Tic Tac Toe with Minimax: Computer sometimes losing when Player goes first; works otherwise

问题

I am working on a Minimax algorithm for unbeatable Tic Tac Toe. I need it to work both for when the Computer goes first as well as when the Player goes first. With the current version, the Computer will never lose when going first. However, it seems that Minimax never finds a best move (always returns -1 as the score) if the Player goes first.

What is causing the Minimax score returned to be -1 for the Computer if the Player makes the first move?

Example:

board.addMark( 1, Mark2.PLAYER ); // add a 'PLAYER' mark to an arbitrary location
Minimax.minimax( board, Mark2.COMPUTER ); // will always return -1

Here's the 'Minimax' class:

public class Minimax {
  public static int minimax( Board board, Mark2 currentMark ) {
    int score = (currentMark == Mark2.COMPUTER) ? -1 : 1;
    int[] availableSpaces = board.getAvailableSpaces();

    if ( board.hasWinningSolution() )
      score = (board.getWinningMark() == Mark2.COMPUTER) ? 1 : -1;
    else if ( availableSpaces.length != 0 ) {
      Mark2 nextMark = (currentMark == Mark2.COMPUTER) ? Mark2.PLAYER : Mark2.COMPUTER;

      for ( int availableIndex = 0; availableIndex < availableSpaces.length; availableIndex++ ) {
        board.addMark( availableSpaces[availableIndex], currentMark );
        int nextScore = minimax( board, nextMark );
        board.eraseMark( availableSpaces[availableIndex] );

        if ( currentMark == Mark2.COMPUTER && nextScore > score
            || currentMark == Mark2.PLAYER && nextScore < score )
          score = nextScore;
      }
    }

    return score;
  }
}

Here is the 'Board' class:

public class Board {
  private Mark2 gameBoard[];
  private int blankSpaces;

  private boolean solutionFound;
  private Mark2 winningMark;

  public final static int winSets[][] = {
      { 0, 1, 2 }, { 3, 4, 5 },
      { 6, 7, 8 }, { 0, 3, 6 },
      { 1, 4, 7 }, { 2, 5, 8 },
      { 0, 4, 8 }, { 2, 4, 6 }
  };

  public Board() {
    gameBoard = new Mark2[9];
    blankSpaces = 9;

    for ( int boardIndex = 0; boardIndex < gameBoard.length; boardIndex++ ) {
      gameBoard[boardIndex] = Mark2.BLANK;
    }
  }

  public void addMark( int spaceIndex, Mark2 mark ) {
    if ( gameBoard[spaceIndex] != mark ) {
      gameBoard[spaceIndex] = mark;

      if ( mark == Mark2.BLANK ) {
        blankSpaces++;
      } else {
        blankSpaces--;
      }
    }
  }

  public void eraseMark( int spaceIndex ) {
    if ( gameBoard[spaceIndex] != Mark2.BLANK ) {
      gameBoard[spaceIndex] = Mark2.BLANK;
      blankSpaces++;
    }
  }

  public int[] getAvailableSpaces() {
    int spaces[] = new int[blankSpaces];
    int spacesIndex = 0;

    for ( int boardIndex = 0; boardIndex < gameBoard.length; boardIndex++ )
      if ( gameBoard[boardIndex] == Mark2.BLANK )
        spaces[spacesIndex++] = boardIndex;

    return spaces;
  }

  public Mark2 getMarkAtIndex( int spaceIndex ) {
    return gameBoard[spaceIndex];
  }

  public boolean hasWinningSolution() {
    this.solutionFound = false;
    this.winningMark = Mark2.BLANK;

    for ( int setIndex = 0; setIndex < winSets.length && !solutionFound; setIndex++ )
      checkSpacesForWinningSolution( winSets[setIndex][0], winSets[setIndex][1], winSets[setIndex][2] );

