Maker-Breaker Games

Abstract

At any point during a strong positional game both players are required to do two things simultaneously: try to occupy a complete winning set for themselves, and prevent their opponent from occupying one for themselves. Apparently this dual job is a feature that we are not able to explicitly handle in any way other than by the brute force of a more or less complete case analysis of the game tree. Due to the exponential size of such game trees, this approach becomes impractical very quickly, and one must look for alternatives to say anything meaningful.

When you’re not concerned with succeeding, you can work with complete freedom.

Larry David