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In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…

Probability · Mathematics 2023-11-28 Yaakov Malinovsky

We introduce a two-player game, in which each player extends a given sequence by picking a free element in a domain D of the real line. The aim of the players is to control the parity of the number of transpositions necessary to put the…

Combinatorics · Mathematics 2009-04-06 Elise Janvresse , Steve Kalikow , Thierry De La Rue

In this paper we study a variant of the Nuel game (a generalization of the duel) which is played in turns by $N$ players. In each turn a single player must fire at one of the other players and has a certain probability of hitting and…

Discrete Mathematics · Computer Science 2025-07-01 S. Mastrakoulis , Ath. Kehagias

In this paper we review some of the main results obtained in the field of truels. A "truel" is a generalization of a duel involving three players. Depending on the rules used for chosing the players, we may distinguish between the random,…

Probability · Mathematics 2007-05-23 Pau Amengual , Raúl Toral

Toral introduced so-called cooperative Parrondo games, in which there are N players (3 or more) arranged in a circle. At each turn one player is randomly chosen to play. He plays either game A or game B, depending on the strategy. Game A…

Probability · Mathematics 2015-02-27 S. N. Ethier , Jiyeon Lee

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

Probability · Mathematics 2015-07-07 Jan Vrbik , Paul Vrbik

The game of Hex has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. Black wins by completing a crossing between two opposite edges, while White wins by completing a…

Probability · Mathematics 2009-02-25 Yuval Peres , Oded Schramm , Scott Sheffield , David B. Wilson

We consider a two player simultaneous-move game where the two players each select any permissible $n$-sided die for a fixed integer $n$. A player wins if the outcome of his roll is greater than that of his opponent. Remarkably, for $n>3$,…

Probability · Mathematics 2018-10-23 Artem Hulko , Mark Whitmeyer

Ultimate Tic-Tac-Toe is a variant of the well known tic-tac-toe (noughts and crosses) board game. Two players compete to win three aligned "fields", each of them being a tic-tac-toe game. Each move determines which field the next player…

Computer Science and Game Theory · Computer Science 2020-06-09 Guillaume Bertholon , Rémi Géraud-Stewart , Axel Kugelmann , Théo Lenoir , David Naccache

Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose…

Optimization and Control · Mathematics 2019-04-24 Joshua B. Miller

Yama Nim is a two heaps Nim game introduced in the second author's Master Thesis, where the player takes more than $2$ tokens from one heap, and return $1$ token to the other heap. Triangular Nim is a generalization, where the player takes…

Combinatorics · Mathematics 2023-10-11 Shun-ichi Kimura , Takahiro Yamashita

This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…

Disordered Systems and Neural Networks · Physics 2025-12-16 Alexander K. Hartmann

We consider the permutation analogue of Penney's game for words. Two players, in order, each choose a permutation of length $k\ge3$; then a sequence of independent random values from a continuous distribution is generated, until the…

Combinatorics · Mathematics 2026-04-29 Sergi Elizalde , Yixin Lin

In a recent article in American Scientist, Theodore Hill described a coin-tossing game whose pay-off is the number of heads over the total number of throws. Suppose that at a given point during the game you have 5 heads and 3 tails, should…

Probability · Mathematics 2010-09-13 Luis A. Medina , Doron Zeilberger

This paper studies the game of guessing riffle-shuffled cards with complete feedback. A deck of $n$ cards labelled 1 to $n$ is riffle-shuffled once and placed on a table. A player tries to guess the cards from top and is given complete…

Probability · Mathematics 2021-07-20 Pengda Liu

Consider the following game between a random player R and a deterministic player D. There is a pile of n elements at the beginning. The rules for playing are as follows: In each turn of R, if the pile contains exactly m elements, R removes…

Combinatorics · Mathematics 2024-03-26 Yehonatan Fridman

Connect Four is a two-player game where each player attempts to be the first to create a sequence of four of their pieces, arranged horizontally, vertically, or diagonally, by dropping pieces into the columns of a grid of width seven and…

Combinatorics · Mathematics 2025-02-18 Robert Steele , Daniel B. Larremore

The angel game is played on $2$-dimensional infinite grid by $2$ players, the angel and the devil. In each turn, the angel of power $c \in \mathbb{N}$ moves from her current point $(x, y)$ to a point $(x', y')$ which $\max\{|x - x'|, |y -…

Combinatorics · Mathematics 2024-01-04 Nuttanon Songsuwan , Anuwat Tangthanawatsakul , Pawaton Kaemawichanurat

The 1996 Donald Duck Holiday Game is a role-playing variant of the historical Game of the Goose, involving characters with unique attributes, event squares, and random event cards. The objective of the game is to reach the camping before…

Computers and Society · Computer Science 2020-01-15 W. J. A. van Heeswijk

For any odd integer $n\geq3$ a board (of size $n$) is a square array of $n\times n$ positions with a simple rule of how to move between positions. The goal of the game we introduce is to find a path from the upper left corner of a board to…

Combinatorics · Mathematics 2025-03-05 Ary Shaviv