
 So two player games in zero sum

28:27.320 --> 28:32.320
 are conceptually easier and computationally easier.

28:32.840 --> 28:36.000
 They're still huge like this one,

28:36.000 --> 28:39.680
 but they're conceptually easier and computationally easier

28:39.680 --> 28:42.920
 in that conceptually, you don't have to worry about

28:42.920 --> 28:45.360
 which equilibrium is the other guy going to play

28:45.360 --> 28:46.640
 when there are multiple,

28:46.640 --> 28:49.920
 because any equilibrium strategy is a best response

28:49.920 --> 28:52.000
 to any other equilibrium strategy.

28:52.000 --> 28:54.360
 So I can play a different equilibrium from you

28:54.360 --> 28:57.320
 and we'll still get the right values of the game.

28:57.320 --> 28:59.240
 That falls apart even with two players

28:59.240 --> 29:01.360
 when you have general sum games.

29:01.360 --> 29:03.120
 Even without cooperation just in general.

29:03.120 --> 29:04.800
 Even without cooperation.

29:04.800 --> 29:07.640
 So there's a big gap from two player zero sum

29:07.640 --> 29:11.160
 to two player general sum or even to three player zero sum.

29:11.160 --> 29:14.280
 That's a big gap, at least in theory.

29:14.280 --> 29:18.920
 Can you maybe non mathematically provide the intuition

29:18.920 --> 29:22.120
 why it all falls apart with three or more players?

29:22.120 --> 29:24.400
 It seems like you should still be able to have

29:24.400 --> 29:29.400
 a Nash equilibrium that's instructive, that holds.

29:31.280 --> 29:36.000
 Okay, so it is true that all finite games

29:36.000 --> 29:38.200
 have a Nash equilibrium.

29:38.200 --> 29:41.080
 So this is what John Nash actually proved.

29:41.080 --> 29:42.920
 So they do have a Nash equilibrium.

29:42.920 --> 29:43.840
 That's not the problem.

29:43.840 --> 29:46.600
 The problem is that there can be many.

29:46.600 --> 29:50.400
 And then there's a question of which equilibrium to select.

29:50.400 --> 29:52.200
 So, and if you select your strategy

29:52.200 --> 29:54.640
 from a different equilibrium and I select mine,

29:57.920 --> 29:59.920
 then what does that mean?

29:59.920 --> 30:02.080
 And in these non zero sum games,

30:02.080 --> 30:05.720
 we may lose some joint benefit

30:05.720 --> 30:07.040
 by being just simply stupid.

30:07.040 --> 30:08.400
 We could actually both be better off

30:08.400 --> 30:09.920
 if we did something else.

30:09.920 --> 30:11.760
 And in three player, you get other problems

30:11.760 --> 30:13.200
 also like collusion.

30:13.200 --> 30:16.560
 Like maybe you and I can gang up on a third player

30:16.560 --> 30:19.800
 and we can do radically better by colluding.

30:19.800 --> 30:22.200
 So there are lots of issues that come up there.

30:22.200 --> 30:25.640
 So Noah Brown, the student you work with on this

30:25.640 --> 30:29.360
 has mentioned, I looked through the AMA on Reddit.

30:29.360 --> 30:31.280
 He mentioned that the ability of poker players

30:31.280 --> 30:33.800
 to collaborate will make the game.

30:33.800 --> 30:35.200
 He was asked the question of,

30:35.200 --> 30:37.920
 how would you make the game of poker,

30:37.920 --> 30:39.280
 or both of you were asked the question,

30:39.280 --> 30:41.560
 how would you make the game of poker

30:41.560 --> 30:46.560
 beyond being solvable by current AI methods?

30:47.000 --> 30:50.560
 And he said that there's not many ways

30:50.560 --> 30:53.120
 of making poker more difficult,

30:53.120 --> 30:57.760
 but a collaboration or cooperation between players

30:57.760 --> 30:59.760
 would make it extremely difficult.

30:59.760 --> 31:03.320
 So can you provide the intuition behind why that is,

31:03.320 --> 31:05.280
 if you agree with that idea?

31:05.280 --> 31:10.200
 Yeah, so I've done a lot of work on coalitional games

31:10.200 --> 31:11.680
 and we actually have a paper here

31:11.680 --> 31:13.680
 with my other student Gabriele Farina

31:13.680 --> 31:16.640
 and some other collaborators at NIPS on that.

31:16.640 --> 31:18.520
 Actually just came back from the poster session

31:18.520 --> 31:19.760
 where we presented this.

31:19.760 --> 31:23.800
 But so when you have a collusion, it's a different problem.

31:23.800 --> 31:26.120
 And it typically gets even harder then.

31:27.520 --> 31:29.600
 Even the game representations,

31:29.600 --> 31:32.320
 some of the game representations don't really allow

31:33.600 --> 31:34.480
 good computation.

31:34.480 --> 31:37.600
 So we actually introduced a new game representation

31:37.600 --> 31:38.720
 for that.

31:38.720 --> 31:42.040
 Is that kind of cooperation part of the model?

31:42.040 --> 31:44.560
 Are you, do you have, do you have information

31:44.560 --> 31:47.040
 about the fact that other players are cooperating

31:47.040 --> 31:50.000
 or is it just this chaos that where nothing is known?

31:50.000 --> 31:52.360
 So there's some things unknown.

31:52.360 --> 31:55.840
 Can you give an example of a collusion type game

31:55.840 --> 31:56.680
 or is it usually?

31:56.680 --> 31:58.360
 So like bridge.

31:58.360 --> 31:59.640
 So think about bridge.

31:59.640 --> 32:02.320
 It's like when you and I are on a team,

32:02.320 --> 32:04.480
 our payoffs are the same.

32:04.480 --> 32:06.400
 The problem is that we can't talk.

32:06.400 --> 32:09.000
 So when I get my cards, I can't whisper to you

32:09.000 --> 32:10.320
 what my cards are.

32:10.320 --> 32:12.480
 That would not be allowed.

32:12.480 --> 32:16.080
 So we have to somehow coordinate our strategies

32:16.080 --> 32:19.920
 ahead of time and only ahead of time.

32:19.920 --> 32:22.760
 And then there's certain signals we can talk about,

32:22.760 --> 32:25.240
 but they have to be such that the other team

32:25.240 --> 32:26.840
 also understands them.

32:26.840 --> 32:30.440
 So that's an example where the coordination

32:30.440 --> 32:33.000
 is already built into the rules of the game.

32:33.000 --> 32:35.640
 But in many other situations like auctions

32:35.640 --> 32:40.640
 or negotiations or diplomatic relationships, poker,

32:40.880 --> 32:44.160
 it's not really built in, but it still can be very helpful

32:44.160 --> 32:45.280
 for the colluders.

32:45.280 --> 32:48.240
 I've read you write somewhere,

32:48.240 --> 32:52.800
 the negotiations you come to the table with prior,

32:52.800 --> 32:56.080
 like a strategy that you're willing to do

32:56.080 --> 32:58.320
 and not willing to do those kinds of things.

32:58.320 --> 33:01.960
 So how do you start to now moving away from poker,

33:01.960 --> 33:04.520
 moving beyond poker into other applications

33:04.520 --> 33:07.000
 like negotiations, how do you start applying this

33:07.000 --> 33:11.640
 to other domains, even real world domains

33:11.640 --> 33:12.520
 that you've worked on?

33:12.520 --> 33:14.440
 Yeah, I actually have two startup companies

33:14.440 --> 33:15.480
 doing exactly that.

33:15.480 --> 33:17.800
 One is called Strategic Machine,

33:17.800 --> 33:20.000
 and that's for kind of business applications,

33:20.000 --> 33:22.880
 gaming, sports, all sorts of things like that.

