![]() We can take this to the extreme, and say that from any starting position on a mini board, we can estimate the probability of a winner for that board by simulating out thousands of random continuations of pieces from either side to empty squares. Good moves almost appear to be random from the prospective of the mini-board. Also, since the macro view of the game dominates the micro view, we find that even when a board could clearly be won on the next move, that doesn't imply that the next move should be to take the win. In fact, it is possible that only one player ever makes moves on a given board. but here, one player could be sent to the same board many more times than their opponent. Where in regular tic-tac-toe, there is always a back and forth of who plays next. We can find some interesting observations looking at one mini board in isolation. ![]()
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