Backward induction on a finite game tree containing maximizing choices, minimizing choices and chance nodes. Terminal utilities are backed up by , and , respectively. Exact chance node evaluation generally needs every positive-probability outcome; ordinary alpha-beta pruning does not transfer unchanged because one child's value does not bound the full weighted sum.
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Expectiminimax is a decision-making algorithm used in game theory, particularly in the context of two-player games involving randomness, such as those where some outcomes are uncertain or probabilistic. It is an extension of the minimax algorithm, which is primarily used for deterministic games.