However, the game is a race, and while I may have better chances of winning the center column, it is balanced with the chances that my opponent wins the left column.

for instance, my chances of winning the vertical center row are. You could sort of use this to speculate on what your chances are for winning a given row or column by combining the probabilities. I wrote a program to pre-populate this table mapping any possible starting position for a little board to a probability that this board would be won by either X or O, given the assumptions of randomness from above.Īpplied at game time, we can reduce our tic-tac-toe board to a 9x9 board of probabilities that any one square is going to be won by a given player. there are 3^9 possible positions to consider, which works out to just 19683 positions. Since each miniboard has nine squares, and each square has either an X, an O, or nothing. We can take this to the extreme, and say that from any starting position on a mini board, we can estimate the probability of a winner for that board by simulating out thousands of random continuations of pieces from either side to empty squares. Good moves almost appear to be random from the prospective of the mini-board.

Also, since the macro view of the game dominates the micro view, we find that even when a board could clearly be won on the next move, that doesn't imply that the next move should be to take the win. In fact, it is possible that only one player ever makes moves on a given board. but here, one player could be sent to the same board many more times than their opponent. Where in regular tic-tac-toe, there is always a back and forth of who plays next. We can find some interesting observations looking at one mini board in isolation.

Ultimate tic tac toe strategy