Alpha-beta pruning for Minimax

Question

I have spent a whole day trying to implement minimax without really understanding it. Now, , I think I understand how minimax works, but not alpha-beta pruning.

Thi

Answer 1

(Very) short explanation for mimimax:

• You (the evaluator of a board position) have the choice of playing n moves. You try all of them and give the board positions to the (opponent) evaluator.

  • The opponent evaluates the new board positions (for him, the opponent side) - by doing essentially the same thing, recursively calling (his opponent) evaluator, unless the maximum depth or some other condition has been reached and a static evaluator is called - and then selects the maximum evaluation and sends the evaluations back to you.

• You select the move that has the minimum of those evaluation. And that evaluation is the evaluation of the board you had to evaluate at the beginning.

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(Very) short explanation for α-β-pruning:

• You (the evaluator of a board position) have the choice of playing n moves. You try all of them one by one and give the board positions to the (opponent) evaluator - but you also pass along your current evaluation (of your board).

  • The opponent evaluates the new board position (for him, the opponent side) and sends the evaluation back to you. But how does he do that? He has the choice of playing m moves. He tries all of them and gives the new board positions (one by one) to (his opponent) evaluator and then chooses the maximum one.
  • Crucial step: If any of those evaluations that he gets back, is bigger than the minimum you gave him, it is certain that he will eventually return an evaluation value at least that large (because he wants to maximize). And you are sure to ignore that value (because you want to minimize), so he stops any more work for boards he hasn't yet evaluated.

• You select the move that has the minimum of those evaluation. And that evaluation is the evaluation of the board you had to evaluate at the beginning.