Game combinations of tic-tac-toe How many combinations are possible in the game tic-tac-toe (Noughts and crosses)?
So for example a game which looked like: (with positions 1-9)
A1   --   B1

A2   --   B2

A3   --   --

[1][3][4][6][7] would be one combination
 A: This information is taken from this website.
A naive estimate would be $9!=362\,880$, since there are $9$ possible first moves, $8$ for the second move, etc. This does not take into account games which finish in less than $9$ moves.


*

*Ending on the $5^\text{th}$ move: $1\,440$ possibilities

*Ending on the $6^\text{th}$ move: $5\,328$ possibilities

*Ending on the $7^\text{th}$ move: $47\,952$ possibilities

*Ending on the $8^\text{th}$ move: $72\,576$ possibilities

*Ending on the $9^\text{th}$ move: $127\,872$ possibilities


This gives a total of $255168$ possible games. This calculation doesn't take into account symmetry in the game.
A: I will say that the board combinations are 3^9, which is 19683 possibilities, and 2032 winning positions. The answer of 9! is related to how many ways we have to fell all the positions, rather than the possible combinations. 
I have answered this question already in another post, please see the next link: https://stackoverflow.com/a/54035004/5117217
Cheers!
