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We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude…

We analyze Solo Chess puzzles, where the input is an $n \times n$ board containing some standard Chess pieces of the same color, and the goal is to make a sequence of capture moves to reduce down to a single piece. Prior work analyzes this…

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…

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…

This article describes how to calculate exact space-state complexities of Korean chess and Chinese chess. The state-space complexity (a.k.a. search-space complexity) of a game is defined as the number of legal game positions reachable from…

The strength of chess engines together with the availability of numerous chess games have attracted the attention of chess players, data scientists, and researchers during the last decades. State-of-the-art engines now provide an…

In imperfect information games, the evaluation of a game state not only depends on the observable world but also relies on hidden parts of the environment. As accessing the obstructed information trivialises state evaluations, one approach…

Chessboard and chess piece recognition is a computer vision problem that has not yet been efficiently solved. However, its solution is crucial for many experienced players who wish to compete against AI bots, but also prefer to make…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

Composition conventions are guidelines used by human composers in composing chess problems. They are particularly significant in composition tournaments. Examples include, not having any check in the first move of the solution and not…

Jigsaw puzzles are typically labeled with their finished area and number of pieces. With this information, is it possible to estimate the area required to lay each piece flat before assembly? We derive a simple formula based on…

Composition theory can be used to analyze and enumerate the number of ways a dealer in Blackjack can reach any given point total. The rules of Blackjack provide several restrictions on the number of compositions of a given number. While…

Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…

Determining the state-space complexity of the game of Shogi (Japanese Chess) has been a challenging problem, with previous combinatorial estimates leaving a gap of five orders of magnitude ($10^{64}$ to $10^{69}$). This large gap arises…

Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played. In an enumerative chess problem, the set of moves in the solution…

This paper proposes a new mechanism for pruning a search game-tree in computer chess. The algorithm stores and then reuses chains or sequences of moves, built up from previous searches. These move sequences have a built-in forward-pruning…

We study strategic similarity of game positions in two-player extensive games of perfect information, by looking at the structure of their local game trees, with the aim of improving the performance of game playing agents in detecting…

This paper suggests a forward-pruning technique for computer chess that uses 'Move Tables', which are like Transposition Tables, but for moves not positions. They use an efficient memory structure and has put the design into the context of…

An unconstrained crossword puzzle is a generalization of the constrained crossword problem. In this problem, only the word vocabulary, and optionally the grid dimensions are known. Hence, it not only requires the algorithm to determine the…

The article describes a model of chess based on information theory. A mathematical model of the partial depth scheme is outlined and a formula for the partial depth added for each ply is calculated from the principles of the model. An…