Related papers: A Complexity of double dummy bridge
This paper provides a complexity analysis for the game of dark Chinese chess (a.k.a. "JieQi"), a variation of Chinese chess. Dark Chinese chess combines some of the most complicated aspects of board and card games, such as long-term…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of two-player parity games over graphs of bounded tree-width, where updates may add or delete edges,…
We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the…
This article presents a new three-player version of the bridge playing card game for the purpose of ending fixed partnerships so that the play can be more dynamic and flexible. By dynamically redefining team makeup in real time, this game…
Retrograde analysis is used in game-playing programs to solve states at the end of a game, working backwards toward the start of the game. The algorithm iterates through and computes the perfect-play value for as many states as resources…
Tablut is a complete-knowledge, deterministic, and asymmetric board game, which has not been solved nor properly studied yet. In this work, its rules and characteristics are presented, then a study on its complexity is reported. An upper…
Bridge is a trick-taking card game requiring the ability to evaluate probabilities since it is a game of incomplete information where each player only sees its cards. In order to choose a strategy, a player needs to gather information about…
We study the complexity of several combinatorial problems in the model of binary networked public goods games. In this game, players are represented by vertices in a network, and the action of each player can be either investing or not…
In this paper we are going to solve an open problem about the game tetris. We are going to give the first results in the complexity of a variant of offline tetris introduced by Erik Demaine, Susan Hohenberger and David Liben Nowell in their…
We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.
Hundreds of years after its creation, the game of chess is still widely played worldwide. Opening Theory is one of the pillars of chess and requires years of study to be mastered. Here we exploit the "wisdom of the crowd" in an online chess…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.
This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze…
We give explicit formulas for ruin probabilities in a multidimensional Generalized Gambler's ruin problem. The generalization is best interpreted as a game of one player against $d$ other players, allowing arbitrary winning and losing…
We provide a lower bound on the complexity function of a typical (in the Lebesgue measure sence) right triangular billiard.
We provide explicit lower estimates on the complexity growth in typical directions for a class of irrational triangle billiards
We provide several positive and negative complexity results for solving games with imperfect recall. Using a one-to-one correspondence between these games on one side and multivariate polynomials on the other side, we show that solving…
Quantum methods allow to reduce communication complexity of some computational tasks, with several separated partners, beyond classical constraints. Nevertheless, experimental demonstrations of this fact are thus far limited to some…