Minimax search ($V(s)={\max }_{s^{\prime }}V(s^{\prime })\text{or}{\min }_{s^{\prime }}V(s^{\prime })$)

Backward induction on a finite deterministic game tree of a two-player zero-sum game. Terminal payoffs are propagated by maximization at one player's decision nodes and minimization at the other's. With full information, the resulting choices give an optimal strategy against the opposing player's best response. A cyclic state graph requires a winning condition on infinite plays and a graph algorithm rather than unrestricted recursive unfolding.

The order in which legal child positions are searched. Good move ordering supplies useful alternatives early and increases alpha-beta pruning; poor move ordering can leave the worst-case time complexity of full minimax search unchanged.