A Discrete Evolutionary Model for Chess Players' Ratings

The Elo system for rating chess players, also used in other games and sports, was adopted by the World Chess Federation over four decades ago. Although not without controversy, it is accepted as generally reliable and provides a method for assessing players' strengths and ranking them in official tournaments. It is generally accepted that the distribution of players' rating data is approximately normal but, to date, no stochastic model of how the distribution might have arisen has been proposed. We propose such an evolutionary stochastic model, which models the arrival of players into the rating pool, the games they play against each other, and how the results of these games affect their ratings. Using a continuous approximation to the discrete model, we derive the distribution for players' ratings at time $t$ as a normal distribution, where the variance increases in time as a logarithmic function of $t$. We validate the model using published rating data from 2007 to 2010, showing that the parameters obtained from the data can be recovered through simulations of the stochastic model. The distribution of players' ratings is only approximately normal and has been shown to have a small negative skew. We show how to modify our evolutionary stochastic model to take this skewness into account, and we validate the modified model using the published official rating data.Comment: 17 pages, 4 figure

Cultural transmission of move choice in chess

The study of cultural evolution benefits from detailed analysis of cultural transmission in specific human domains. Chess provides a platform for understanding the transmission of knowledge due to its active community of players, precise behaviors, and long-term records of high-quality data. In this paper, we perform an analysis of chess in the context of cultural evolution, describing multiple cultural factors that affect move choice. We then build a population-level statistical model of move choice in chess, based on the Dirichlet-multinomial likelihood, to analyze cultural transmission over decades of recorded games played by leading players. For moves made in specific positions, we evaluate the relative effects of frequency-dependent bias, success bias, and prestige bias on the dynamics of move frequencies. We observe that negative frequency-dependent bias plays a role in the dynamics of certain moves, and that other moves are compatible with transmission under prestige bias or success bias. These apparent biases may reflect recent changes, namely the introduction of computer chess engines and online tournament broadcasts. Our analysis of chess provides insights into broader questions concerning evolution of human behavioral preferences and modes of social learning.Comment: 25 page

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

The 2014 General Video Game Playing Competition

This paper presents the framework, rules, games, controllers, and results of the first General Video Game Playing Competition, held at the IEEE Conference on Computational Intelligence and Games in 2014. The competition proposes the challenge of creating controllers for general video game play, where a single agent must be able to play many different games, some of them unknown to the participants at the time of submitting their entries. This test can be seen as an approximation of general artificial intelligence, as the amount of game-dependent heuristics needs to be severely limited. The games employed are stochastic real-time scenarios (where the time budget to provide the next action is measured in milliseconds) with different winning conditions, scoring mechanisms, sprite types, and available actions for the player. It is a responsibility of the agents to discover the mechanics of each game, the requirements to obtain a high score and the requisites to finally achieve victory. This paper describes all controllers submitted to the competition, with an in-depth description of four of them by their authors, including the winner and the runner-up entries of the contest. The paper also analyzes the performance of the different approaches submitted, and finally proposes future tracks for the competition