Saying there are 9^3 possible games for tic-tac-toe is incorrect

[birgersp]

As stated here;

There are 9 choices for the 1st move, 8 for the 2nd move, 7 for the 3rd move, etc., giving us an upper bound of 9! = 987654321 = 362880. But this is an overestimate, because some games end in 5, 6, 7 or 8 moves. The true figure is actually 255168.
If we take symmetry into account, the number reduces substancially. For example, there are now only 3 choices for the first move and at most 5 choices for the second move. In fact, the total is reduced to 26830 distinct games, of which 172 end in 5 moves, 579 end in 6 moves, 5115 end in 7 moves, 7426 end in 8 moves, 8670 result in a win in 9 moves and 4868 result in a draw. There are a number of Web sites providing a full analysis. See for example http://www.se16.info/hgb/tictactoe.htm

[JKCooper2]

Thanks, I'll update a bit later