# 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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### Bingo patterns probability [closed]

I want to calculate the probability of winning a patterns bingo I have some rules. 60 unique numbers on 4 tickets one ticket has a 3x5 (3 rows, 5 colons), I have a patterns one of them is to fill all ...
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### Expected number of edges to draw in a bipartite graph until you get a crossing

I was asked by a friend to calculate the number of edge crossings in a $m \times n$ complete bipartite graph: Now play a game where you randomly select an edge with equal probability each turn: what ...
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### Game - two players take turn moving a marker to an adjacent square in a 9x9 grid

A marker is placed in the centre of a $9$x$9$ grid. Ann and Beth take turns moving the marker to one of the adjacent squares (one sharing a side) provided that this square has never been occupied by a ...
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### Even-Nim and Odd-Nim are like Nim in that they are played with piles of stones.

Even-Nim and Odd-Nim are like Nim in that they are played with piles of stones. However, in Even-Nim, a move consists of removing a positive even number of stones from a pile, while in Odd-Nim, a move ...
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### Conway's Angel Problem: Strategy for Devil to catch $1-$Angel

I am learning about Conway's Angel Problem, which is in the image below. How can the Devil devise a strategy that will successfully capture the $1$-Angel, or an angel of power $1$, which is also a ...
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### For a given pair of positions in a family of winning sets, how many winning sets contain it?

This is a lot of exposition for what (I think) amounts to be a pretty simple combinatorics question. It's about bounding the Max Pair-Degree from Beck's Combinatorial Games: Tic-Tac-Toe Theory. On ...
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### $2$-for-$2$ asymmetric Hex

If the game of Hex is played on an asymmetric board (where the hexes are arranged in a $k\times k+1$ parallelogram), the player who wants to connect the closer pair of sides can force a win, ...
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### Game where players remove up to $t$ stones on turn number $t$

Please help me with following problem. There are 100 stones. Two persons play the following game: the first person takes 1 stone. The second takes one or two. Then the first person takes one or two or ...
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### A game on a rectangular board

Setup Let there be a board looking like a rectangular table. A piece is placed at any square of the board. Two players play a game. They move the piece in turns. The piece can only be moved to an ...
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### Game with 2024 chips to remove

Two players play with a pile of 2024 chips placed on a table. Each in turn, a player removes a certain number of chips from the gaming table: at least one chip, but no more than half of the chips ...
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1 vote
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### coin flipping competition

A, B, C are flipping a coin independently until they got a head (same experiment "to get a head" is repeated by these 3 people). Denote X, Y, Z stand for ...
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### WWfYMP: Bypassing reversible moves

This question concerns the theory developed in Winning Ways for Your Mathematical Plays. The relevant Volume 1 can be found online here. I'm unclear about the intuition behind the authors' "...
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### Combinatorial game played on a grid

Let the grid consist of r rows and k columns. Two players take turns moving a piece to an adjacent square (no diagonal moves). Once a square has been visited it cannot be visited again. The piece ...
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### Taking stones game beginning with 1 to 4 stones in a 2 player game. If we started with 18 stones, is the a winning strategy for the first player?

Amy and Beck are playing 'taking the stones game'. There are 18 stones on the table, and the two people take stones in turns. The first move of the starting player can take 1 to 4 stones. For the ...
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### A combinatorial game about split chocolate bar [duplicate]

The chocolate bar is a rectangle $m*n$ , divided by a recess into single squares. Two players play the next game in turn. On each turn, it is allowed to pick up one square of chocolate that has not ...
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### game coloring points rioplatense olympiad 1999

This problem is from the Rioplatense MO 1999/3 L3. The question is the following: Two players $A$ and $B$ play the following game: $A$ chooses a point, with integer coordinates, on the plane and ...
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### Should the maximal flow through a parted jungle uniquely prescribe its atomic weight?

This paper (pages 19-22) offers an algorithm for deciding which player will win Hackenbush when the position is a parted jungle. The key step seems to be very similar to the Ford-Fulkerson algorithm, ...
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