33:22.880 --> 33:27.200
 Any applications of this to business and to sports

33:27.200 --> 33:32.120
 and to gaming, to various types of things

33:32.120 --> 33:34.240
 in finance, electricity markets and so on.

33:34.240 --> 33:36.600
 And the other is called Strategy Robot,

33:36.600 --> 33:40.640
 where we are taking these to military security,

33:40.640 --> 33:43.520
 cyber security and intelligence applications.

33:43.520 --> 33:46.240
 I think you worked a little bit in,

33:48.000 --> 33:51.000
 how do you put it, advertisement,

33:51.000 --> 33:55.360
 sort of suggesting ads kind of thing, auction.

33:55.360 --> 33:57.800
 That's another company, optimized markets.

33:57.800 --> 34:00.880
 But that's much more about a combinatorial market

34:00.880 --> 34:02.840
 and optimization based technology.

34:02.840 --> 34:06.840
 That's not using these game theoretic reasoning technologies.

34:06.840 --> 34:11.600
 I see, okay, so what sort of high level

34:11.600 --> 34:15.280
 do you think about our ability to use

34:15.280 --> 34:18.040
 game theoretic concepts to model human behavior?

34:18.040 --> 34:21.640
 Do you think human behavior is amenable

34:21.640 --> 34:24.720
 to this kind of modeling outside of the poker games,

34:24.720 --> 34:27.520
 and where have you seen it done successfully in your work?

34:27.520 --> 34:32.520
 I'm not sure the goal really is modeling humans.

34:33.640 --> 34:36.480
 Like for example, if I'm playing a zero sum game,

34:36.480 --> 34:39.840
 I don't really care that the opponent

34:39.840 --> 34:42.960
 is actually following my model of rational behavior,

34:42.960 --> 34:46.400
 because if they're not, that's even better for me.

34:46.400 --> 34:50.200
 Right, so see with the opponents in games,

34:51.120 --> 34:56.120
 the prerequisite is that you formalize

34:56.120 --> 34:57.800
 the interaction in some way

34:57.800 --> 35:01.000
 that can be amenable to analysis.

35:01.000 --> 35:04.160
 And you've done this amazing work with mechanism design,

35:04.160 --> 35:08.160
 designing games that have certain outcomes.

35:10.040 --> 35:12.320
 But, so I'll tell you an example

35:12.320 --> 35:15.460
 from my world of autonomous vehicles, right?

35:15.460 --> 35:17.040
 We're studying pedestrians,

35:17.040 --> 35:20.200
 and pedestrians and cars negotiate

35:20.200 --> 35:22.160
 in this nonverbal communication.

35:22.160 --> 35:25.040
 There's this weird game dance of tension

35:25.040 --> 35:27.280
 where pedestrians are basically saying,

35:27.280 --> 35:28.800
 I trust that you won't kill me,

35:28.800 --> 35:31.840
 and so as a jaywalker, I will step onto the road

35:31.840 --> 35:34.720
 even though I'm breaking the law, and there's this tension.

35:34.720 --> 35:36.640
 And the question is, we really don't know

35:36.640 --> 35:40.720
 how to model that well in trying to model intent.

35:40.720 --> 35:43.080
 And so people sometimes bring up ideas

35:43.080 --> 35:44.880
 of game theory and so on.

35:44.880 --> 35:49.120
 Do you think that aspect of human behavior

35:49.120 --> 35:53.080
 can use these kinds of imperfect information approaches,

35:53.080 --> 35:57.860
 modeling, how do you start to attack a problem like that

35:57.860 --> 36:00.940
 when you don't even know how to design the game

36:00.940 --> 36:04.280
 to describe the situation in order to solve it?

36:04.280 --> 36:06.800
 Okay, so I haven't really thought about jaywalking,

36:06.800 --> 36:10.120
 but one thing that I think could be a good application

36:10.120 --> 36:13.000
 in autonomous vehicles is the following.

36:13.000 --> 36:16.320
 So let's say that you have fleets of autonomous cars

36:16.320 --> 36:18.340
 operating by different companies.

36:18.340 --> 36:22.120
 So maybe here's the Waymo fleet and here's the Uber fleet.

36:22.120 --> 36:24.320
 If you think about the rules of the road,

36:24.320 --> 36:26.560
 they define certain legal rules,

36:26.560 --> 36:30.080
 but that still leaves a huge strategy space open.

36:30.080 --> 36:32.840
 Like as a simple example, when cars merge,

36:32.840 --> 36:36.000
 how humans merge, they slow down and look at each other

36:36.000 --> 36:39.240
 and try to merge.

36:39.240 --> 36:40.920
 Wouldn't it be better if these situations

36:40.920 --> 36:43.480
 would already be prenegotiated

36:43.480 --> 36:45.200
 so we can actually merge at full speed

36:45.200 --> 36:47.440
 and we know that this is the situation,

36:47.440 --> 36:50.540
 this is how we do it, and it's all gonna be faster.

36:50.540 --> 36:54.120
 But there are way too many situations to negotiate manually.

36:54.120 --> 36:56.400
 So you could use automated negotiation,

36:56.400 --> 36:57.780
 this is the idea at least,

36:57.780 --> 36:59.840
 you could use automated negotiation

36:59.840 --> 37:02.060
 to negotiate all of these situations

37:02.060 --> 37:04.320
 or many of them in advance.

37:04.320 --> 37:05.460
 And of course it might be that,

37:05.460 --> 37:09.180
 hey, maybe you're not gonna always let me go first.

37:09.180 --> 37:11.280
 Maybe you said, okay, well, in these situations,

37:11.280 --> 37:13.560
 I'll let you go first, but in exchange,

37:13.560 --> 37:14.520
 you're gonna give me too much,

37:14.520 --> 37:17.260
 you're gonna let me go first in this situation.

37:17.260 --> 37:20.680
 So it's this huge combinatorial negotiation.

37:20.680 --> 37:24.080
 And do you think there's room in that example of merging

37:24.080 --> 37:25.600
 to model this whole situation

37:25.600 --> 37:27.160
 as an imperfect information game

37:27.160 --> 37:30.120
 or do you really want to consider it to be a perfect?

37:30.120 --> 37:32.240
 No, that's a good question, yeah.

37:32.240 --> 37:33.080
 That's a good question.

37:33.080 --> 37:37.080
 Do you pay the price of assuming

37:37.080 --> 37:38.640
 that you don't know everything?

37:39.800 --> 37:40.760
 Yeah, I don't know.

37:40.760 --> 37:42.120
 It's certainly much easier.

37:42.120 --> 37:45.060
 Games with perfect information are much easier.

37:45.060 --> 37:49.280
 So if you can't get away with it, you should.

37:49.280 --> 37:52.640
 But if the real situation is of imperfect information,

37:52.640 --> 37:55.160
 then you're gonna have to deal with imperfect information.

37:55.160 --> 37:58.080
 Great, so what lessons have you learned

37:58.080 --> 38:00.680
 the Annual Computer Poker Competition?

38:00.680 --> 38:03.440
 An incredible accomplishment of AI.

38:03.440 --> 38:07.000
 You look at the history of Deep Blue, AlphaGo,

38:07.000 --> 38:10.400
 these kind of moments when AI stepped up

38:10.400 --> 38:13.960
 in an engineering effort and a scientific effort combined

38:13.960 --> 38:16.400
 to beat the best of human players.

38:16.400 --> 38:19.480
 So what do you take away from this whole experience?

38:19.480 --> 38:22.440
 What have you learned about designing AI systems

38:22.440 --> 38:23.960
 that play these kinds of games?

