Questions tagged [combinatorial-game-theory]
Two-player turn-based perfect-information games, surreal numbers, impartial games and Sprague-Grundy theory, partizan games
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Placing triangles around a central triangle: Optimal Strategy?
This question has gone for a while without an answer on MSE (despite a bounty that came and went) so I am now cross-posting it here, on MO, in the hope that someone may have an idea about how to ...
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$2$-for-$2$ asymmetric Hex
This is a crosspost from Math stackexchange as I left the question open a while and bountied it but received no answers.
If the game of Hex is played on an asymmetric board (where the hexes are ...
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Connection properties of a single stone on an infinite Hex board
This includes a series of questions.
One of the most typical examples is shown as the picture below.
An half-infinite Hex board with an one row of black stones. Black stones are separated by one ...
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"Infinity": A card game based on prime factorization and a question
I have been developing a card game called "Infinity", which involves a unique play mechanic based on card interactions. In this game, each card displays a set of symbols, and players match ...
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How many ways to win a game between two teams with arbitrary player skills
Suppose we have $n\geq 4$ players $p_1,\cdots,p_n$ of a game between two teams: team $A$ and team $B$ (disjoint sets, each with two or more players, so that $|A|+|B|=n$). Assume that each player $p_i$ ...
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Are gaps and loopy games interchangeable in the Surreal Numbers?
The class of surreal numbers (commonly called $No$) is not complete: it contains gaps. Some people have studied the "Dedekind completion" of the surreal numbers in order to do limits and ...
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Chip firing on hypergraphs
A (finite) hypergraph is a pair $(V, \mathcal{E})$ where $V$ is a finite set of vertices and $\mathcal{E}\subseteq\mathcal{P}(V)$ with each $E\in\mathcal{E}$ having at least two elements; a ...
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For which set $A$, Alice has a winning strategy?
Cross-posted from MSE: https://math.stackexchange.com/questions/4775193/for-which-set-a-alice-has-a-winning-strategy
Alice and Bob are playing a game. They take an integer $n>1$, and partition the ...
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Are infinite loops possible in the game Prodway?
I'd like to know if infinitely repeating sequences of moves (i.e. cycles) are possible in the following game:
Prodway is a game for two players (Black and White) that is
played on the intersections (...
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Negative of combinatorial game
I am having problem understanding what negative of a combinatorial game $G$ exactly means in combinatorial game theory. Does it mean that if I have normal game, if I create inverse, i.e., $-G = \{-G^R ...
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Is "do-almost-nothing" ever winning on large CHOMP boards?
This is a special case of a question asked but unanswered at MSE:
Consider the combinatorial game CHOMP (presented as in the linked notes so that the "poison" square is bottom-left). In any $...
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Uniform strategy on Kastanas' game
I think my question applies to most games, but for the sake of concreteness, I shall consider one specific game in this question. We consider the game posed by Ilias Kastanas in his paper On the ...
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A combinatorial game with seemingly curious arithmetic properties
We consider the following combinatorial game (with two players
alternatively playing optimally). Posititions are given by heaps containing $b\geq 0$ black and $w\geq 0$ white stones and are
encoded by ...
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A little number theoretic game
I came up with this little two player game:
The players take turns naming a positive integer. When one player says the number n, the other player can only reply in two different ways: They can either ...
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Eventual stabilization for repeatedly adding multiplayer games
This question is an outgrowth of a couple previous questions of mine. In order: 1,2,3. This should be fully self-contained, but those questions may help motivate this one.
To keep things readable, I'...
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