Naughts-And-Crosses

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I think you're conflating two or three different rule sets there. In standard tic-tac-toe, X goes first and never loses unless misplayed. If both players are optimal, every game ends in a tie. So once you put in randomness and take out strategy, you're not looking at the standard statistics any longer. That said, I'm not entirely sure what the rules are for the random version you describe at the end, so I can't really comment further.

In the random version, are the actual positions of the X's and O's determined by the odd or even cards, or do the cards simply determine who gets to put their X or O in whatever box they want first?

If player's get to chose where to place their X or O, it is a skill, and should result in a tie everytime, unless the player and dealer are working as a team.

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