38:23.960 --> 38:28.280
 And what does that mean for AI in general,

38:28.280 --> 38:30.760
 for the future of AI development?

38:30.760 --> 38:32.800
 Yeah, so that's a good question.

38:32.800 --> 38:34.560
 So there's so much to say about it.

38:35.440 --> 38:39.120
 I do like this type of performance oriented research.

38:39.120 --> 38:42.000
 Although in my group, we go all the way from like idea

38:42.000 --> 38:44.880
 to theory, to experiments, to big system building,

38:44.880 --> 38:47.960
 to commercialization, so we span that spectrum.

38:47.960 --> 38:51.080
 But I think that in a lot of situations in AI,

38:51.080 --> 38:53.440
 you really have to build the big systems

38:53.440 --> 38:55.640
 and evaluate them at scale

38:55.640 --> 38:57.520
 before you know what works and doesn't.

38:57.520 --> 39:00.080
 And we've seen that in the computational

39:00.080 --> 39:02.880
 game theory community, that there are a lot of techniques

39:02.880 --> 39:04.280
 that look good in the small,

39:05.200 --> 39:07.120
 but then they cease to look good in the large.

39:07.120 --> 39:10.160
 And we've also seen that there are a lot of techniques

39:10.160 --> 39:13.280
 that look superior in theory.

39:13.280 --> 39:16.200
 And I really mean in terms of convergence rates,

39:16.200 --> 39:18.440
 like first order methods, better convergence rates,

39:18.440 --> 39:20.880
 like the CFR based algorithms,

39:20.880 --> 39:24.880
 yet the CFR based algorithms are the fastest in practice.

39:24.880 --> 39:28.240
 So it really tells me that you have to test this in reality.

39:28.240 --> 39:30.880
 The theory isn't tight enough, if you will,

39:30.880 --> 39:34.360
 to tell you which algorithms are better than the others.

39:34.360 --> 39:38.600
 And you have to look at these things in the large,

39:38.600 --> 39:41.480
 because any sort of projections you do from the small

39:41.480 --> 39:43.800
 can at least in this domain be very misleading.

39:43.800 --> 39:46.240
 So that's kind of from a kind of a science

39:46.240 --> 39:49.120
 and engineering perspective, from a personal perspective,

39:49.120 --> 39:51.280
 it's been just a wild experience

39:51.280 --> 39:54.160
 in that with the first poker competition,

39:54.160 --> 39:57.200
 the first brains versus AI,

39:57.200 --> 39:59.840
 man machine poker competition that we organized.

39:59.840 --> 40:01.760
 There had been, by the way, for other poker games,

40:01.760 --> 40:03.240
 there had been previous competitions,

40:03.240 --> 40:06.360
 but this was for Heads Up No Limit, this was the first.

40:06.360 --> 40:09.560
 And I probably became the most hated person

40:09.560 --> 40:10.880
 in the world of poker.

40:10.880 --> 40:12.880
 And I didn't mean to, I just saw.

40:12.880 --> 40:13.720
 Why is that?

40:13.720 --> 40:15.840
 For cracking the game, for something.

40:15.840 --> 40:20.000
 Yeah, a lot of people felt that it was a real threat

40:20.000 --> 40:22.760
 to the whole game, the whole existence of the game.

40:22.760 --> 40:26.080
 If AI becomes better than humans,

40:26.080 --> 40:28.520
 people would be scared to play poker

40:28.520 --> 40:30.680
 because there are these superhuman AIs running around

40:30.680 --> 40:32.760
 taking their money and all of that.

40:32.760 --> 40:36.200
 So I just, it's just really aggressive.

40:36.200 --> 40:37.880
 The comments were super aggressive.

40:37.880 --> 40:40.920
 I got everything just short of death threats.

40:40.920 --> 40:44.000
 Do you think the same was true for chess?

40:44.000 --> 40:45.760
 Because right now they just completed

40:45.760 --> 40:47.720
 the world championships in chess,

40:47.720 --> 40:49.560
 and humans just started ignoring the fact

40:49.560 --> 40:52.920
 that there's AI systems now that outperform humans

40:52.920 --> 40:55.520
 and they still enjoy the game, it's still a beautiful game.

40:55.520 --> 40:56.360
 That's what I think.

40:56.360 --> 40:58.800
 And I think the same thing happens in poker.

40:58.800 --> 41:01.040
 And so I didn't think of myself

41:01.040 --> 41:02.360
 as somebody who was gonna kill the game,

41:02.360 --> 41:03.800
 and I don't think I did.

41:03.800 --> 41:05.600
 I've really learned to love this game.

41:05.600 --> 41:06.960
 I wasn't a poker player before,

41:06.960 --> 41:10.520
 but learned so many nuances about it from these AIs,

41:10.520 --> 41:12.480
 and they've really changed how the game is played,

41:12.480 --> 41:13.320
 by the way.

41:13.320 --> 41:16.240
 So they have these very Martian ways of playing poker,

41:16.240 --> 41:18.400
 and the top humans are now incorporating

41:18.400 --> 41:21.400
 those types of strategies into their own play.

41:21.400 --> 41:26.400
 So if anything, to me, our work has made poker

41:26.560 --> 41:29.800
 a richer, more interesting game for humans to play,

41:29.800 --> 41:32.160
 not something that is gonna steer humans

41:32.160 --> 41:34.200
 away from it entirely.

41:34.200 --> 41:35.960
 Just a quick comment on something you said,

41:35.960 --> 41:39.400
 which is, if I may say so,

41:39.400 --> 41:42.400
 in academia is a little bit rare sometimes.

41:42.400 --> 41:45.520
 It's pretty brave to put your ideas to the test

41:45.520 --> 41:47.200
 in the way you described,

41:47.200 --> 41:49.360
 saying that sometimes good ideas don't work

41:49.360 --> 41:52.760
 when you actually try to apply them at scale.

41:52.760 --> 41:54.200
 So where does that come from?

41:54.200 --> 41:58.880
 I mean, if you could do advice for people,

41:58.880 --> 42:00.760
 what drives you in that sense?

42:00.760 --> 42:02.360
 Were you always this way?

42:02.360 --> 42:04.080
 I mean, it takes a brave person.

42:04.080 --> 42:06.760
 I guess is what I'm saying, to test their ideas

42:06.760 --> 42:08.640
 and to see if this thing actually works

42:08.640 --> 42:11.680
 against human top human players and so on.

42:11.680 --> 42:12.960
 Yeah, I don't know about brave,

42:12.960 --> 42:15.000
 but it takes a lot of work.

42:15.000 --> 42:17.320
 It takes a lot of work and a lot of time

42:18.400 --> 42:20.360
 to organize, to make something big

42:20.360 --> 42:22.920
 and to organize an event and stuff like that.

42:22.920 --> 42:24.760
 And what drives you in that effort?

42:24.760 --> 42:26.880
 Because you could still, I would argue,

42:26.880 --> 42:30.280
 get a best paper award at NIPS as you did in 17

42:30.280 --> 42:31.440
 without doing this.

42:31.440 --> 42:32.960
 That's right, yes.

42:32.960 --> 42:37.640
 And so in general, I believe it's very important

42:37.640 --> 42:41.480
 to do things in the real world and at scale.

42:41.480 --> 42:46.160
 And that's really where the pudding, if you will,

42:46.160 --> 42:48.400
 proof is in the pudding, that's where it is.

42:48.400 --> 42:50.080
 In this particular case,

42:50.080 --> 42:55.080
 it was kind of a competition between different groups

42:55.160 --> 42:59.080
 and for many years as to who can be the first one

42:59.080 --> 43:02.040
 to beat the top humans at Heads Up No Limit, Texas Holdem.

