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We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position,…

Computational Complexity · Computer Science 2018-03-13 Jeffrey Bosboom , Erik D. Demaine , Mikhail Rudoy

Consider the following game: You are given two indistinguishable envelopes, each containing money. One contains twice as much as the other. You may pick one envelope and keep the money it contains. Having chosen an envelope, you are given…

Probability · Mathematics 2021-01-29 Nemo Semret

N players are randomly fitted with a colored hat (q different colors). All players guess simultaneously the color of their own hat observing only the hat colors of the other N-1 players. The team wins if all players guess right. No…

Combinatorics · Mathematics 2020-02-25 Theo van Uem

We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3…

Quantum Physics · Physics 2018-02-07 Emilio Bagan , John Calsamiglia , Janos A. Bergou , Mark Hillery

In the game of Matching Pennies, Alice and Bob each hold a penny, and at every tick of the clock they simultaneously display the head or the tail sides of their coins. If they both display the same side, then Alice wins Bob's penny; if they…

Computer Science and Game Theory · Computer Science 2018-02-05 Dusko Pavlovic , Peter-Michael Seidel , Muzamil Yahia

Consider a P\'olya urn where a drawn ball of colour $i$ is replaced together with a fixed number $m_i$ of balls of the same colour. We give a simple proof that if, for example, there are two colours and the urn starts with more balls of…

Probability · Mathematics 2025-06-19 Svante Janson

We study the following game. Three players start with initial capitals of $s_{1},s_{2},s_{3}$ dollars; in each round player $P_{m}$ is selected with probability $\frac{1}{3}$; then \emph{he} selects player $P_{n}$ and they play a game in…

Computer Science and Game Theory · Computer Science 2024-06-13 Ath. Kehagias , G. Gkyzis , A. Karakoulakis , A. Kyprianidis

We propose a definition of generalized Cops and Robbers games where there are two players, the Pursuer and the Evader, who each move via prescribed rules. If the Pursuer can ensure that the game enters into a fixed set of final positions,…

Combinatorics · Mathematics 2017-04-20 Anthony Bonato , Gary MacGillivray

We consider a two-player game in which the first player (the Guesser) tries to guess, edge-by-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of…

Probability · Mathematics 2009-07-14 Marcus Pendergrass

In this paper, we formulate and analyze generalizations of the quantum penny flip game. In the penny flip game, one coin has two states, heads or tails, and two players apply alternating operations on the coin. In the original Meyer game,…

Quantum Physics · Physics 2018-02-02 Hiroaki Mishima

We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial…

Quantum Physics · Physics 2009-11-07 F. Guinea , M. A. Martin-Delgado

Duality games are a way of looking at wave-particle duality. In these games. Alice and Bob together are playing against the House. The House specifies, at random, which of two sub-games Alice and Bob will play. One game, Ways, requires that…

Quantum Physics · Physics 2021-12-08 Mark Hillery

We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several…

Combinatorics · Mathematics 2025-10-31 Sean Fiscus , Glenn Hurlbert , Eric Myzelev , Travis Pence

Circular Nim is a two-player impartial combinatorial game consisting of $n$ stacks of tokens placed in a circle. A move consists of choosing $k$ consecutive stacks and taking at least one token from one or more of the stacks. The last…

Combinatorics · Mathematics 2024-04-11 Matthieu Dufour , Silvia Heubach

We give a simple human-playable winning strategy for the second player in the game of Sim.

Combinatorics · Mathematics 2020-01-14 Weronika Wrzos-Kaminska

We solve the game of Babylon when played with chips of two colors, giving a winning strategy for the second player in all previously unsolved cases.

Combinatorics · Mathematics 2011-11-18 Agelos Georgakopoulos , Peter Winkler

Mirror games were invented by Garg and Schnieder (ITCS 2019). Alice and Bob take turns (with Alice playing first) in declaring numbers from the set {1,2, ...2n}. If a player picks a number that was previously played, that player loses and…

Computational Complexity · Computer Science 2023-07-14 Roey Magen , Moni Naor

In this paper we introduce novel algorithmic strategies for effciently playing two-player games in which the players have different or identical player roles. In the case of identical roles, the players compete for the same objective (that…

Computer Science and Game Theory · Computer Science 2013-03-26 Mugurel Ionut Andreica , Nicolae Tapus

The game of memory is played with a deck of n pairs of cards. The cards in each pair are identical. The deck is shuffled and the cards laid face down. A move consists of flipping over first one card then another. The cards are removed from…

Probability · Mathematics 2012-08-27 Daniel J. Velleman , Gregory S. Warrington

Here, we present a variant of Nim with two piles. In the first pile, we have stones with a weight of 1, and in the second pile, we have stones with a weight of -2. Two Players take turns to take stones from one of the piles, and the total…

Combinatorics · Mathematics 2023-12-06 Shoei Takahashi , Hikaru Manabe , Aoi Murakami , Ryohei Miyadera