Beating a minimax opponent

Question

I have to create an AI which has to compete against other AIs.

Both AIs will run on the same hardware, have the same amount of processing time and memory. I know the opponent AI will be using the minimax algorithm with alpha beta pruning.

Now my question is - what are some approaches for beating such an opponent? If I use minimax myself - then both AI's perfectly predict each other's moves and the game resolves based on an inherent property of the game (first move wins etc).

The obvious solution is to somehow see further ahead into the possible moves which would allow for a better evaluation - since the processor time is the same I couldn't evaluate to a greater depth (assuming the opposing AI code is equally optimized). I could use a precomputed tree for an extra advantage but without a super computer I certainly couldn't "solve" any nontrivial game.

Is there some value in intentionally picking a non optimal node such as one that alpha beta would have pruned? This could potentially incur a CPU time penalty on the opponent as they'd have to go back and re-evaluate the tree. It would incur a penalty on me as well as I'd have to evaluate the minimax tree + alpha beta to see which nodes alpha beta would prune without reaping any direct benefits.

What are some other strategies for optimizing against such an opponent?

Answer 1

First, there isn't any value in choosing a non-optimal line of play. Assuming your opponent will play optimally (and that's a fundamental assumption of minimax search), your opponent will make a move that capitalizes on the mistake. A good game engine will have a hashed refutation table entry containing the countermove for your blunder, so you'll gain no time by making a wild move. Making bad moves allows a computer opponent to find good moves faster.

The key thing to realize with a game like Othello is that you can't be sure what the optimal move is until late in the game. That's because the search tree is almost always too large to be exhaustively searched for all won or lost positions, and so minimax can't tell you with certainty which moves will lead to victory or defeat. You can only heuristically decide where to stop searching, arbitrarily call those nodes "terminal", and then run an evaluation function that guesses the win/loss potential of a position.

The evaluation function's job is to assess the value of a position, typically using static metrics that can be computed without searching the game tree further. Piece counts, positional features, endgame tablebases, and even opponent psychology can play a role here. The more intelligence you put into your evaluation function, generally the better your engine will play. But the point of static evaluation is replace searches that would be too expensive. If your evaluation function does too much or does what it does too inefficiently, it can become slower than the game tree search needed to obtain the same information. Knowing what to put in an evaluation function and when to use static evaluation instead of search is a large part of the art of writing a good game engine.

Answer 2

There are a lot of ways to improve standard minimax with AB pruning. For example, the killer heuristic attempts to improve the order moves are looked at, since AB's efficiency is better with well-ordered moves.

A lot of information on different search enhancements and variations on AB can be found at chessprogramming.wikispaces.com.