43:02.040 --> 43:07.040
 So it became kind of like a competition who can get there.

43:09.560 --> 43:11.800
 Yeah, so a little friendly competition

43:11.800 --> 43:14.040
 could do wonders for progress.

43:14.040 --> 43:15.040
 Yes, absolutely.

43:16.400 --> 43:19.040
 So the topic of mechanism design,

43:19.040 --> 43:22.280
 which is really interesting, also kind of new to me,

43:22.280 --> 43:25.680
 except as an observer of, I don't know, politics and any,

43:25.680 --> 43:27.600
 I'm an observer of mechanisms,

43:27.600 --> 43:31.440
 but you write in your paper an automated mechanism design

43:31.440 --> 43:34.000
 that I quickly read.

43:34.000 --> 43:37.880
 So mechanism design is designing the rules of the game

43:37.880 --> 43:40.200
 so you get a certain desirable outcome.

43:40.200 --> 43:44.920
 And you have this work on doing so in an automatic fashion

43:44.920 --> 43:46.720
 as opposed to fine tuning it.

43:46.720 --> 43:50.680
 So what have you learned from those efforts?

43:50.680 --> 43:52.280
 If you look, say, I don't know,

43:52.280 --> 43:56.200
 at complexes like our political system,

43:56.200 --> 43:58.560
 can we design our political system

43:58.560 --> 44:01.800
 to have, in an automated fashion,

44:01.800 --> 44:03.360
 to have outcomes that we want?

44:03.360 --> 44:08.360
 Can we design something like traffic lights to be smart

44:09.000 --> 44:11.800
 where it gets outcomes that we want?

44:11.800 --> 44:14.840
 So what are the lessons that you draw from that work?

44:14.840 --> 44:17.240
 Yeah, so I still very much believe

44:17.240 --> 44:19.400
 in the automated mechanism design direction.

44:19.400 --> 44:20.840
 Yes.

44:20.840 --> 44:23.000
 But it's not a panacea.

44:23.000 --> 44:26.520
 There are impossibility results in mechanism design

44:26.520 --> 44:30.240
 saying that there is no mechanism that accomplishes

44:30.240 --> 44:33.920
 objective X in class C.

44:33.920 --> 44:36.120
 So it's not going to,

44:36.120 --> 44:39.000
 there's no way using any mechanism design tools,

44:39.000 --> 44:41.000
 manual or automated,

44:41.000 --> 44:42.800
 to do certain things in mechanism design.

44:42.800 --> 44:43.800
 Can you describe that again?

44:43.800 --> 44:47.480
 So meaning it's impossible to achieve that?

44:47.480 --> 44:48.320
 Yeah, yeah.

44:48.320 --> 44:50.440
 And it's unlikely.

44:50.440 --> 44:51.280
 Impossible.

44:51.280 --> 44:52.120
 Impossible.

44:52.120 --> 44:55.240
 So these are not statements about human ingenuity

44:55.240 --> 44:57.120
 who might come up with something smart.

44:57.120 --> 44:59.880
 These are proofs that if you want to accomplish

44:59.880 --> 45:02.480
 properties X in class C,

45:02.480 --> 45:04.880
 that is not doable with any mechanism.

45:04.880 --> 45:07.080
 The good thing about automated mechanism design

45:07.080 --> 45:10.840
 is that we're not really designing for a class.

45:10.840 --> 45:14.160
 We're designing for specific settings at a time.

45:14.160 --> 45:16.720
 So even if there's an impossibility result

45:16.720 --> 45:18.240
 for the whole class,

45:18.240 --> 45:21.360
 it just doesn't mean that all of the cases

45:21.360 --> 45:22.560
 in the class are impossible.

45:22.560 --> 45:25.080
 It just means that some of the cases are impossible.

45:25.080 --> 45:28.240
 So we can actually carve these islands of possibility

45:28.240 --> 45:30.920
 within these known impossible classes.

45:30.920 --> 45:31.960
 And we've actually done that.

45:31.960 --> 45:35.160
 So one of the famous results in mechanism design

45:35.160 --> 45:37.360
 is the Meyerson Satethweight theorem

45:37.360 --> 45:41.000
 by Roger Meyerson and Mark Satethweight from 1983.

45:41.000 --> 45:43.480
 It's an impossibility of efficient trade

45:43.480 --> 45:45.200
 under imperfect information.

45:45.200 --> 45:48.560
 We show that you can, in many settings,

45:48.560 --> 45:51.480
 avoid that and get efficient trade anyway.

45:51.480 --> 45:54.160
 Depending on how they design the game, okay.

45:54.160 --> 45:55.880
 Depending how you design the game.

45:55.880 --> 46:00.240
 And of course, it doesn't in any way

46:00.240 --> 46:01.800
 contradict the impossibility result.

46:01.800 --> 46:03.920
 The impossibility result is still there,

46:03.920 --> 46:08.000
 but it just finds spots within this impossible class

46:08.920 --> 46:12.440
 where in those spots, you don't have the impossibility.

46:12.440 --> 46:14.760
 Sorry if I'm going a bit philosophical,

46:14.760 --> 46:17.480
 but what lessons do you draw towards,

46:17.480 --> 46:20.160
 like I mentioned, politics or human interaction

46:20.160 --> 46:24.880
 and designing mechanisms for outside of just

46:24.880 --> 46:26.960
 these kinds of trading or auctioning

46:26.960 --> 46:31.960
 or purely formal games or human interaction,

46:33.480 --> 46:34.920
 like a political system?

46:34.920 --> 46:39.160
 How, do you think it's applicable to, yeah, politics

46:39.160 --> 46:44.160
 or to business, to negotiations, these kinds of things,

46:46.280 --> 46:49.040
 designing rules that have certain outcomes?

46:49.040 --> 46:51.360
 Yeah, yeah, I do think so.

46:51.360 --> 46:54.200
 Have you seen that successfully done?

46:54.200 --> 46:56.440
 They haven't really, oh, you mean mechanism design

46:56.440 --> 46:57.280
 or automated mechanism design?

46:57.280 --> 46:59.000
 Automated mechanism design.

46:59.000 --> 47:01.520
 So mechanism design itself

47:01.520 --> 47:06.440
 has had fairly limited success so far.

47:06.440 --> 47:07.600
 There are certain cases,

47:07.600 --> 47:10.200
 but most of the real world situations

47:10.200 --> 47:14.680
 are actually not sound from a mechanism design perspective,

47:14.680 --> 47:16.920
 even in those cases where they've been designed

47:16.920 --> 47:20.000
 by very knowledgeable mechanism design people,

47:20.000 --> 47:22.760
 the people are typically just taking some insights

47:22.760 --> 47:25.040
 from the theory and applying those insights

47:25.040 --> 47:26.280
 into the real world,

47:26.280 --> 47:29.280
 rather than applying the mechanisms directly.

47:29.280 --> 47:33.520
 So one famous example of is the FCC spectrum auctions.

47:33.520 --> 47:36.880
 So I've also had a small role in that

47:36.880 --> 47:40.600
 and very good economists have been working,

47:40.600 --> 47:42.560
 excellent economists have been working on that

47:42.560 --> 47:44.040
 with no game theory,

47:44.040 --> 47:47.440
 yet the rules that are designed in practice there,

47:47.440 --> 47:49.840
 they're such that bidding truthfully

47:49.840 --> 47:51.800
 is not the best strategy.

47:51.800 --> 47:52.960
 Usually mechanism design,

47:52.960 --> 47:56.160
 we try to make things easy for the participants.

