How are probabilities of x winning in tic-tac-toe calculated?

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Below is an example of a board state showing the probabilities of x winning in each cell. Is there a mathematical way to calculating the probabilities? I understand that the bottom left corner for x is 1 because the game will end but for the other cells i tried combinatorics/permutations but am getting no where unless I draw every possibility.

|X|0.45|0.4|
|:-|:-|:-|
|**O**|**X**|**0.1**|
|**O**|**0.25**|**1**|

In: Mathematics

3 Answers

Anonymous 0 Comments

Probability = Winning Outcomes/Total Outcomes

So for each board state, there are N number of sequences that can happen from there, and X number of ones that result in a win.

So if a cell has 0.45 it means that “45% of all possible sequences where this is the next move result in a win”

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