What if humble TicTacToe game hid interesting math secrets? Using KNIME, @HansS shows that out of 362,880 possible move sequences, only 255,168 are realistic, and starting position + first move hugely shape your chances. A simple game becomes a combinatorial playground and perfect read before holiday matches! 
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I was thinking about this a while ago about more efficient ways to look at it. For example, there are only really three opening moves, (corner, middle, edge) since you simply rotate the board.
If the first player chose a corner there would only be five places (not eight) the opponent could move if you draw a line of reflection through the corner of the first move.
Similarly, if the edge was the first move you’d only have five places if you draw your reflection across the board through the first marker.
If the first player chose the centre, there would only be two places (corner or middle, all others are rotations).
So while there are 362,880 move sequences, there are going to be far fewer actual possible games since sequences will be rotations and/or reflections of a core set.
Anyone care to have a go at calculating how many there are? Or if you’ve read about a more elegant way of approaching it?
@Vexatious_Outlier You are right that symmetries help to reduce the count of possible moves dramatically.
May be this publication A Combinatorial Analysis of Tic-Tac-Toe and The Theoretical Advantage of Playing First gives you more insights
What if most Tic-Tac-Toe games are just the same board in disguise? In his follow-up piece,
@HansS shows that once you account for rotations and reflections, ~255k games shrink to ~32k truly unique ones—revealing how symmetry simplifies complexity and sharpens insights. Of course, using KNIME. Enjoy the data story!
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Thanks for the update, can’t wait to dive into this. When I gave this a few minutes thought I kept thinking I’d have to fall back to code. It’s going to be really interesting to see how he deals with the transformations in KNIME.
Best wishes for the New Year.