Suggestion on Tic Tac Toe

I am designing my implementation strategy for Tic-Tac-Toe game. Since this is my 1st game implementation, I am a bit confused and need some general pointers.

Now, the total number of winning combinations in a Tic-Tac-Toe are 8. Currently, I plan to store these winning combinations in an array. Once the end user has made at least 3 moves, I would start checking if the Player has won the game by comparing the current positions used by a Player against this array. However, I am sure this is not an efficient way to check if the player has a winning combination.

Can anyone please suggest me on how to go about with design the logic for the game?

Don't worry about efficiency. I wrote a backtracking solution and there are only 549,945 possible game states. It takes less than 0.25 seconds to run through these on my laptop. Here was my logic to see if the game was over - clearly not very efficient, but it doesn't matter:

private boolean isWinningMove(int row, int col) {
    int piece = board[row][col];

    // check current row
    boolean w = true;
    for (int x = 0; x < 3; x++) { w = w && (board[row][x] == piece); }
    if (w) { return true; }

    // check current column
    w = true;
    for (int x = 0; x < 3; x++) { w = w && (board[x][col] == piece); }
    if (w) { return true; }

    // check 0,0 diagonal
    w = true;
    for (int x = 0; x < 3; x++) { w = w && (board[x][x] == piece); }
    if (w) { return true; }

    // check 0,2 diagonal
    w = true;
    for (int x = 0; x < 3; x++) { w = w && (board[x][2 - x] == piece); }
    return w;

Here were my results, which match data on the Wikipedia page for tic-tac-toe:

Moves Simulated: 549945
Draws=46080   Player1-Wins=131184   Player2-Wins=77904
Perfect Strategy Implies: Always a tie.

Games won in 0 moves? 0
Games won in 1 moves? 0
Games won in 2 moves? 0
Games won in 3 moves? 0
Games won in 4 moves? 0
Games won in 5 moves? 1440
Games won in 6 moves? 5328
Games won in 7 moves? 47952
Games won in 8 moves? 72576
Games won in 9 moves? 81792

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Consider representing the board by integers.

-1 = X
 0 = empty
 1 = O

now, add up the value of the squares for each of the 8 possibilities (3 up and down, 3 left and right, 2 diagionals).

if the sum is 3, O wins if the sum is -3, X wins

if the sum is 2, then O has a winning move in one of those positions if the sum i -2, then X has a winning move in one of those positions.

The AI can use that as a basis for making decisions. A one move look ahead is sufficient to never lose.

If the AI starts the game, the best move is a corner. If the opponent fails to take the center, the AI wins. If he does take the center, then either the AI wins, or draws.

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Instead of iterating over something I just wrote the 8 combinations.

My evaluation func does the following: if A is side to move & if there is two A elements and a 0 (empty) in one of all combinations then it's a win:

boolean player_can_win(int value) { //value is side's element*2
    return board[0] + board[1] + board[2] == value
            || board[3] + board[4] + board[5] == value
            || board[6] + board[7] + board[8] == value
            || board[0] + board[3] + board[6] == value
            || board[1] + board[4] + board[7] == value
            || board[2] + board[5] + board[8] == value
            || board[0] + board[4] + board[8] == value
            || board[2] + board[4] + board[6] == value;

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Explicitly storing and comparing to the solutions isnt the most efficient if you were playing generalized N X N tic-tac-toe, but since it's such as small board and there are only 8 such combos there is nothing wrong with explicitly storing solutions like this.

The bigger issue is that depending on storage style, spaces that aren't relevant to the solution might be an issue.

O - -        - O -
X X X   vs.  X X X
O - O        O - O

comparing 3x3 state arrays these are different and as such this method would require well over 8 end states

I presume you keep something like a gameState 3x3 array with blank=0, X=1, O=2 ?

Besides those explicit comparisons, you can do something like

win = false   
// rows/columns
for i in 0,1,2
   if (state[i][0] != BLANK && state[i][0] == state[i][1] == state[i][2]) win = true
          #extensible to NxN - all(j == state[i][0] for j in state[i])
   if (state[0][i] != BLANK && state[0][i] == state[1][i] == state[2][i]) win = true
          #extensible to NxN - all(j == state[0][i] for j in zip(*state)[i])
if (state[0][0] != BLANK && state[0][0] == state[1][1] == state[2][2]) win = true
          #extensible to NxN - all(state[j][j] == state[0][0] for j in range(len(state))
if (state [2][0] != BLANK && state[2][0] == state[1][1] == state[0][2]) win = true

If you want win to store the winner rather than flag, then make win = BLANK up top, and set to the value of any of the involved squares. Shouldn't be necessary tho, winner is obviously the most recent move!

I think the part of writing tic-tac-toe that you may find most challenging, but not too hard, would the AI. It is not too difficult, but not exactly trivial, to write an AI that wont lose (can always at least force a tie). If you want a relatively good AI that is capable of losing occasionally, youll need to add some randomness or something.

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  • There are at most 9! states, which is 362880 (there are actually less because many of those states reach a winning condition before the last move). Not sure how you managed to get 549945 states.
  • The backtracking tree size is 549,945 - it includes all the games in progress.
  • I did not understand the need for 7x7 array. Can you please elaborate? Also, I am not clear on the statement: check all around the square that was chosen for for 3-in-a-row; 2 above, 2 below, 2 left, 2 right, 2 upper left, 2 lower right, 2 upper right, 2 lower left . Thank you
  • I added clarification for why the 7x7 array is handy.
  • This seems way more complicated than just checking the 8 possible combinations. You haven't even covered all cases (1 above & 1 below, 1 right and 1 left, etc). This is the overthinking way. The OP's way is the obvious and straight-forward way.
  • True, I missed 2 cases. However, this solution generalizes to any NxM board and is highly efficient in terms of CPU and memory.
  • Common, high CPU efficiency to compute a tic-tac-toe winning position ?
  • @Shaggy: How is that not exactly what jon said? Jon referred generically to NxN and you're saying what he said is true for N=10. What part of what he said is "not necessarily true"?