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Related papers: Generalizations of the M&M Game

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For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then…

General Topology · Mathematics 2016-04-01 Leandro F. Aurichi , Angelo Bella , Rodrigo R. Dias

The concept of intransitiveness for games, which is the condition for which there is no first-player winning strategy can arise surprisingly, as happens in the Penney game, an extension of the heads or tails. Since a game can be converted…

Physics and Society · Physics 2024-03-07 Alberto Baldi , Franco Bagnoli

Children, sitting in a circle, each have a nonnegative number of candies in front of them. A whistle is blown and each child with more than one candy passes one candy to the left and one to the right. The sharing process is repeated until a…

Combinatorics · Mathematics 2015-12-14 Grant Cairns

We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…

Combinatorics · Mathematics 2024-12-23 Nathan Bowler , Florian Gut

We define a variant of the two-dimensional Silver Dollar game. Two coins are placed on a chessboard of unbounded size, and two players take turns choosing one of the coins and moving it. Coins are to be moved to the left or upward…

General Mathematics · Mathematics 2025-06-10 Ryohei Miyadera , Enchong Li , Akito Tsujii

The game of war is one of the most popular international children's card games. In the beginning of the game, the pack is split into two parts, then on each move the players reveal their top cards. The player having the highest card…

Dynamical Systems · Mathematics 2012-04-05 Evgeny Lakshtanov , Vera Roshchina

Alice and Bob take turns (with Alice playing first) in declaring numbers from the set $[1,2N]$. If a player declares a number that was previously declared, that player looses and the other player wins. If all numbers are declared without…

Data Structures and Algorithms · Computer Science 2019-01-24 Uriel Feige

Toral (2002) considered an ensemble of N\geq2 players. In game B a player is randomly selected to play Parrondo's original capital-dependent game. In game A' two players are randomly selected without replacement, and the first transfers one…

Probability · Mathematics 2012-03-19 S. N. Ethier , Jiyeon Lee

Dreidel is a popular game played during the festival of Chanukah. Players start with an equal number of tokens, donate one token each to a common pot, and take turns spinning a four-sided top, called the dreidel. Depending on the side…

Combinatorics · Mathematics 2007-05-23 Thomas Robinson , Sujith Vijay

The following problem is considered. Two players are each required to allocate a quota of~$n$ counters among~$k$ boxes labelled~$1,2,\ldots,k$. At times $t=1,2,3,\ldots$ a random box is identified; the probability of choosing box~$i$…

Combinatorics · Mathematics 2022-10-06 Robin K. S. Hankin

Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of…

Number Theory · Mathematics 2024-12-11 Dzmitry Badziahin , Stephen Harrap , Erez Nesharim , David Simmons

The classic game of Nim has been well-known for many years, inspiring numerous variations. One such variant is Delete Nim, where players take turns eliminating one pile of stones and splitting the remaining pile into two smaller piles. In…

Combinatorics · Mathematics 2024-12-02 Masato Shinoda

The domination game is played on a graph $G$ by two players, named Dominator and Staller. They alternatively select vertices of $G$ such that each chosen vertex enlarges the set of vertices dominated before the move on it. Dominator's goal…

Combinatorics · Mathematics 2013-07-23 Boštjan Brešar , Paul Dorbec , Sandi Klavžar , Gašper Košmrlj

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…

Computer Science and Game Theory · Computer Science 2025-04-09 Guy Avni , Pranav Ghorpade , Shibashis Guha

This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo methodology based on a sample of 10,000 randomly generated…

Computer Science and Game Theory · Computer Science 2009-07-14 Matthew C. Clarke

The cordiality game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting \track{unlabeled} vertices of $G$. Admirable labels the selected vertices by $0$ and Impish by $1$, and the resulting label…

Combinatorics · Mathematics 2024-03-28 Elliot Krop , Aryan Mittal , Michael C. Wigal

We consider the following two-player game: Maxi and Mini start with the empty graph on $n$ vertices and take turns, always adding one additional edge to the graph such that the chromatic number is at most $k$, where $k \in \mathbb{N}$ is a…

Combinatorics · Mathematics 2018-02-19 Ralph Keusch

A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…

Combinatorics · Mathematics 2024-11-14 Kengo Hashimoto

We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider…

Computer Science and Game Theory · Computer Science 2013-06-21 Krishnendu Chatterjee

We provide a mechanism that uses two biased coins and implements any distribution on a finite set of elements, in such a way that even if the outcomes of one of the coins is determined by an adversary, the final distribution remains…

Probability · Mathematics 2018-03-05 Eilon Solan , Omri Nisan Solan , Ron Solan