相关论文: A game-theoretic analysis of baccara chemin de fer
In a previous paper, we considered several models of the parlor game baccara chemin de fer, including Model B2 (a $2\times2^{484}$ matrix game) and Model B3 (a $2^5\times2^{484}$ matrix game), both of which depend on a positive-integer…
Baccara banque is a three-person zero-sum game parameterized by $\theta\in(0,1)$. A study of the game by Downton and Lockwood claimed that the Nash equilibrium is of only academic interest. Their preferred alternative is what we call the…
A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…
The mathematics of shuffling a deck of $2n$ cards with two "perfect shuffles" was brought into clarity by Diaconis, Graham and Kantor. Here we consider a generalisation of this problem, with a so-called "many handed dealer" shuffling $kn$…
In 1979, David Fabian found a complete game of two-person Chinese Checkers in 30 moves (15 by each player) [Martin Gardner, Penrose Tiles to Trapdoor Ciphers, MAA, 1997]. This solution requires that the two players cooperate to generate a…
Joseph Bertrand [1822--1900], who is often credited with a model of duopoly that has a unique Nash equilibrium, made another significant contribution to game theory. Specifically, his 1888 analysis of baccarat was the starting point for…
Abalone is a 2-player board game with perfect information. The game is played on a 5x5x5 hexagonal grid and ends when a player pushes 6 of their opponents' pieces off the board. Abalone is similar to games like chess and Go in that all…
The game of baccarat has evolved from a parlor game played by French aristocrats in the first half of the 19th century to a casino game that generated over US\$41 billion in revenue for the casinos of Macau in 2013. The parlor game was…
The triangle game introduced by Chv\'{a}tal and Erd\H{o}s (1978) is one of the most famous combinatorial games. For $n,q\in\mathbb{N}$, the $(n,q)$-triangle game is played by two players, called Maker and Breaker, on the complete graph…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
We are investigating who has the winning strategy in a game in which two players take turns drawing arrows trying to complete cycle cells in a graph. A cycle cell is a cycle with no chords. We examine game boards where the winning strategy…
We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces…
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…
We study so-called invariant games played with a fixed number $d$ of heaps of matches. A game is described by a finite list $\mathcal{M}$ of integer vectors of length $d$ specifying the legal moves. A move consists in changing the current…
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…
The classical Maker-Breaker positional game is played on a board which is a hypergraph $\mathcal{H}$, with two players, Maker and Breaker, alternately claiming vertices of $\mathcal{H}$ until all the vertices are claimed. When the game…
Contract bridge is a game characterized by incomplete information, posing an exciting challenge for artificial intelligence methods. This paper proposes the BridgeHand2Vec approach, which leverages a neural network to embed a bridge…
A rank-3 Maker-Breaker game is played on a hypergraph in which all hyperedges are sets of at most 3 vertices. The two players of the game, called Maker and Breaker, move alternately. On his turn, maker chooses a vertex to be withdrawn from…
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…
The McCarty Conjecture states that any McCarty Matrix (an $n\times n$ matrix $A$ with positive integer entries and each of the $2n$ row and column sums equal to $n$), can be additively decomposed into two other matrices, $B$ and $C$, such…