Abstract For the unbiased Maker-Breaker game, played on the hypergraph H, let τ M (H) be the smallest integer t such that Maker can win the game within t moves (if the game is a Breaker's win then set τ M (H) = ∞). Similarly, for the unbiased Avoider-Enforcer game played on H, let τ E (H) be the smallest integer t such that Enforcer can win the game within t moves (if the game is an Avoider's win then set τ E (H) = ∞). In this paper, we investigate τ M and τ E and determine their value for various positional games
