I have found information on how many various unique games of tic-tac-toe (naughts and crosses) can be played.
However, I am working to build an AI on the TI-84+ which uses a learning system which was originally implemented in M.E.N.A.C.E
I have created all the inputs, and have started the logic. In order to continue I need to know how much memory to allocate. Since I am not good at combinatorics, I thouggt I would ask here:
How many unique gameboards are there in tic-tac-toe which contain 1, 3, 5, or 7 moves and no winning pattern? I know that there is 9 boards after the first move, and 504 after the third move. After the fifth move there is 15,120 but we remove the 1440 winning boards for 13680 boards after the fifth move. 13680+504+9= 14193 boards. This is where I get stuck. How do I deal with the board layouts with 7 moves given that there are boards which have winning combinations after 6 moves?