C++ minimax function

Question

I have searched Google and Stackoverflow for this question, but I still don't understand how a minimax function works.

I found the wikipedia entry has a pseudocode version of the function:

function integer minimax(node, depth)
    if node is a terminal node or depth <= 0:
        return the heuristic value of node
    α = -∞
    for child in node:                       # evaluation is identical for both players 
        α = max(α, -minimax(child, depth-1))
    return α

Several other minimax functions I found with Google are basically the same thing; I'm trying to implement this in C++, and this is what I have come up with so far:

double miniMax(Board eval, int iterations)
{
    //I evaluate the board from both players' point of view and subtract the difference
    if(iterations == 0)
        return boardEval(eval, playerNumber) - boardEval(eval, opponentSide());

    /*Here, playerTurn tells the findPossibleMoves function whose turn it is;
    I mean, how do you generate a list of possible moves if you don't even know
    whose turn it's supposed to be? But the problem is, I don't see where I can
    get playerTurn from, as there are only 2 parameters in all the examples of
    minimax I've seen*/
    vector<int> moves = eval.findPossibleMoves(playerTurn);

    //I'm assuming -∞ in the wikipedia article means a very low number?
    int result = -999999999;

    //Now I run this loop to evaluate each possible move
    /*Also, the Lua example in the wiki article has
      alpha = node.player==1 and math.max(alpha,score) or math.min(alpha,score)
      Is alpha a boolean there?!*/
    for(int i = 0; i * 2 < moves.size(); i++)
    {
        //I make a copy of the board...
        Board temp = eval;

        /*and make the next possible move... once again playerTurn crops up, and I
        don't know where I can get that variable from*/
        temp.putPiece(moves[i * 2], moves[i * 2 + 1], playerTurn);

        /*So do I create a function max that returns the bigger of two doubles?*/
        result = max(result, -miniMax(temp, iterations - 1));
    }

    return result;
    /*So now I've returned the maximum score from all possible moves within a certain
    # of moves; so how do I know which move to make? I have the score; how do I know
    which sequence of moves that score belongs to?*/
}

As you can see, I'm pretty confused about this minimax function. Please at the very least give me some hints to help me with this.

Thanks! :)

Answer 1

That sample from Wikipedia is doing NegaMax with Alpha/Beta pruning.

You may be helped by getting the naming straight:

• The basis is MiniMax, a literal implementation would involve 2 methods that take turns (mutually recursive), 1 for each side.

• Lazy programmers turn this into NegaMax, one method with a strategically placed - operator.

• Alpha/Beta pruning is keeping track of a Window of best moves (over multiple depths) to detect dead branches.

Your playerTurn is used to determine whose turn it is . In NegaMax you can derive this from the depth (iterations) being odd or even. But it would be easier to use 2 parameters (myColor, otherColor) and switch them at each level.

Answer 2

Your miniMax() function should remember the best move it found so far. So instead of this code:

  /*So do I create a function max that returns the bigger of two doubles?*/
  result = max(result, -miniMax(temp, iterations - 1));

You should do something like this:

  /*So do I create a function max that returns the bigger of two doubles?*/
  double score = -miniMax(temp, iterations - 1);
  if (score > result)
  {
     result = score;
     bestMove = i;
  }

Of course, you need a variable "bestMove" and a way to return the best move found to the caller.

Answer 3

Add the playerTurn variable as an argument to miniMax, and call miniMax which the current player's move initially and recursively.

Also, opponentSide needs to be a function of playerTurn.

Answer 4

A good place to start with game tree searching is the chess programming wiki. For your question about the move: I think it is most common to have two max-functions. The difference between the two max functions is that one returns only the score and the other returns the score and the best move. A recursive call order would be like following:

maxWithBestMoveReturn(...) --> min(...) --> max(...) --> min(...)

There are some good papers with pseudocode for the Alpha Beta algorithm:

• TA Marsland - Computer Chess and Search
• J Schaeffer - The games Computers (and People) Play

To your question in the comment: and math.max(alpha,score) or math.min(alpha,score) Is alpha a boolean there?!

No alpha is a window bound in a alpha beta algorithm. The alpha value gets updated with a new value. Because alpha and beta are swapped with the recursive call of the negamax-Function the alpha variable refers to the beta variable in the next recursive call.

One note to the playerTurn variable: The minimax or alpha-beta algorithm doesn't need this information. So i would give the information -- who's next --, into the Board-Structure. The functions findPossibleMoves and boardEval get all information they need from the Board-Structure.

One note to the recursive break condition: If i understand your code right, then you only have the one with iterations == o. I think this means the algorithm has reached the desired depth. But what if there are no possible moves left befor the algorithm reaches this depth. Maybe you should write following:

vector<int> moves = findPossibleMoves(...);
if (!moves.size())
    return boardEval(...);

Answer 5

In your pseudocode, the node variable has to contain all the information about the current board position (or whatever). This information would include whose turn it is to move.