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Questions tagged [tic-tac-toe]

Tic-tac-toe is a paper-and-pencil game for two players, $X$ and $O$, who take turns marking the spaces in a $3 \times 3 $ grid.

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Tic Tac Toe: Probabilities of Outcomes with Random Moves *Including* Game-Ending Illegal Moves

I have a toy problem I've been playing with simulating for fun and learning, and I'd like to have a deeper understanding of the math involved. So, I'm curious: Given a randomly-played game between ...
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1answer
94 views

Tic-Tac-Toe on the Real Projective Plane is a trivial first-player win in three moves

Consider a $3 \times 3$ Tic-Tac-Toe board with opposite sides identified in opposite orientation. We play Tic-Tac-Toe in the Real Projective Plane. More precisely, consider a $3 \times 3$ Tic-Tac-Toe ...
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Is the aim of this Tic-Tac-Toe puzzle possible to achieve?

I was playing Tic-Tac-Toe with my friend when I came up with a puzzle. I might have to put this on the Puzzling Stack Exchange, but I do not know if the aim of the puzzle can be achieved. I am aware ...
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2answers
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Winning strategies in n-circular TicTacToe

The game of N-Circular TicTacToe is defined as follows: Informally, there is a circular board with $N$ empty slots where Alice and Bob place $X$'s and $O$'s. Whoever gets to place three consecutive ...
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1answer
1k views

Is it possible to never lose in tic-tac-toe?

Although it is impossible to win every game of tic-tac-toe, is it possible to never lose? Is there a specific placement or strategy for the game?
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1answer
218 views

Is Nash equilibrium strategy in zero-sum game a good response to non-rational player?

Let's say, we have sequential finite game with 2 players. The first player is rational and given the other player is also rational, there is a Nash equilibrium. Now let's say that only the first ...
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0answers
380 views

Does following nash equilibrium strategy in tic-tac-toe mean, that the game always ends in a tie?

Let's say, two players are playing extended version of tic-tac-toe on 10X10 board (who first has 5 tiles next to each other, wins). Should both players play Nash equilibrium strategy, would it mean, ...
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1answer
277 views

Prove that $5 \times 5 \times 5$ tic-tac-toe ends in a draw

I am pretty sure that when played perfectly, $5 \times 5 \times 5$ tic-tac-toe will end in a draw. Is anyone able to prove this?
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2answers
343 views

Is there a winning strategy for this tic-tac-toe?

The figure shows a variation of a tic-tac-toe board, with the usual rules: three small balls each player and three in a row wins. Is it possible to transform the layout isomorphically so the same ...
3
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1answer
746 views

Strategy set in Tic-Tac-Toe [closed]

I read in a book that the cardinality of the strategy set of the first player in a game of Tic-Tac-Toe is approximately equal to $10^{126}$ but I cannot see how to arrive at this result. Disclaimer: ...
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1answer
1k views

Tic-Tac-Toe Game [duplicate]

What is the total number of strategies (pure strategies in game theory) in a Tic Tac Toe game for each player? Assume that it is a 3x3 game and 2 players. Rule: The players put marks such as X and ...
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3answers
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Winning strategies in multidimensional tic-tac-toe

This question is a result of having too much free time years ago during military service. One of the many pastimes was playing tic-tac-toe in varying grid sizes and dimensions, and it lead me to a ...
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3answers
4k views

A non-losing strategy for tic-tac-toe $\times$ tic-tac-toe

Consider a $9 \times 9$ matrix that consists of $9$ block matrices of $3 \times 3$. Let each $3 \times 3$ block be a game of tic-tac-toe. For each game, label the $9$ cells of the game from $1$ to $9$...
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2answers
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Game combinations of tic-tac-toe [closed]

How many combinations are possible in the game tic-tac-toe (Noughts and crosses)? So for example a game which looked like: (...