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Predicting the relative value of any given chess piece in a position remains an open challenge, as a piece's contribution depends on its spatial relationships with every other piece on the board. We demonstrate that incorporating the state…

Machine Learning · Computer Science 2026-04-20 Ethan Tang , Hasan Davulcu , Jia Zou , Zhongju Zhang

We use logistic regression to estimate the value of the pieces in standard chess and several chess variants, namely Chess 960, Atomic chess, Antichess, and Horde chess. We perform our regressions on several years of data from Lichess, the…

Applications · Statistics 2025-09-26 Steven Pav

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…

Logic · Mathematics 2012-05-17 Dan Brumleve , Joel David Hamkins , Philipp Schlicht

Suppose some cleverness score parameter is sufficiently interesting to be defined and then measured, perhaps for different strata of specialists or for the broader population. Such phenomena could have Gaussian distributions, when it comes…

Other Statistics · Statistics 2026-05-19 Nils Lid Hjort

It has long been believed that Chess is the \emph{Drosophila} of Artificial Intelligence (AI). Studying Chess can productively provide valid knowledge about complex systems. Although remarkable progress has been made on solving Chess, the…

Artificial Intelligence · Computer Science 2021-10-25 Ricky Sanjaya , Jun Wang , Yaodong Yang

The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…

Combinatorics · Mathematics 2019-11-06 Brant Jones

AI research in chess has been primarily focused on producing stronger agents that can maximize the probability of winning. However, there is another aspect to chess that has largely gone unexamined: its aesthetic appeal. Specifically, there…

Artificial Intelligence · Computer Science 2024-08-06 Kamron Zaidi , Michael Guerzhoy

Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such…

Computer Science and Game Theory · Computer Science 2021-05-20 Thomas Orton

In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to…

Data Structures and Algorithms · Computer Science 2010-06-09 Tobias Friedrich , Thomas Sauerwald , Dan Vilenchik

In each round of a Swiss-system tournament, players of similar score are paired against each other. An intentional early loss therefore might lead to weaker opponents in later rounds and thus to a better final tournament result - a…

Computer Science and Game Theory · Computer Science 2023-02-22 Ágnes Cseh , Pascal Führlich , Pascal Lenzner

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…

Artificial Intelligence · Computer Science 2025-12-02 Daren Zhong , Dingcheng Huang , Clayton Greenberg

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…

Physics and Society · Physics 2022-07-26 Giordano De Marzo , Vito DP Servedio

Positions of chess players in intransitive (rock-paper-scissors) relations are considered. Namely, position A of White is preferable (it should be chosen if choice is possible) to position B of Black, position B of Black is preferable to…

History and Overview · Mathematics 2022-12-22 Alexander Poddiakov

It is non-trivial to design engaging and balanced sets of game rules. Modern chess has evolved over centuries, but without a similar recourse to history, the consequences of rule changes to game dynamics are difficult to predict. AlphaZero…

Artificial Intelligence · Computer Science 2020-09-16 Nenad Tomašev , Ulrich Paquet , Demis Hassabis , Vladimir Kramnik

Game playing has long served as a fundamental benchmark for evaluating Artificial General Intelligence. While Large Language Models (LLMs) have demonstrated impressive capabilities in general reasoning, their effectiveness in spatial…

Artificial Intelligence · Computer Science 2025-11-19 Yuhao Chen , Shuochen Liu , Yuanjie Lyu , Chao Zhang , Jiayao Shi , Tong Xu

Empirically, many strategic settings are characterized by stable outcomes in which players' decisions are publicly observed, yet no player takes the opportunity to deviate. To analyze such situations in the presence of incomplete…

Econometrics · Economics 2024-04-12 Paul S. Koh

We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…

Computer Science and Game Theory · Computer Science 2021-03-15 Krzysztof R. Apt , Sunil Simon , Dominik Wojtczak

We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this work we focus on the case of Breaker playing randomly and Maker being "clever". The…

Combinatorics · Mathematics 2016-04-01 Jonas Groschwitz , Tibor Szabó

A fundamental shortcoming of the concept of Nash equilibrium is its computational intractability: approximating Nash equilibria in normal-form games is PPAD-hard. In this paper, inspired by the ideas of smoothed analysis, we introduce a…

Computer Science and Game Theory · Computer Science 2024-07-23 Constantinos Daskalakis , Noah Golowich , Nika Haghtalab , Abhishek Shetty

Complexity develops via the incorporation of innovative properties. Chess is one of the most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study…

Physics and Society · Physics 2013-12-19 Juan I. Perotti , Hang-Hyun Jo , Ana L. Schaigorodsky , Orlando V. Billoni