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Related papers: Measuring the Non-Transitivity in Chess

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Dragonchess, a three-dimensional chess variant introduced by Gary Gygax, presents unique strategic and computational challenges that make it an ideal environment for studying the transfer of artificial intelligence (AI) heuristics across…

Artificial Intelligence · Computer Science 2026-03-17 Jim O'Connor , Annika Hoag , Sarah Goyette , Gary B. Parker

There is a common belief that humans and many animals follow transitive inference (choosing A over C on the basis of knowing that A is better than B and B is better than C). Transitivity seems to be the essence of rational choice. We…

Computer Science and Game Theory · Computer Science 2014-09-23 Marcin Makowski , Edward W. Piotrowski

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We…

Populations and Evolution · Quantitative Biology 2013-02-19 Alessandra F. Lütz , Sebastián Risau-Gusman , Jeferson J. Arenzon

The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a…

Data Analysis, Statistics and Probability · Physics 2013-02-19 H. V. Ribeiro , R. S. Mendes , E. K. Lenzi , M. del Castillo-Mussot , L. A. N. Amaral

Do neural networks learn to implement algorithms such as look-ahead or search "in the wild"? Or do they rely purely on collections of simple heuristics? We present evidence of learned look-ahead in the policy network of Leela Chess Zero,…

Machine Learning · Computer Science 2024-06-05 Erik Jenner , Shreyas Kapur , Vasil Georgiev , Cameron Allen , Scott Emmons , Stuart Russell

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…

Artificial Intelligence · Computer Science 2019-01-18 Kieran Greer

Powerful artificial intelligence systems are often used in settings where they must interact with agents that are computationally much weaker, for example when they work alongside humans or operate in complex environments where some tasks…

Artificial Intelligence · Computer Science 2024-05-09 Karim Hamade , Reid McIlroy-Young , Siddhartha Sen , Jon Kleinberg , Ashton Anderson

Nontransitive dice are dice beating one another in a cyclic way: die A wins die B, B wins C, and C wins A (like in a rock-paper-scissors game). In this article, it has been shown that a structure of mutual wins of 3 nontransitive dice (with…

General Mathematics · Mathematics 2023-11-23 Alexander Poddiakov

This report presents Giraffe, a chess engine that uses self-play to discover all its domain-specific knowledge, with minimal hand-crafted knowledge given by the programmer. Unlike previous attempts using machine learning only to perform…

Artificial Intelligence · Computer Science 2015-09-15 Matthew Lai

Accurately estimating human skill levels is crucial for designing effective human-AI interactions so that AI can provide appropriate challenges or guidance. In games where AI players have beaten top human professionals, strength estimation…

Machine Learning · Computer Science 2025-05-02 Kyota Kuboki , Tatsuyoshi Ogawa , Chu-Hsuan Hsueh , Shi-Jim Yen , Kokolo Ikeda

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of…

Machine Learning · Computer Science 2019-05-14 David Balduzzi , Marta Garnelo , Yoram Bachrach , Wojciech M. Czarnecki , Julien Perolat , Max Jaderberg , Thore Graepel

Gambits are central to human decision-making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study gambits…

Theoretical Economics · Economics 2022-04-14 Shiva Maharaj , Nicholas Polson , Christian Turk

Learning chess strategies has been investigated widely, with most studies focussing on learning from previous games using search algorithms. Chess textbooks encapsulate grandmaster knowledge, explain playing strategies and require a smaller…

Computation and Language · Computer Science 2023-11-01 Haifa Alrdahi , Riza Batista-Navarro

Current chess rating systems update ratings incrementally and may not always accurately reflect a player's true strength at all times, especially for rapidly improving players or very rusty players. To overcome this, we explore a method to…

Machine Learning · Computer Science 2025-04-04 Michael Omori , Prasad Tadepalli

Cheating in chess, by using advice from powerful software, has become a major problem, reaching the highest levels. As opposed to the large majority of previous work, which concerned {\em detection} of cheating, here we try to evaluate the…

Artificial Intelligence · Computer Science 2026-05-28 Daniel Keren

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

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…

Computer Science and Game Theory · Computer Science 2020-05-25 Thodoris Lykouris , Vasilis Syrgkanis , Eva Tardos

A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players' actions. The players communicate over a strongly connected digraph to…

Systems and Control · Computer Science 2019-12-10 Farzad Salehisadaghiani , Lacra Pavel

This paper presents an empirical exploration of non-transitivity in perfect-information games, specifically focusing on Xiangqi, a traditional Chinese board game comparable in game-tree complexity to chess and shogi. By analyzing over…

Artificial Intelligence · Computer Science 2023-08-10 Yang Li , Kun Xiong , Yingping Zhang , Jiangcheng Zhu , Stephen Mcaleer , Wei Pan , Jun Wang , Zonghong Dai , Yaodong Yang

We consider an example of cyclic competition bimatrix game which is a Rock-Scissors-Paper game with assumption about perfect memory of the playing agents. At first we investigate the dynamics in the neighbourhood of the Nash equilibrium as…

Dynamical Systems · Mathematics 2016-09-06 Cezary Olszowiec