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Some of those boards are impossible, and there are multiple ways to get to most of them, so you only need maybe half of that. There are 5,478 possible valid boards in total if you allow the computer to play any legal move.
As I described, I’d need way fewer, as the optimal computer counter-move would already be included in the next board.
So if you placed your X in the top left field in the starter image, the link would directly go to a field with the X in the top left, the O in the center position, and links in all the remaining seven positions. And of course the pre-calculation will eliminate some of the boards already, e.g. if the player or computer already won after the third move, where placing a fourth will not make sense.