I'm trying to figure out how to increase the speed of this algorithm. It works perfectly for two games (2-person games, CPU vs Human), but the problems is when I assign more than three piles (that contains a number of stones, so each player can pick up more than one), the computer player takes forever to compute the moves:
public Object[] minimax(int depth, int player) {
if(hasPlayer1Won(player)){
return new Object[]{get_default_input(1),1};
}else if(hasPlayer2Won(player)){
return new Object[]{get_default_input(1),-1};
}
List<T> movesAvailable = getNextStates();
if(movesAvailable.isEmpty()){
return new Object[]{get_default_input(0), 0};
}
int min = Integer.MAX_VALUE;
int max = Integer.MIN_VALUE;
T computersMove = getNextStates().get(0);
int i = 0;
for (T move: movesAvailable) {
makeAMove(move, player);
Object[] result = minimax(depth + 1, player == G.PLAYER1 ? G.PLAYER2 : G.PLAYER1);
int currentScore = (int)result[1];
if(player == G.PLAYER1){
max = Math.max(currentScore, max);
if(currentScore >= 0 && depth == 0) {
computersMove = move;
}
if(currentScore == 1){
resetMove(move);
break;
}
if(i==movesAvailable.size() - 1 && max < 0){
if (depth == 0){
computersMove = move;
}
}
}else{
min = Math.min(currentScore, min);
if(min == -1) {
resetMove(move);
break;
}
}
i++;
resetMove(move);
}
return new Object[]{computersMove, player == G.PLAYER1 ? max: min};
}
I have sucessfully tested the following methods for improving minimax (used it to play Tic-Tac-Toe and Domineering):
Alpha beta pruning - used a special variant of this type of pruning, in conjunction with Lazy evaluation - basically instead of generating the whole tree I just generated an optimal move on each layer and kept Lazy holders for the other state-action pairs (applying the Lazy evaluation method, by making use of a supplier and calling it when a move different than the one I held was made).
Heuristic pruning - see the chapter on heuristics in that book. I basically only generated the first d branches of the tree and instead of having a deterministic outcome, I applied the heuristic function described in that book to the current state to determine a heuristic outcome. Whenever move (d+1) was made, I generated another branch using the same approach. Here, d is the level that you choose (safest way is by testing)
Parallel computing also have a look at this, you may find it harder to implement but it pays off
First 2 options brought me a lot of computational time save, such that I was able to play Domineering optimally up to a 5x5 board and heuristically up to 10x10 (it can be better depending on how well you want it to play).