Alpha Beta pruning problems in Othello

Question

I'm creating a simple engine that plays Othello, using minimax with alpha beta cuts. It's playing well, but sometimes i get a weird index out of bounds exception (near the endgame, always).

Here' my algorithm

private float minimax(OthelloBoard board, OthelloMove best, float alpha, float beta, int depth)
{
    calls++;

    float bestResult = -Float.MAX_VALUE;
    OthelloMove garbage = new OthelloMove();

    int state = board.getState();
    int currentPlayer = board.getCurrentPlayer();

    if (state == OthelloBoard.STATE_DRAW)
        return 0.0f;
    if ((state == OthelloBoard.STATE_BLACK_WINS) && (currentPlayer == OthelloBoard.BLACK))
        return Float.MAX_VALUE;
    if ((state == OthelloBoard.STATE_WHITE_WINS) && (currentPlayer == OthelloBoard.WHITE))
        return Float.MAX_VALUE;
    if ((state == OthelloBoard.STATE_BLACK_WINS) && (currentPlayer == OthelloBoard.WHITE))
        return -Float.MAX_VALUE;
    if ((state == OthelloBoard.STATE_WHITE_WINS) && (currentPlayer == OthelloBoard.BLACK))
        return -Float.MAX_VALUE;

    if (depth == maxDepth)
        return OthelloHeuristics.eval(currentPlayer, board);

    ArrayList<OthelloMove> moves = board.getAllMoves(currentPlayer);

    for (OthelloMove mv : moves)
    {            
        board.makeMove(mv);
        alpha = - minimax(board, garbage, -beta, -alpha, depth + 1);
        board.undoMove(mv);

        if (beta <= alpha)
            return alpha;
        if (alpha > bestResult)
        {                
            best.setFlipSquares(mv.getFlipSquares());
            best.setIdx(mv.getIdx());        
            best.setPlayer(mv.getPlayer());
            bestResult = alpha;
        }
    }     
     return bestResult;
}

Inside makeMove and undoMove i update the game state(black wins, white wins, draw). I also toggle the players inside these methods. When a player has no moves i make a dummy move without changing the board, and toggle the players.

There's a lot more of code, but i think the problem happens when the algorithm hits the game over position. This problem doesn't happen when i set the engine to play random moves, so the problem should be the alpha beta algorithm.

Here is getAllMoves, this call getFlips:

   public ArrayList<OthelloMove> getAllMoves(int player)
   {
    ArrayList<OthelloMove> moves = new ArrayList<OthelloMove>();

    for (int i = 10; i < 90; i++) 
    {
        int col = i % 10;

        if (col != 0 && col != 9)            
        {
            if (cells[i] == EMPTY)
            {
                ArrayList<Integer> flips = getFlips(i, player);                    
                if (flips.size() > 0)
                {
                    OthelloMove mv = new OthelloMove();
                    mv.setFlipSquares(flips);
                    mv.setIdx(i);                        
                    mv.setPlayer(player);
                    moves.add(mv);
                }
            }
        }

    }                                     

    return moves;
}

Here is getFlips.

    public ArrayList<Integer> getFlips(int idx, int player)
    {        
    int opponent = getOpponent(player);
    ArrayList<Integer> flips = new ArrayList<Integer>();

    if (cells[idx] != EMPTY)
        return flips;

    for (Integer dir : DIRECTIONS)
    {
        int distance = 1;
        int tempIdx = idx;

        while (cells[tempIdx += dir] == opponent)
            distance++;

        if ((cells[tempIdx] == player) && (distance > 1)) 
        {

            while (distance-- > 1)
            {                    
                tempIdx -= dir;
                flips.add(tempIdx);
            }                            
        }            
    }
    return flips;
}

Here is updateState:

    public void updateState()
    {                   
    int opponent = getOpponent(currentPlayer);
    int playerMoves = getAllMoves(currentPlayer).size();
    int opponentMoves = getAllMoves(opponent).size();

    if ( ((playerMoves == 0) && (opponentMoves == 0)) ||  (emptyCells == 0))
    {                        
        int blackDiscs = countDiscs(BLACK);
        int whiteDiscs = countDiscs(WHITE);

        if (blackDiscs > whiteDiscs)
            state = STATE_BLACK_WINS;
        else if (blackDiscs < whiteDiscs)
            state = STATE_WHITE_WINS;
        else 
            state = STATE_DRAW;

    }                       

}

Thanks!

Answer 1

Found the problem, thanks anyway.

The bug was a situation where a player can't move, and must pass the turn. The tricky is to play a 'ghost move' (i.e. a move that doesn't change the board), and toggle the players turn, so that the Minimax doesn't even notice this situation.

I was doing this, but in the wrong place! The code is like:

   public void makeMove (OthelloMove move)
   {                    
    int player = move.getPlayer();        
    ArrayList<Integer> flips = move.getFlipSquares();

    if (flips != null)
    {                                   
        int idx = move.getIdx();                    
        cells[idx] = player;
        for (Integer flip : flips)
            cells[flip] = player;        

        emptyCells--;    
        this.updatePhase();           
    }
    this.toogleCurrentPlayer();                    
}

public void undoMove (OthelloMove move)
{                    
    int player = move.getPlayer();        
    ArrayList<Integer> flips = move.getFlipSquares();
    int opponent = getOpponent(player);

    if (flips != null)
    {
        int idx = move.getIdx();

        cells[idx] = EMPTY;
        for (Integer flip : flips)
            cells[flip] = opponent;

        emptyCells++;                                         
        this.updatePhase();
    }
    this.toogleCurrentPlayer();         
 }

Answer 2

I am not familiar with the game specifically, but I believe it has something to do with the fact hat in the line:

while (cells[tempIdx += dir] == opponent)

You should also check you are not out of bound, otherwise - if there is still an opponent on the end of the board, you will keep increasing dir

Try changing this line to:

while (tempIdx + dir >= 0 && tempIdx + dir < cells.length && cells[tempIdx += dir] == opponent)

As a rule of thumb, usually it is a good practice in array accesses, especially in loops, to guard against going out of bound by checking the length explicitly.