47:56.160 --> 47:58.560
 So telling the truth is the best strategy,

47:58.560 --> 48:01.480
 but even in those very high stakes auctions

48:01.480 --> 48:03.080
 where you have tens of billions of dollars

48:03.080 --> 48:05.200
 worth of spectrum being auctioned,

48:06.360 --> 48:08.280
 truth telling is not the best strategy.

48:08.280 --> 48:10.040
 And by the way,

48:10.040 --> 48:12.920
 nobody knows even a single optimal bidding strategy

48:12.920 --> 48:14.120
 for those auctions.

48:14.120 --> 48:15.960
 What's the challenge of coming up with an optimal,

48:15.960 --> 48:18.160
 because there's a lot of players and there's imperfect.

48:18.160 --> 48:20.040
 It's not so much that a lot of players,

48:20.040 --> 48:22.320
 but many items for sale,

48:22.320 --> 48:26.000
 and these mechanisms are such that even with just two items

48:26.000 --> 48:28.400
 or one item, bidding truthfully

48:28.400 --> 48:30.400
 wouldn't be the best strategy.

48:31.400 --> 48:34.560
 If you look at the history of AI,

48:34.560 --> 48:37.160
 it's marked by seminal events.

48:37.160 --> 48:40.160
 AlphaGo beating a world champion human Go player,

48:40.160 --> 48:43.680
 I would put Liberatus winning the Heads Up No Limit Holdem

48:43.680 --> 48:45.000
 as one of such event.

48:45.000 --> 48:46.040
 Thank you.

48:46.040 --> 48:51.040
 And what do you think is the next such event,

48:52.560 --> 48:56.640
 whether it's in your life or in the broadly AI community

48:56.640 --> 48:59.040
 that you think might be out there

48:59.040 --> 49:01.640
 that would surprise the world?

49:01.640 --> 49:02.800
 So that's a great question,

49:02.800 --> 49:04.520
 and I don't really know the answer.

49:04.520 --> 49:06.160
 In terms of game solving,

49:07.360 --> 49:08.920
 Heads Up No Limit Texas Holdem

49:08.920 --> 49:13.920
 really was the one remaining widely agreed upon benchmark.

49:14.400 --> 49:15.880
 So that was the big milestone.

49:15.880 --> 49:17.800
 Now, are there other things?

49:17.800 --> 49:18.920
 Yeah, certainly there are,

49:18.920 --> 49:21.080
 but there's not one that the community

49:21.080 --> 49:22.920
 has kind of focused on.

49:22.920 --> 49:25.240
 So what could be other things?

49:25.240 --> 49:27.640
 There are groups working on StarCraft.

49:27.640 --> 49:29.840
 There are groups working on Dota 2.

49:29.840 --> 49:31.560
 These are video games.

49:31.560 --> 49:36.240
 Or you could have like Diplomacy or Hanabi,

49:36.240 --> 49:37.080
 things like that.

49:37.080 --> 49:38.640
 These are like recreational games,

49:38.640 --> 49:42.040
 but none of them are really acknowledged

49:42.040 --> 49:45.840
 as kind of the main next challenge problem,

49:45.840 --> 49:50.000
 like chess or Go or Heads Up No Limit Texas Holdem was.

49:50.000 --> 49:52.360
 So I don't really know in the game solving space

49:52.360 --> 49:55.400
 what is or what will be the next benchmark.

49:55.400 --> 49:57.840
 I kind of hope that there will be a next benchmark

49:57.840 --> 49:59.560
 because really the different groups

49:59.560 --> 50:01.120
 working on the same problem

50:01.120 --> 50:05.120
 really drove these application independent techniques

50:05.120 --> 50:07.480
 forward very quickly over 10 years.

50:07.480 --> 50:09.120
 Do you think there's an open problem

50:09.120 --> 50:11.480
 that excites you that you start moving away

50:11.480 --> 50:15.000
 from games into real world games,

50:15.000 --> 50:17.200
 like say the stock market trading?

50:17.200 --> 50:19.320
 Yeah, so that's kind of how I am.

50:19.320 --> 50:23.120
 So I am probably not going to work

50:23.120 --> 50:27.640
 as hard on these recreational benchmarks.

50:27.640 --> 50:30.200
 I'm doing two startups on game solving technology,

50:30.200 --> 50:32.320
 Strategic Machine and Strategy Robot,

50:32.320 --> 50:34.160
 and we're really interested

50:34.160 --> 50:36.560
 in pushing this stuff into practice.

50:36.560 --> 50:40.080
 What do you think would be really

50:43.160 --> 50:45.920
 a powerful result that would be surprising

50:45.920 --> 50:49.960
 that would be, if you can say,

50:49.960 --> 50:53.280
 I mean, five years, 10 years from now,

50:53.280 --> 50:56.480
 something that statistically you would say

50:56.480 --> 50:57.920
 is not very likely,

50:57.920 --> 51:01.480
 but if there's a breakthrough, would achieve?

51:01.480 --> 51:03.800
 Yeah, so I think that overall,

51:03.800 --> 51:08.800
 we're in a very different situation in game theory

51:09.000 --> 51:11.760
 than we are in, let's say, machine learning.

51:11.760 --> 51:14.360
 So in machine learning, it's a fairly mature technology

51:14.360 --> 51:16.480
 and it's very broadly applied

51:16.480 --> 51:19.680
 and proven success in the real world.

51:19.680 --> 51:22.840
 In game solving, there are almost no applications yet.

51:24.320 --> 51:26.680
 We have just become superhuman,

51:26.680 --> 51:29.600
 which machine learning you could argue happened in the 90s,

51:29.600 --> 51:30.640
 if not earlier,

51:30.640 --> 51:32.960
 and at least on supervised learning,

51:32.960 --> 51:35.400
 certain complex supervised learning applications.

51:36.960 --> 51:39.000
 Now, I think the next challenge problem,

51:39.000 --> 51:40.560
 I know you're not asking about it this way,

51:40.560 --> 51:42.640
 you're asking about the technology breakthrough,

51:42.640 --> 51:44.240
 but I think that big, big breakthrough

51:44.240 --> 51:46.120
 is to be able to show that, hey,

51:46.120 --> 51:48.280
 maybe most of, let's say, military planning

51:48.280 --> 51:50.080
 or most of business strategy

51:50.080 --> 51:52.200
 will actually be done strategically

51:52.200 --> 51:54.120
 using computational game theory.

51:54.120 --> 51:55.800
 That's what I would like to see

51:55.800 --> 51:57.640
 as the next five or 10 year goal.

51:57.640 --> 51:59.520
 Maybe you can explain to me again,

51:59.520 --> 52:01.920
 forgive me if this is an obvious question,

52:01.920 --> 52:04.000
 but machine learning methods,

52:04.000 --> 52:07.840
 neural networks suffer from not being transparent,

52:07.840 --> 52:09.280
 not being explainable.

52:09.280 --> 52:12.400
 Game theoretic methods, Nash equilibria,

52:12.400 --> 52:15.280
 do they generally, when you see the different solutions,

52:15.280 --> 52:19.640
 are they, when you talk about military operations,

52:19.640 --> 52:21.800
 are they, once you see the strategies,

52:21.800 --> 52:23.880
 do they make sense, are they explainable,

52:23.880 --> 52:25.840
 or do they suffer from the same problems

52:25.840 --> 52:27.120
 as neural networks do?

52:27.120 --> 52:28.720
 So that's a good question.

52:28.720 --> 52:31.240
 I would say a little bit yes and no.

