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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Standard Tic Tac Toe is -- Impartial or Partisan?

I am currently studying basic game theory (combinatorial) and was introduced to impartial games. The "definition" of impartial games I saw was: "An impartial game is a two-player game ...
42 views

Probability of draw with random play on $N\times N$ Tic Tac Toe

I was coding a tic tac toe game where $2$ players play tic tac toe randomly on a given $N$ board size $(N\times N)$. $X$ starts first. If one side gets $N$ consecutive (horizontal/vertical/diagonal) ...
85 views

Game Theory for Tic-Tac-Toe on a Torus [closed]

I recently discovered playing tic-tac-toe on a torus; I have not been able to achieve a draw. Is there a proof using game theory that says that tic-tac-toe on torus cannot end in draw?
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Minimum number of blocked squares to ensure a draw in a generically sized tic-tac-toe grid

There is a Japanese puzzle called marupeke which involves an $x$ by $y$ sized grid, where the objective is to place a $O$ or $X$ on every square so that there is not a "chain" of length 3. ...
79 views

Tic Tac Toe Combinations

I am creating a Tic-Tac-Toe game and was wondering how many combinations there are. I am an amateur coder and was going to code all the combinations by hand. Also if I do not do then what am I ...
525 views

Determinant Tic Tac Toe Part 2

In Determinant Tic-Tac-Toe, Player 1 enters a 1 in an empty 3 × 3 matrix. Player 0 counters with a 0 in a vacant position, and play continues in turn until the 3 × 3 matrix is completed with five 1’s ...
250 views

Two players put fill $1$ and $0$ in a $3\times 3$ matrix and compute its determinant when it is full. Can Player $0$ win if $1$ starts at the center?

In Determinant Tic-Tac-Toe, Player 1 enters a 1 in an empty 3 × 3 matrix. Player 0 counters with a 0 in a vacant position, and play continues in turn until the 3 × 3 matrix is completed with five 1’s ...
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Atleast one winner in extended tic-tac-toe

In tic-tac-toe we have 3X3 matrix. Suppose we play it and the game ends in a tie position. This means neither 'X' nor 'O' won. Now we pad the matrix equally on all its sides to make a bigger 5X5 ...
85 views

Number of lines in a tic tac toe of width $w$ and dimension $d$

I was watching a video by pbs infinite series on tic-tac-toe(https://www.youtube.com/watch?v=FwJZa-helig). Here, they discuss if there is a winning strategy for the starting player in tic-tac-toe of ...
211 views

How to prove that there is no strategy to always win in tic tac toe

I’m doing a game theory project and I’m trying to show the win strategies for different games but there is none for tic tac toe. However, I’m not sure how to prove it except for using experimental ...
557 views

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 ...
312 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 ...
309 views

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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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?
279 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 ...
808 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, ...
334 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?
450 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 ...
902 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: ...
2k 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 ...
2k views

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 ...
3k views

Prove that a game of Tic-Tac-Toe played on the torus can never end in a draw. (Graph theoretic solutions only.)

Here's a problem I assigned to my graph theory class. The only caveat is that I insisted that their solutions be entirely graph theoretic. Have fun with it. Prove that a game of Tic-Tac-Toe played ...
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 $9$...