If every move in a game of tic-tac-toe is made at random, spread evenly over the remaining spaces, what is the probability the first player wins, the second player wins, or that there is a tie?
There are (only?) 126 boards of 5 X and 4 O. Most of these were likely wins before the last move, but I wanted to see what they looked like.
So I drew them all out.
On 16 boards there are no wins.
On 36 boards there wins for both X and O.
On 12 boards there a win for O but not X.
On 62 boards there's at least one X win and no O.
So the probability of a tie is 16/126.
Next step will be to undo the boards with 2 wins to decide who won first.
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Posted by Jer
on 2025-02-17 14:18:14 |
hand counted Ties
