If there are 200 hockey cards in the bag and 4 times as many football cards as hockey cards, there are 4*200 = <<200*4=800>>800 football cards.
The total number of football and hockey cards in the bag is 800+200 = <<800+200=1000>>1000 cards.
The bag contains 50 fewer baseball cards than football cards, meaning there are 800-50 = 750 baseball cards.
Altogether, there are 750+1000 = <<750+1000=1750>>1750 cards.
#### 1750