Learning of winning strategies for terminal games with linear-size memory

We prove that if one or more players in a locally finite positional game have winning strategies, then they can find it by themselves, not losing more than a bounded number of plays and not using more than a linear-size memory, independently of the strategies applied by the other players. We design two algorithms for learning how to win. One of them can also be modified to determine a strategy that achieves a draw, provided that no winning strategy exists for the player in question but with properly chosen moves a draw can be ensured from the starting position. If a drawing- or winning strategy exists, then it is learnt after no more than a linear number of plays lost (linear in the number of edges of the game graph). Z. Tuza’s research has been supported in part by the grant OTKA T-049613.