52:31.240 --> 52:34.560
 And what I mean by that is that

52:34.560 --> 52:36.160
 these game theoretic strategies,

52:36.160 --> 52:38.520
 let's say, Nash equilibrium,

52:38.520 --> 52:40.320
 it has provable properties.

52:40.320 --> 52:42.360
 So it's unlike, let's say, deep learning

52:42.360 --> 52:44.440
 where you kind of cross your fingers,

52:44.440 --> 52:45.680
 hopefully it'll work.

52:45.680 --> 52:47.880
 And then after the fact, when you have the weights,

52:47.880 --> 52:48.920
 you're still crossing your fingers,

52:48.920 --> 52:50.160
 and I hope it will work.

52:51.160 --> 52:55.400
 Here, you know that the solution quality is there.

52:55.400 --> 52:58.040
 There's provable solution quality guarantees.

52:58.040 --> 53:00.920
 Now, that doesn't necessarily mean

53:00.920 --> 53:03.480
 that the strategies are human understandable.

53:03.480 --> 53:04.720
 That's a whole other problem.

53:04.720 --> 53:08.680
 So I think that deep learning and computational game theory

53:08.680 --> 53:10.720
 are in the same boat in that sense,

53:10.720 --> 53:12.680
 that both are difficult to understand.

53:13.760 --> 53:15.680
 But at least the game theoretic techniques,

53:15.680 --> 53:19.840
 they have these guarantees of solution quality.

53:19.840 --> 53:22.880
 So do you see business operations, strategic operations,

53:22.880 --> 53:26.040
 or even military in the future being

53:26.040 --> 53:28.320
 at least the strong candidates

53:28.320 --> 53:32.760
 being proposed by automated systems?

53:32.760 --> 53:34.000
 Do you see that?

53:34.000 --> 53:35.040
 Yeah, I do, I do.

53:35.040 --> 53:39.640
 But that's more of a belief than a substantiated fact.

53:39.640 --> 53:42.320
 Depending on where you land in optimism or pessimism,

53:42.320 --> 53:45.720
 that's a really, to me, that's an exciting future,

53:45.720 --> 53:48.760
 especially if there's provable things

53:48.760 --> 53:50.560
 in terms of optimality.

53:50.560 --> 53:54.040
 So looking into the future,

53:54.040 --> 53:58.760
 there's a few folks worried about the,

53:58.760 --> 54:01.200
 especially you look at the game of poker,

54:01.200 --> 54:03.360
 which is probably one of the last benchmarks

54:03.360 --> 54:05.480
 in terms of games being solved.

54:05.480 --> 54:07.520
 They worry about the future

54:07.520 --> 54:10.520
 and the existential threats of artificial intelligence.

54:10.520 --> 54:13.840
 So the negative impact in whatever form on society.

54:13.840 --> 54:17.440
 Is that something that concerns you as much,

54:17.440 --> 54:21.600
 or are you more optimistic about the positive impacts of AI?

54:21.600 --> 54:24.720
 Oh, I am much more optimistic about the positive impacts.

54:24.720 --> 54:27.560
 So just in my own work, what we've done so far,

54:27.560 --> 54:29.920
 we run the nationwide kidney exchange.

54:29.920 --> 54:32.960
 Hundreds of people are walking around alive today,

54:32.960 --> 54:34.080
 who would it be?

54:34.080 --> 54:36.120
 And it's increased employment.

54:36.120 --> 54:39.920
 You have a lot of people now running kidney exchanges

54:39.920 --> 54:42.200
 and at the transplant centers,

54:42.200 --> 54:45.560
 interacting with the kidney exchange.

54:45.560 --> 54:49.440
 You have extra surgeons, nurses, anesthesiologists,

54:49.440 --> 54:51.400
 hospitals, all of that.

54:51.400 --> 54:53.560
 So employment is increasing from that

54:53.560 --> 54:55.320
 and the world is becoming a better place.

54:55.320 --> 54:59.040
 Another example is combinatorial sourcing auctions.

54:59.040 --> 55:04.040
 We did 800 large scale combinatorial sourcing auctions

55:04.040 --> 55:08.240
 from 2001 to 2010 in a previous startup of mine

55:08.240 --> 55:09.400
 called CombineNet.

55:09.400 --> 55:13.080
 And we increased the supply chain efficiency

55:13.080 --> 55:18.080
 on that $60 billion of spend by 12.6%.

55:18.080 --> 55:21.440
 So that's over $6 billion of efficiency improvement

55:21.440 --> 55:22.240
 in the world.

55:22.240 --> 55:23.760
 And this is not like shifting value

55:23.760 --> 55:25.240
 from somebody to somebody else,

55:25.240 --> 55:28.200
 just efficiency improvement, like in trucking,

55:28.200 --> 55:31.120
 less empty driving, so there's less waste,

55:31.120 --> 55:33.440
 less carbon footprint and so on.

55:33.440 --> 55:36.720
 So a huge positive impact in the near term,

55:36.720 --> 55:40.680
 but sort of to stay in it for a little longer,

55:40.680 --> 55:43.080
 because I think game theory has a role to play here.

55:43.080 --> 55:45.320
 Oh, let me actually come back on that as one thing.

55:45.320 --> 55:49.400
 I think AI is also going to make the world much safer.

55:49.400 --> 55:53.760
 So that's another aspect that often gets overlooked.

55:53.760 --> 55:54.920
 Well, let me ask this question.

55:54.920 --> 55:56.960
 Maybe you can speak to the safer.

55:56.960 --> 55:59.960
 So I talked to Max Tegmark and Stuart Russell,

55:59.960 --> 56:02.680
 who are very concerned about existential threats of AI.

56:02.680 --> 56:06.240
 And often the concern is about value misalignment.

56:06.240 --> 56:10.240
 So AI systems basically working,

56:11.880 --> 56:14.680
 operating towards goals that are not the same

56:14.680 --> 56:17.920
 as human civilization, human beings.

56:17.920 --> 56:21.160
 So it seems like game theory has a role to play there

56:24.200 --> 56:27.880
 to make sure the values are aligned with human beings.

56:27.880 --> 56:29.960
 I don't know if that's how you think about it.

56:29.960 --> 56:34.960
 If not, how do you think AI might help with this problem?

56:35.280 --> 56:39.240
 How do you think AI might make the world safer?

56:39.240 --> 56:43.000
 Yeah, I think this value misalignment

56:43.000 --> 56:46.480
 is a fairly theoretical worry.

56:46.480 --> 56:49.960
 And I haven't really seen it in,

56:49.960 --> 56:51.840
 because I do a lot of real applications.

56:51.840 --> 56:53.920
 I don't see it anywhere.

56:53.920 --> 56:55.240
 The closest I've seen it

56:55.240 --> 56:57.920
 was the following type of mental exercise really,

56:57.920 --> 57:00.720
 where I had this argument in the late eighties

57:00.720 --> 57:01.560
 when we were building

57:01.560 --> 57:03.560
 these transportation optimization systems.

57:03.560 --> 57:05.360
 And somebody had heard that it's a good idea

57:05.360 --> 57:08.160
 to have high utilization of assets.

57:08.160 --> 57:11.400
 So they told me, hey, why don't you put that as objective?

57:11.400 --> 57:14.720
 And we didn't even put it as an objective

57:14.720 --> 57:16.480
 because I just showed him that,

57:16.480 --> 57:18.480
 if you had that as your objective,

57:18.480 --> 57:20.320
 the solution would be to load your trucks full

57:20.320 --> 57:21.840
 and drive in circles.

57:21.840 --> 57:23.000
 Nothing would ever get delivered.

57:23.000 --> 57:25.120
 You'd have a hundred percent utilization.

57:25.120 --> 57:27.240
 So yeah, I know this phenomenon.

