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We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…

Artificial Intelligence · Computer Science 2025-11-18 David H. Silver

The paper aims to investigate the degree of cognitive skills required for success in online versions of the popular card game rummy and poker. The study focuses on analyzing the impact of experience and learnable skills on success in the…

Human-Computer Interaction · Computer Science 2023-08-30 Taranjit Kaur , Manas Pati Tripathi , Ashirbad Samantaray , Tapan K. Gandhi

Rating systems play a crucial role in evaluating player skill across competitive environments. The Elo rating system, originally designed for deterministic and information-complete games such as chess, has been widely adopted and modified…

Computer Science and Game Theory · Computer Science 2025-12-23 Avirup Chakraborty , Shirsa Maitra , Tathagata Banerjee , Diganta Mukherjee , Tridib Mukherjee

In fantasy sports, strategic thinking-not mere luck-often defines who wins and who falls short. As fantasy cricket grows in popularity across India, understanding whether success stems from skill or chance has become both an analytical and…

Applications · Statistics 2025-12-23 Supratim Das , Sarthak Sarkar , Subhamoy Maitra , Tridib Mukherjee

Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of…

Artificial Intelligence · Computer Science 2025-03-05 James Goodman , Diego Perez-Liebana , Simon Lucas

Gauging an individual's skill level is crucial, as it inherently shapes their behavior. Quantifying skill, however, is challenging because it is latent to the observed actions. To explore skill understanding in human behavior, we focus on…

Computer Vision and Pattern Recognition · Computer Science 2026-03-27 Akihiro Kubota , Tomoya Hasegawa , Ryo Kawahara , Ko Nishino

In this paper, we study the problem of learning the skill distribution of a population of agents from observations of pairwise games in a tournament. These games are played among randomly drawn agents from the population. The agents in our…

Machine Learning · Statistics 2020-06-16 Ali Jadbabaie , Anuran Makur , Devavrat Shah

From sports to science, the recent availability of large-scale data has allowed to gain insights on the drivers of human innovation and success in a variety of domains. Here we quantify human performance in the popular game of chess by…

Physics and Society · Physics 2022-07-19 Sandeep Chowdhary , Iacopo Iacopini , Federico Battiston

Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…

Physics and Society · Physics 2025-11-03 Maximilian Jerdee , M. E. J. Newman

"The chance to win given a certain move" is an easily obtainable quantity from data and often quoted in gaming statistics. It is also the fundamental quantity that reinforcement learning AI bases on. Unfortunately, this conditional…

Physics and Society · Physics 2018-03-16 I-Sheng Yang

In multi-player card games such as Skat or Bridge, the early stages of the game, such as bidding, game selection, and initial card selection, are often more critical to the success of the play than refined middle- and end-game play. At the…

Artificial Intelligence · Computer Science 2025-12-18 Stefan Edelkamp

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…

Methodology · Statistics 2025-07-14 Mark E. Glickman

Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…

Applications · Statistics 2018-11-05 Daniel E. Gilbert , Martin T. Wells

In this paper, I formalize intelligence measurement in games by introducing mechanisms that assign a real number -- interpreted as an intelligence score -- to each player in a game. This score quantifies the ex-post strategic ability of the…

Theoretical Economics · Economics 2025-10-28 Mehmet Mars Seven

We present a new way of estimation of the role of chance in achieving success, by comparing the empirical data from 100-meter dash competitions (one of the sports disciplines with the most stringent controls of external randomness), with…

Physics and Society · Physics 2020-08-26 Pawel Sobkowicz , Robert H Frank , Alessio E Biondo , Alessandro Pluchino , Andrea Rapisarda

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

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…

Computer Science and Game Theory · Computer Science 2024-11-12 Tathagata Banerjee , Diganta Mukherjee

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

Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…

Machine Learning · Computer Science 2017-11-27 Raquel YS Aoki , Renato M Assuncao , Pedro OS Vaz de Melo

We propose a controlled simulation within a competitive sum-zero environment as a proxy for disaggregating components of success. Given a simulation of the Risk board game, we consider (a) Talent to be one of three rule-based strategies…

Physics and Society · Physics 2020-02-18 Bernardo Alves Furtado
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