By this I mean a single axiom for placement. (I'm working on a solution that involves positional valuation and vectors, and appears to be solid, but my assumption would be this has been done previously, like most mathematical techniques one "discovers";)
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$\begingroup$ Why would you assume? $\endgroup$– quintumniaCommented Jul 21, 2017 at 16:54
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1$\begingroup$ @quintumnia because there are a lot of smart people, and, in general, whenever I'm thinking through a problem from first principles, my conclusion almost always reflect what has already been proven or defined. While it's true that per M games I might be thinking about matricies in a new way (it appears that *no one has thought about Sudoku the way I am, which has led to some pretty exciting results)* but Tic-tac-toe has been very thoroughly analyzed. $\endgroup$– DukeZhouCommented Jul 21, 2017 at 17:06
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$\begingroup$ What do you mean by question? I'm sure you already know of minimax, does that count? Tic-Tac-Toe is also simple enough to store the entire possible game tree in memory $\endgroup$– k.c. sayz 'k.c sayz'Commented Jul 21, 2017 at 23:39
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$\begingroup$ @k.c.'aktual'ly I guess it depends on how many rules are being applied in conjunction with the minimax algorithm. (For context, I'm currently working on axiomatic intelligence, and the solution I'm envisioning involves no lookahead/gametrees.) $\endgroup$– DukeZhouCommented Jul 24, 2017 at 22:35
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