# Questions tagged [combinatorial-game-theory]

Combinatorial game theory (abbreviated CGT) is the subfield of combinatorics (not traditional game theory) which deals with games of perfect information such as Nim and Go. It includes topics such as the Sprague-Grundy theorem and is tangentially related to the Surreal Numbers.

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### Reference for combinatorial game theory.

What is a good reference material for elementary combinatorial game theory? By combinatorial game theory I mean chiefly the study of zero-sum, deterministic two-player games (perhaps even more ...
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### Tutorials for Sprague-Grundy Theorem/Nimbers?

Help needed in understanding S-Grundy Number , any good tutorial. I am trying to solve Mathalon Problem 146 S-Grundy Game (dead link).
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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: (...
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### Converting a Gomoku winning strategy from a small board to a winning strategy on a larger board

Gomoku is the game where Black and White take turns placing stones of their own color, and the winner is the player who first gets five of their own stones in a row. Black moves first. In Gomoku on ...
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### Game involving tiling a 1 by n board with 1 x 2 tiles?

Consider a $1$ by $n$ tiled rectangle. You want to play a game with one opponent in which you place $1$ by $2$ "dominoes" on this rectangle. The player who places the last domino wins. Which player ...
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### Alice and Bob play the determinant game

Alice and Bob play the following game with an $n \times n$ matrix, where $n$ is odd. Alice fills in one of the entries of the matrix with a real number, then Bob, then Alice and so forth until the ...
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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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### Name for a certain “product game”

Let $G,H$ be two (combinatorial impartial) games. Consider the following new game $P$: The positions are the pairs of positions of $G$ and $H$. A move in $P$ is a move in $G$, or a move in $H$, or a ...
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### How to determine the size of the complete game tree for basic [M]?

You can read the rules of the game here, or actually play it free on the mobile mbrane app, but it's not required to address the question. Essentially: players take turns placing integers onto an ...
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### The Ring Game on $K[x,y,z]$

I recently read about the Ring Game on MathOverflow, and have been trying to determine winning strategies for each player on various rings. The game has two players and begins with a commutative ...
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### Hat 'trick': Can one of them guess right?

There are $n$ boys and $n$ girls. Each of them is given a hat of only 4 possible (known) colors and doesn't know its color. Now each can only see all the colors of hats of those of the other gender ...
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### Maximum board position in 2048 game

A game called 2048 is making rounds on social media. I am trying to determine the maximum score attainable for this game. Let's assume WLOG that only 2s are returned (if 4s are possible the max score ...
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### Does a finite game that cannot be drawn imply a winning strategy exists?

The author of this page, about a simple game (Chomp) http://plus.maths.org/content/mathematical-mysteries-chomp makes the following statement: "One of the players is sure to have a winning strategy. ...
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### Who has a winning strategy in “knight” and why?

Perhaps, this game is already known, but I did not find anything about it, I call it "knight". The rules : Player 1 chooses the starting square of a knight on a normal 8x8 - chessboard. The ...
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### Nimbers for misère games

Let $G$ be an impartial combinatorial game. I claim that there is a game $G'$ such that $G$ (without terminal positions; see below) under the misère play rule is equivalent to $G'$ under the normal ...
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### Game: two pots with coins

Rules of the game with two players. First player puts any number of coins in the first pot. Then second player, knowing that number, puts any amount of coins in the second pot. Then they in turns (...
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### Winning strategy for a matchstick game

There are $N$ matchsticks at the table. Two players play the game. Rules: (i) A player in his or her turn can pick $a$ or $b$ match sticks. (ii) The player who picks the last matchstick loses the game....
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### What does she mean by star?

I was looking at this video http://www.youtube.com/watch?v=ygqIfLHGTu4&feature=g-all-f#t=06m33s33 and i wondered what she means by star. How is this number defined and where does it come up. ...
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