Related papers: The Value of Chess Squares

We study the problem of checking for the existence of constrained pure Nash equilibria in a subclass of polymatrix games defined on weighted directed graphs. The payoff of a player is defined as the sum of nonnegative rational weights on…

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…

Is there an algorithm that takes a game in normal form as input, and outputs a Nash equilibrium? If the payoffs are integers, the answer is yes, and lot of work has been done in its computational complexity. If the payoffs are permitted to…

Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of…

Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic…

It is unknown at present whether a magic square of squared integers exists. Such an object is defined to be a 3 by 3 grid of 9 distinct integer squares, such that the entries of each row, column, and two main diagonals sum to the same…

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…

Predicting player behavior in strategic games, especially complex ones like chess, presents a significant challenge. The difficulty arises from several factors. First, the sheer number of potential outcomes stemming from even a single…

Chess, a deterministic game with perfect information, has long served as a benchmark for studying strategic decision-making and artificial intelligence. Traditional chess engines or tools for analysis primarily focus on calculating optimal…

In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested…

We study the weighted Myerson value for Network games extending a similar concept for communication situations. Network games, unlike communication situations, treat direct and indirect links among players differently and distinguish their…

On the n x n chessboard, the move totals of distinct pieces satisfy a small number of striking arithmetic identities. The total diagonal mobility of the bishop and the total 8-neighbor mobility of the king are exactly proportional, with…

We have seen numerous machine learning methods tackle the game of chess over the years. However, one common element in these works is the necessity of a finely optimized look ahead algorithm. The particular interest of this research lies…

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…

What are the prices of random variables? In this paper, we define the least-squares prices of coin-flipping games, which are proved to be minimal, positive linear, and arbitrage-free. These prices depend both on a set of games that are…

We introduce a new artificial intelligence (AI) approach called, the 'Digital Synaptic Neural Substrate' (DSNS). It uses selected attributes from objects in various domains (e.g. chess problems, classical music, renowned artworks) and…

Following the original interpretation of the Shapley value (Shapley, 1953a) as a priori evaluation of the prospects of a player in a multi-person interaction situation, we propose a group value, which we call the Shapley group value, as a…

Parts I-IV showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function of $n$ whose coefficients are essentially polynomials in $q$. For partial queens,…

In games like chess, strategy evolves dramatically across distinct phases - the opening, middlegame, and endgame each demand different forms of reasoning and decision-making. Yet, many modern chess engines rely on a single neural network to…

Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network's success, usually done in a manual manner. As a straightforward…