Well now. A few things, here:
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there are not 9 × 9 × 9 × 9 × .... possible ways to play. After the first move, 8 squares remain, and so on, so there's at most 9 × 8 × 7 × ... = 9! = 362880 ways that the game can be played, ignoring the fact that most of those can be eliminated as reflections and rotations, or as win positions before you fill the whole board.
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we don't care how we got there. Each square can either be blank, a cross, or a nought, so 3^9 combos = 19683, and most of those are illegal, as only the boards where there's (one or zero) more crosses than noughts are good. And you don't need to store 'the computer's move', just jump directly to letting the player go again. Let's guess we need at most a quarter of that.
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we could have created a single web page with 5k anchor elements on it back in the HTML 1.0 days, ignoring the fact that it would have taken a while to download on our 28.8K modems. That wouldn't have been 170 Mb of unnecessary tagging, even with the 'lay it out with tables' style we had at the time.
Google do seem to have a predilection for reinventing the past, poorly. I hear that their bonuses are based on inventing 'new' things, though, so it's in their interest to pass it off?