57:27.240 --> 57:29.680
 I've known this for over 30 years,

57:29.680 --> 57:33.360
 but I've never seen it actually be a problem in reality.

57:33.360 --> 57:35.240
 And yes, if you have the wrong objective,

57:35.240 --> 57:37.800
 the AI will optimize that to the hilt

57:37.800 --> 57:39.800
 and it's gonna hurt more than some human

57:39.800 --> 57:43.800
 who's kind of trying to solve it in a half baked way

57:43.800 --> 57:45.480
 with some human insight too.

57:45.480 --> 57:49.160
 But I just haven't seen that materialize in practice.

57:49.160 --> 57:52.720
 There's this gap that you've actually put your finger on

57:52.720 --> 57:57.080
 very clearly just now between theory and reality.

57:57.080 --> 57:59.680
 That's very difficult to put into words, I think.

57:59.680 --> 58:02.240
 It's what you can theoretically imagine,

58:03.240 --> 58:08.000
 the worst possible case or even, yeah, I mean bad cases.

58:08.000 --> 58:10.520
 And what usually happens in reality.

58:10.520 --> 58:11.960
 So for example, to me,

58:11.960 --> 58:15.720
 maybe it's something you can comment on having grown up

58:15.720 --> 58:17.680
 and I grew up in the Soviet Union.

58:19.120 --> 58:22.120
 There's currently 10,000 nuclear weapons in the world.

58:22.120 --> 58:24.200
 And for many decades,

58:24.200 --> 58:28.360
 it's theoretically surprising to me

58:28.360 --> 58:30.880
 that the nuclear war is not broken out.

58:30.880 --> 58:33.760
 Do you think about this aspect

58:33.760 --> 58:36.080
 from a game theoretic perspective in general,

58:36.080 --> 58:38.440
 why is that true?

58:38.440 --> 58:40.720
 Why in theory you could see

58:40.720 --> 58:42.600
 how things would go terribly wrong

58:42.600 --> 58:44.280
 and somehow yet they have not?

58:44.280 --> 58:45.600
 Yeah, how do you think about it?

58:45.600 --> 58:47.240
 So I do think about that a lot.

58:47.240 --> 58:50.320
 I think the biggest two threats that we're facing as mankind,

58:50.320 --> 58:53.320
 one is climate change and the other is nuclear war.

58:53.320 --> 58:57.200
 So those are my main two worries that I worry about.

58:57.200 --> 58:59.920
 And I've tried to do something about climate,

58:59.920 --> 59:01.320
 thought about trying to do something

59:01.320 --> 59:02.880
 for climate change twice.

59:02.880 --> 59:05.040
 Actually, for two of my startups,

59:05.040 --> 59:06.760
 I've actually commissioned studies

59:06.760 --> 59:09.480
 of what we could do on those things.

59:09.480 --> 59:11.040
 And we didn't really find a sweet spot,

59:11.040 --> 59:12.680
 but I'm still keeping an eye out on that.

59:12.680 --> 59:15.160
 If there's something where we could actually

59:15.160 --> 59:17.800
 provide a market solution or optimizations solution

59:17.800 --> 59:20.960
 or some other technology solution to problems.

59:20.960 --> 59:23.360
 Right now, like for example,

59:23.360 --> 59:26.760
 pollution critic markets was what we were looking at then.

59:26.760 --> 59:30.040
 And it was much more the lack of political will

59:30.040 --> 59:32.840
 by those markets were not so successful

59:32.840 --> 59:34.640
 rather than bad market design.

59:34.640 --> 59:37.080
 So I could go in and make a better market design,

59:37.080 --> 59:38.600
 but that wouldn't really move the needle

59:38.600 --> 59:41.160
 on the world very much if there's no political will.

59:41.160 --> 59:43.600
 And in the US, the market,

59:43.600 --> 59:47.520
 at least the Chicago market was just shut down and so on.

59:47.520 --> 59:48.760
 So then it doesn't really help

59:48.760 --> 59:51.040
 how great your market design was.

59:51.040 --> 59:53.560
 And then the nuclear side, it's more,

59:53.560 --> 59:57.560
 so global warming is a more encroaching problem.

1:00:00.840 --> 1:00:03.280
 Nuclear weapons have been here.

1:00:03.280 --> 1:00:05.720
 It's an obvious problem that's just been sitting there.

1:00:05.720 --> 1:00:07.480
 So how do you think about,

1:00:07.480 --> 1:00:09.240
 what is the mechanism design there

1:00:09.240 --> 1:00:12.280
 that just made everything seem stable?

1:00:12.280 --> 1:00:14.800
 And are you still extremely worried?

1:00:14.800 --> 1:00:16.640
 I am still extremely worried.

1:00:16.640 --> 1:00:20.040
 So you probably know the simple game theory of mad.

1:00:20.040 --> 1:00:23.760
 So this was a mutually assured destruction

1:00:23.760 --> 1:00:27.360
 and it doesn't require any computation with small matrices.

1:00:27.360 --> 1:00:28.600
 You can actually convince yourself

1:00:28.600 --> 1:00:31.480
 that the game is such that nobody wants to initiate.

1:00:31.480 --> 1:00:34.600
 Yeah, that's a very coarse grained analysis.

1:00:34.600 --> 1:00:36.880
 And it really works in a situational way.

1:00:36.880 --> 1:00:40.400
 You have two superpowers or small number of superpowers.

1:00:40.400 --> 1:00:41.960
 Now things are very different.

1:00:41.960 --> 1:00:43.080
 You have a smaller nuke.

1:00:43.080 --> 1:00:47.240
 So the threshold of initiating is smaller

1:00:47.240 --> 1:00:51.520
 and you have smaller countries and non nation actors

1:00:51.520 --> 1:00:53.760
 who may get a nuke and so on.

1:00:53.760 --> 1:00:58.320
 So I think it's riskier now than it was maybe ever before.

1:00:58.320 --> 1:01:03.320
 And what idea, application of AI,

1:01:03.640 --> 1:01:04.640
 you've talked about a little bit,

1:01:04.640 --> 1:01:07.560
 but what is the most exciting to you right now?

1:01:07.560 --> 1:01:10.160
 I mean, you're here at NIPS, NeurIPS.

1:01:10.160 --> 1:01:14.920
 Now you have a few excellent pieces of work,

1:01:14.920 --> 1:01:16.680
 but what are you thinking into the future

1:01:16.680 --> 1:01:17.840
 with several companies you're doing?

1:01:17.840 --> 1:01:21.120
 What's the most exciting thing or one of the exciting things?

1:01:21.120 --> 1:01:23.160
 The number one thing for me right now

1:01:23.160 --> 1:01:26.360
 is coming up with these scalable techniques

1:01:26.360 --> 1:01:30.440
 for game solving and applying them into the real world.

1:01:30.440 --> 1:01:33.160
 I'm still very interested in market design as well.

1:01:33.160 --> 1:01:35.400
 And we're doing that in the optimized markets,

1:01:35.400 --> 1:01:37.560
 but I'm most interested if number one right now

1:01:37.560 --> 1:01:40.000
 is strategic machine strategy robot,

1:01:40.000 --> 1:01:41.440
 getting that technology out there

1:01:41.440 --> 1:01:45.560
 and seeing as you were in the trenches doing applications,

1:01:45.560 --> 1:01:47.120
 what needs to be actually filled,

1:01:47.120 --> 1:01:49.800
 what technology gaps still need to be filled.

1:01:49.800 --> 1:01:52.040
 So it's so hard to just put your feet on the table

1:01:52.040 --> 1:01:53.800
 and imagine what needs to be done.

