‘Minimax is not good for game playing when the opponent is not playing optimally.’ Justify, using a suitable example.

         ·         Minimax assumes a perfectly rational opponent, who also takes optimal actions.

         ·         However, in practice, most human opponents depart from rationality.

         ·         In this case, the best move, at any given step, may not be one that is indicated by Minimax, but an algorithm that takes human imperfections into consideration will perform better.

   

    ·         If the tree is too large to explore fully, then, there is a possibility that a sub-optimal move could take MAX into an area of the tree he hadn’t considered worse than he thought.

         ·         So, how to deal with sub-optimal play, is still a problem.

       ·         Most algorithms assume an optimal opponent, and it doesn’t seem to hurt them very much, but that’s an empirical, not theoretical result.

        ·         Optimality is still well defined, even if your opponent isn’t playing well.

         ·         Moreover, if the game tree is small enough that your agent can fully explore it, then the optimal player really doesn’t care what the other one does.

·         Let’s say MAX goes first. What will MAX do? He will look at every possible game sequence.

         ·         He will then take the action which guarantees that he will get a score of at least X.

         

         ·         No matter what MIN does in subsequent moves, MIN can never get a score less than

X. So, MAX’s score will only go up if MIN doesn’t play well.