In an infinite game, winners teach losers better plays. In a finite game, the winner takes all. In an infinite game, winning is widely shared. In a finite game, rules are fixed in advance to guarantee a single winner. In an infinite game, rules are changed along the way by agreement.
Finite games focus on how they end.
Infinite games focus on how they continue. Good schools, like good communities, good economies and good families, are playing an infinite game. They may include finite games within them, but they ensure that these games don't displace the larger play or corrupt it. The story of that one infinite game is the right story for schools to organize their practices around. That's quite a bit.