1:01:53.800 --> 1:01:56.280
 But when you're actually doing real applications,

1:01:56.280 --> 1:01:59.120
 the applications tell you what needs to be done.

1:01:59.120 --> 1:02:00.840
 And I really enjoy that interaction.

1:02:00.840 --> 1:02:04.480
 Is it a challenging process to apply

1:02:04.480 --> 1:02:07.760
 some of the state of the art techniques you're working on

1:02:07.760 --> 1:02:12.760
 and having the various players in industry

1:02:14.080 --> 1:02:17.720
 or the military or people who could really benefit from it

1:02:17.720 --> 1:02:19.040
 actually use it?

1:02:19.040 --> 1:02:21.400
 What's that process like of,

1:02:21.400 --> 1:02:23.680
 autonomous vehicles work with automotive companies

1:02:23.680 --> 1:02:28.200
 and they're in many ways are a little bit old fashioned.

1:02:28.200 --> 1:02:29.240
 It's difficult.

1:02:29.240 --> 1:02:31.840
 They really want to use this technology.

1:02:31.840 --> 1:02:34.640
 There's clearly will have a significant benefit,

1:02:34.640 --> 1:02:37.480
 but the systems aren't quite in place

1:02:37.480 --> 1:02:41.080
 to easily have them integrated in terms of data,

1:02:41.080 --> 1:02:43.760
 in terms of compute, in terms of all these kinds of things.

1:02:43.760 --> 1:02:48.680
 So is that one of the bigger challenges that you're facing

1:02:48.680 --> 1:02:50.000
 and how do you tackle that challenge?

1:02:50.000 --> 1:02:52.360
 Yeah, I think that's always a challenge.

1:02:52.360 --> 1:02:54.520
 That's kind of slowness and inertia really

1:02:55.560 --> 1:02:57.920
 of let's do things the way we've always done it.

1:02:57.920 --> 1:03:00.120
 You just have to find the internal champions

1:03:00.120 --> 1:03:02.120
 at the customer who understand that,

1:03:02.120 --> 1:03:04.680
 hey, things can't be the same way in the future.

1:03:04.680 --> 1:03:06.960
 Otherwise bad things are going to happen.

1:03:06.960 --> 1:03:08.600
 And it's in autonomous vehicles.

1:03:08.600 --> 1:03:09.680
 It's actually very interesting

1:03:09.680 --> 1:03:11.120
 that the car makers are doing that

1:03:11.120 --> 1:03:12.440
 and they're very traditional,

1:03:12.440 --> 1:03:14.360
 but at the same time you have tech companies

1:03:14.360 --> 1:03:17.120
 who have nothing to do with cars or transportation

1:03:17.120 --> 1:03:21.880
 like Google and Baidu really pushing on autonomous cars.

1:03:21.880 --> 1:03:23.240
 I find that fascinating.

1:03:23.240 --> 1:03:25.160
 Clearly you're super excited

1:03:25.160 --> 1:03:29.320
 about actually these ideas having an impact in the world.

1:03:29.320 --> 1:03:32.680
 In terms of the technology, in terms of ideas and research,

1:03:32.680 --> 1:03:36.600
 are there directions that you're also excited about?

1:03:36.600 --> 1:03:40.840
 Whether that's on some of the approaches you talked about

1:03:40.840 --> 1:03:42.760
 for the imperfect information games,

1:03:42.760 --> 1:03:44.000
 whether it's applying deep learning

1:03:44.000 --> 1:03:45.120
 to some of these problems,

1:03:45.120 --> 1:03:46.520
 is there something that you're excited

1:03:46.520 --> 1:03:48.840
 in the research side of things?

1:03:48.840 --> 1:03:51.120
 Yeah, yeah, lots of different things

1:03:51.120 --> 1:03:53.240
 in the game solving.

1:03:53.240 --> 1:03:56.400
 So solving even bigger games,

1:03:56.400 --> 1:03:59.760
 games where you have more hidden action

1:03:59.760 --> 1:04:02.040
 of the player actions as well.

1:04:02.040 --> 1:04:05.880
 Poker is a game where really the chance actions are hidden

1:04:05.880 --> 1:04:07.080
 or some of them are hidden,

1:04:07.080 --> 1:04:08.720
 but the player actions are public.

1:04:11.440 --> 1:04:14.000
 Multiplayer games of various sorts,

1:04:14.000 --> 1:04:18.080
 collusion, opponent exploitation,

1:04:18.080 --> 1:04:21.280
 all and even longer games.

1:04:21.280 --> 1:04:23.160
 So games that basically go forever,

1:04:23.160 --> 1:04:24.680
 but they're not repeated.

1:04:24.680 --> 1:04:27.880
 So see extensive fun games that go forever.

1:04:27.880 --> 1:04:30.080
 What would that even look like?

1:04:30.080 --> 1:04:31.040
 How do you represent that?

1:04:31.040 --> 1:04:32.040
 How do you solve that?

1:04:32.040 --> 1:04:33.440
 What's an example of a game like that?

1:04:33.440 --> 1:04:35.600
 Or is this some of the stochastic games

1:04:35.600 --> 1:04:36.440
 that you mentioned?

1:04:36.440 --> 1:04:37.320
 Let's say business strategy.

1:04:37.320 --> 1:04:40.840
 So it's not just modeling like a particular interaction,

1:04:40.840 --> 1:04:44.440
 but thinking about the business from here to eternity.

1:04:44.440 --> 1:04:49.040
 Or let's say military strategy.

1:04:49.040 --> 1:04:51.000
 So it's not like war is gonna go away.

1:04:51.000 --> 1:04:54.280
 How do you think about military strategy

1:04:54.280 --> 1:04:55.520
 that's gonna go forever?

1:04:56.680 --> 1:04:58.080
 How do you even model that?

1:04:58.080 --> 1:05:01.000
 How do you know whether a move was good

1:05:01.000 --> 1:05:05.200
 that somebody made and so on?

1:05:05.200 --> 1:05:06.960
 So that's kind of one direction.

1:05:06.960 --> 1:05:09.800
 I'm also very interested in learning

1:05:09.800 --> 1:05:13.440
 much more scalable techniques for integer programming.

1:05:13.440 --> 1:05:16.560
 So we had an ICML paper this summer on that.

1:05:16.560 --> 1:05:20.280
 The first automated algorithm configuration paper

1:05:20.280 --> 1:05:23.560
 that has theoretical generalization guarantees.

1:05:23.560 --> 1:05:26.200
 So if I see this many training examples

1:05:26.200 --> 1:05:28.560
 and I told my algorithm in this way,

1:05:28.560 --> 1:05:30.560
 it's going to have good performance

1:05:30.560 --> 1:05:33.200
 on the real distribution, which I've not seen.

1:05:33.200 --> 1:05:34.840
 So, which is kind of interesting

1:05:34.840 --> 1:05:37.680
 that algorithm configuration has been going on now

1:05:37.680 --> 1:05:41.200
 for at least 17 years seriously.

1:05:41.200 --> 1:05:45.000
 And there has not been any generalization theory before.

1:05:45.960 --> 1:05:47.200
 Well, this is really exciting

1:05:47.200 --> 1:05:49.840
 and it's a huge honor to talk to you.

1:05:49.840 --> 1:05:51.160
 Thank you so much, Tomas.

1:05:51.160 --> 1:05:52.880
 Thank you for bringing Labradus to the world

1:05:52.880 --> 1:05:54.160
 and all the great work you're doing.

1:05:54.160 --> 1:05:55.000
 Well, thank you very much.

1:05:55.000 --> 1:05:55.840
 It's been fun.

1:05:55.840 --> 1:06:16.840
 No more questions.