The following quotes are an extract from AIMA, 3ed.

The definition of optimal play for MAX assumes that MIN also plays optimally—it maximizes the worst-case outcome for MAX. What if MIN does not play optimally? Then it is easy to show (...) that MAX will do even better.

Consider a MIN node whose children are terminal nodes. If MIN plays suboptimally, then the value of the node is greater than or equal to the value it would have if MIN played optimally. Hence, the value of the MAX node that is the MIN node’s parent can only be increased. This argument can be extended by a simple induction all the way to the root. If the suboptimal play by MIN is predictable, then one can do better than a minimax strategy. For example, if MIN always falls for a certain kind of trap and loses, then setting the trap guarantees a win even if there is actually a devastating response for MIN.

What happens if the MIN plays both suboptimally and unpredictably? What happens if MIN plays randomly, for example?

Is it ok to say that MAX will do better playing against a suboptimal and unpredictable MIN than playing against an optimal MIN?



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