How to deal with draws by repetition in a transposition table?

Question

I'm trying to solve Three Men's Morris. The details of the game don't matter, that that it's a game similar to tic tac toe, but players may be able to force a win from some positions, or be able to force the game to repeat forever by playing the same moves over and over in other positions. So I want to make a function to tell whether a player can force a win, or force a draw by repetition.

I've tried using simple negamax, which works fine but is way too slow to traverse the game tree with unlimited depth. I want to use transposition tables since the number of possible positions is very low (<6000) but that's where my problem comes from. As soon as I add in the transposition table (just a list of all fully searched positions and their values, 0, 1, or -1) the AI starts making weird moves, suddenly saying its a draw in positions where I have a forced win.

I think the problem comes from transposition table entries being saved as draws, since it seemed to work when I limited the depth and only saved forced wins, but I'm not sure how to fix the problem and allow for unlimited depth.

Here's the code in case there's an issue with my implementation:

int evaluate(ThreeMensMorris &board){
    //game is won or drawn
    if(board.isGameWon()) return -1; //current player lost
    if(board.isRepetition()) return 0; //draw by repetition

    //check if this position is already in the transposition table
    //if so, return its value
    uint32_t pos = board.getPosInt();
    for(int i = 0; i < transIdx; i++)
        if(transList[i] == pos)
            return valueList[i];

    //negamax
    //NOTE: moves are formatted as two numbers, "from" and "to",
    //where "to" is -1 to place a piece for the first time
    //so this nested for loop goes over all possible moves
    int bestValue = -100;
    for(int i = 0; i < 9; i++){
        for(int j = -1; j < 9; j++){
            if(!board.makeMove(i, j)) continue; //illegal move
            int value = -1 * evaluate(board, depth+1);
            board.unmakeMove(i, j);
            if(value > bestValue) bestValue = value;
        }
    }
    
    //we have a new position complete with a value, push it to the end of the list
    transList[transIdx] = pos;
    valueList[transIdx] = bestValue;
    transIdx++;
    
    return bestValue;
}

score 0 · Answer 1 · answered Nov 08 '22 at 05:53

I suggest you start looking at transposition tables for chess: https://www.chessprogramming.org/Transposition_Table. You need to give each gamestate an (almost) unique number, e.g. through Zobrist hashing, maybe this is what you do in board.getPosInt()?

A possible fault is that you don't consider who's turn it is? Even if a position is the same on the board, it is not the same if in one position it is player A turn and in the other player B. Are there other things to consider in this game? In chess there are things like en passant possibilities that needs to be considered, and other special cases, to know if the position is actually the same, not just the pieces themselves.

Transposition tables are really complex and super hard to debug unfortunately. I hope you get it to work though!

How to deal with draws by repetition in a transposition table?

1 Answers1