Related papers: Fast Algorithm for Calculating Probability of Ches…
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…
This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…
In all competitions where results are based upon an individual's performance the question of whether the outcome is a consequence of skill or luck arises. We explore this question through an analysis of a large dataset of approximately one…
In trick-taking card games, a two-step process of state sampling and evaluation is widely used to approximate move values. While the evaluation component is vital, the accuracy of move value estimates is also fundamentally linked to how…
The game of Hex has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. Black wins by completing a crossing between two opposite edges, while White wins by completing a…
We report a new result on lotteries --- that a well-funded syndicate has a purely mechanical strategy to achieve expected returns of 10\% to 25\% in an equiprobable lottery with no take and no carryover pool. We prove that an optimal…
The increasing number of spectators and players in e-sports, along with the development of optimized communication solutions and cloud computing technology, has motivated the constant growth of the online game industry. Even though…
To get estimators that work within a certain error bound with high probability, a common strategy is to design one that works with constant probability, and then boost the probability using independent repetitions. Important examples of…
"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…
Predicting player behavior in strategic games, especially complex ones like chess, presents a significant challenge. The difficulty arises from several factors. First, the sheer number of potential outcomes stemming from even a single…
Algorithms for equilibrium computation generally make no attempt to ensure that the computed strategies are understandable by humans. For instance the strategies for the strongest poker agents are represented as massive binary files. In…
We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
Consider the following one player game. A deck containing $m$ copies of $n$ different card types is shuffled uniformly at random. Each round the player tries to guess the next card in the deck, and then the card is revealed and discarded.…
According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
In this paper we introduce a novel method for automatically tuning the search parameters of a chess program using genetic algorithms. Our results show that a large set of parameter values can be learned automatically, such that the…
Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…
The sudoku puzzles have a long history, with variations going back more than a hundred years, but its current and perhaps surprising world-wide prominence goes back to certain initiatives and then puzzle-generating computer programmes from…
This paper introduces a novel algorithm for two-player deterministic games with perfect information, which we call PROBS (Predict Results of Beam Search). Unlike existing methods that predominantly rely on Monte Carlo Tree Search (MCTS) for…