Related papers: Sequencing Chess
Monte Carlo simulation is used to study the dynamical crossover from single file diffusion to normal diffusion in fluids confined to narrow channels. We show that the long time diffusion coefficients for a series of systems involving hard…
Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics…
Complex networks are a great tool for simulating the outcomes of different strategies used within the iterated prisoners' dilemma game. However, because the strategies themselves rely on the connection between nodes, then initial network…
We propose a neural network-based approach to calculate the value of a chess square-piece combination. Our model takes a triplet (Color, Piece, Square) as an input and calculates a value that measures the advantage/disadvantage of having…
We examine the transport behaviour of non-interacting particles in a simple channel billiard, at equilibrium and in the presence of an external field. The channel walls are constructed from straight line-segments. We observe a sensitive…
We consider uniformly random set partitions of size $n$ with exactly $k$ blocks, and uniformly random permutations of size $n$ with exactly $k$ cycles, under the regime where $n-k \sim t\sqrt{n}$, $t>0$. In this regime, there is a simple…
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…
Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical advice which was adopted by the manufacturer.…
This study addresses the challenge of quantifying chess puzzle difficulty - a complex task that combines elements of game theory and human cognition and underscores its critical role in effective chess training. We present GlickFormer, a…
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…
We describe method for calculating the density of states by combining several canonical monte carlo runs. We discuss how critical properties reveal themselves in $g(\epsilon)$ and demonstrate this by applying the method several different…
The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60},…
We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of…
This paper investigates the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure resemble a spinning top, with the upright axis representing transitive strength,…
This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
This paper examines two different variants of the Ludo game, involving multiple dice and a fixed number of total turns. Within each variant, multiple game lengths (total no. of turns) are considered. To compare the two variants, a set of…
We consider generalizations of the familiar fifteen-piece sliding puzzle on the 4 by 4 square grid. On larger grids with more pieces and more holes, asymptotically how fast can we move the puzzle into the solved state? We also give a…
In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average)…
This is a fairy tale taking place in Chessland, located in the Bermuda triangle. The chess pieces survey their land and trap enemy pieces. Behind the story, there is fascinating mathematics on how to optimize surveying and trapping. The…