Related papers: Sequencing Chess
This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and…
Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The…
A famous (and hard) chess problem asks what is the maximum number of safe squares possible in placing $n$ queens on an $n\times n$ board. We examine related problems from placing $n$ rooks. We prove that as $n\to\infty$, the probability…
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…
The opening book is an important component of a chess engine, and thus computer chess programmers have been developing automated methods to improve the quality of their books. For chess, which has a very rich opening theory, large databases…
The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…
Phase transition is a war game. It widely exists in different kinds of complex system beyond physics. Where there is revolution, there is phase transition. The renormalization group transformation, which was proved to be a powerful tool to…
In the field of computational game theory, games are often compared in terms of their size. This can be measured in several ways, including the number of unique game states, the number of decision points, and the total number of legal…
We compare four different `game-spaces' in terms of their usefulness in characterising multi-player tabletop games, with a particular interest in any underlying change to a game's characteristics as the number of players changes. In each…
The thesis consider the mixing of few (3-4) card shuffling as well as of large (52 card) deck. The thesis is showing the limit on the shuffling to homogeneity elaborated in short program; the thesis is in italian.
We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on chess.com. The standard version of the game is played on a regular 8 x 8 chessboard by a single player, with only white pieces, using…
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…
Consider a randomly shuffled deck of $2n$ cards with $n$ red cards and $n$ black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck that alternates in color by performing the following move:…
The Master equation describes the time evolution of the probabilities of a system with a discrete state space. This time evolution approaches for long times a stationary state that will in general depend on the initial probability…
Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several…
A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a…
Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…
In this paper we develop the theory of how to count, in thin concurrent games, the configurations of a strategy witnessing that it reaches a certain configuration of the game. This plays a central role in many recent developments in…
Quasi-stationary distributions (QSDs)arise from stochastic processes that exhibit transient equilibrium behaviour on the way to absorption QSDs are often mathematically intractable and even drawing samples from them is not straightforward.…
We introduce a two player game on an n x n chessboard where queens are placed by alternating turns on a chessboard square whose availability is determined by the number of queens already on the board which can attack that square modulo two.…