    return solutionFound;
  }

  public Mark2 getWinningMark() {
    return this.winningMark;
  }

  private void checkSpacesForWinningSolution( int first, int second, int third ) {
    if ( gameBoard[first] == gameBoard[second] && gameBoard[third] == gameBoard[first]
        && gameBoard[first] != Mark2.BLANK ) {
      solutionFound = true;
      winningMark = gameBoard[first];
    }
  }

  public void printBoard() {
    System.out.printf( " %c | %c | %c\n", getMarkCharacter( gameBoard[0] ), getMarkCharacter( gameBoard[1] ),
        getMarkCharacter( gameBoard[2] ) );
    System.out.println( "------------" );
    System.out.printf( " %c | %c | %c\n", getMarkCharacter( gameBoard[3] ), getMarkCharacter( gameBoard[4] ),
        getMarkCharacter( gameBoard[5] ) );
    System.out.println( "------------" );
    System.out.printf( " %c | %c | %c\n", getMarkCharacter( gameBoard[6] ), getMarkCharacter( gameBoard[7] ),
        getMarkCharacter( gameBoard[8] ) );
  }

  public char getMarkCharacter( Mark2 mark ) {
    char result = (mark == Mark2.PLAYER) ? 'O' : ' ';
    result = (mark == Mark2.COMPUTER) ? 'X' : result;
    return result;
  }
}

And here's the 'Mark2' class if there was any confusion:

public enum Mark2 {
  BLANK,
  PLAYER,
  COMPUTER
}

回答1:

Let's look at something simpler - the board is 1x1, and the first player to place a mark there wins.

Now the computer starts, score=-1. There is no winning solution (the one winning set is checked, it is not a 1-in-a-row), and there is an available space. So we proceed by backtracking to try the one available position.

Now Mark=PLAYER, and the board has a winning solution. So the computer wins, score = -1.

Returning to the first call, the line "int nextScore = minimax( board, nextMark );" returns -1 again, and the final score is -1.

The same thing happens to you with the larger problem.

回答2:

In a Tic Tac Toe game, there are 3 possibilities and not just 2: Player1 wins, Player2 wins, Nobody wins.

You should replace lines like this one:

int score = (currentMark == Mark2.COMPUTER) ? -1 : 1;

by something like this:

int score = (currentMark == Mark2.COMPUTER) ? -1 : ((currentMark == Mark2.PLAYER) ? 1 : 0);

回答3:

After taking an extended break, and with the help of the response by @GuyAdini, I had an epiphany. I wrote a test to count the occurrence of the three possible scores returned by minimax(). It yielded nothing for 0 as a result, which clued me in to the fact that I needed 0 to be considered by the algorithm as a possible score.

I had originally changed the initialization of 'score' to be the lowest/highest possible results (-1/1) and compared against them. However, this prohibited the result from getting the lowest/highest value exclusively from the set of scores returned and instead also included the initialized value. This spoiled the results.

I added the following comparison to the conditional changing of 'score':

|| availableIndex == 0

This forced all remaining comparisons to be made against a value that belonged to the set of returned scores.

public class Minimax {
  public static int minimax( Board board, Mark2 currentMark ) {
    int score = 0;
    int[] availableSpaces = board.getAvailableSpaces();

    if ( board.hasWinningSolution() )
      score = (board.getWinningMark() == Mark2.COMPUTER) ? 1 : -1;
    else if ( availableSpaces.length != 0 ) {
      Mark2 nextMark = (currentMark == Mark2.COMPUTER) ? Mark2.PLAYER : Mark2.COMPUTER;

      for ( int availableIndex = 0; availableIndex < availableSpaces.length; availableIndex++ ) {
        board.addMark( availableSpaces[availableIndex], currentMark );
        int nextScore = minimax( board, nextMark );
        board.eraseMark( availableSpaces[availableIndex] );

        if ( currentMark == Mark2.COMPUTER && nextScore > score
            || currentMark == Mark2.PLAYER && nextScore < score
            || availableIndex == 0 )
          score = nextScore;
      }
    }

    return score;
  }
}

来源：https://stackoverflow.com/questions/10679269/tic-tac-toe-with-minimax-computer-sometimes-losing-when-player-goes-first-work