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We study the asymptotic behavior of the ratio of total return (or total profit) to total amount bet in a casino game. While the limit is well understood when the sequence of wagers is independent and identically distributed, here we…
In competitive games, players frequently switch strategies after losing streaks, yet our analysis of 926,334 match records from 34,619 Clash Royale players reveals a counterintuitive pattern: switching frequency is inversely associated with…
In this paper we examine the effectiveness of five mathematical models used to predict the outcomes of amateur darts games. These models not only predict the outcomes at the start of the game, but also update their estimations as the game…
Stochastic games are fundamental in various applications, including the control of cyber-physical systems (CPS), where both controller and environment are modeled as players. Traditional algorithms typically aim to determine a single…
We use a simple machine learning model, logistically-weighted regularized linear least squares regression, in order to predict baseball, basketball, football, and hockey games. We do so using only the thirty-year record of which visiting…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
High performance machine learning models have become highly dependent on the availability of large quantity and quality of training data. To achieve this, various central agencies such as the government have suggested for different data…
Games have long been a microcosm for studying planning and reasoning in both natural and artificial intelligence, especially with a focus on expert-level or even super-human play. But real life also pushes human intelligence along a…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
A $p$-beauty contest is a wide class of games of guessing the most popular strategy among other players. In particular, guessing a fraction of a mean of numbers chosen by all players is a classic behavioral experiment designed to test…
Difficulty is one of the key drivers of player engagement and it is often one of the aspects that designers tweak most to optimise the player experience; operationalising it is, therefore, a crucial task for game development studios. A…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
This paper presents an empirical investigation of the relation between decision speed and decision quality for a real-world setting of cognitively-demanding decisions in which the timing of decisions is endogenous: professional chess.…
While Artificial Intelligence has successfully outperformed humans in complex combinatorial games (such as chess and checkers), humans have retained their supremacy in social interactions that require intuition and adaptation, such as…
We investigate systematically the impact of human intervention in the training of computer players in a strategy board game. In that game, computer players utilise reinforcement learning with neural networks for evolving their playing…
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…
This study proposes a statistically grounded framework for real-time win probability evaluation and player assessment in score-based team sports, based on minute-by-minute cumulative box-score data. We introduce a continuous dominance…
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…
Since the advent of computers, many tasks which required humans to spend a lot of time and energy have been trivialized by the computers' ability to perform repetitive tasks extremely quickly. Playing chess is one such task. It was one of…