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I know the upper bound for the size of the game tree is 9! = 362,880 in a 3X3 Tic Tac Toe. After deducted the invalid case and the rotation and reflection, only 26,830 possible games are left. So complexity of decision trees in 3X3 Tic Tac Toe is 5 which is the number of digit of the leaf nodes (26,830). Am I conclusion right?

If so, how can i calculate a decision tree complexity of 4X4 Tic Tac Toe without drawing out a full decision tree?

Sorry for my dump question

miketsui3a
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You probably want to use some kind of model-checker, that can count the solutions, e.g. a #SAT solver https://en.wikipedia.org/wiki/Sharp-SAT. I don't believe there is any trick possible beyond exploring the state space, apart from using symmetries (but that only alleviates the exploration).

This is like the N-queens problem https://en.wikipedia.org/wiki/Eight_queens_puzzle there is no analytical solution for the number of solutions when you scale the board up.

Yann TM
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