相关论文: The Value of Chess Squares
A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations…
The game of bridge consists of two stages: bidding and playing. While playing is proved to be relatively easy for computer programs, bidding is very challenging. During the bidding stage, each player knowing only his/her own cards needs to…
This paper aims to study the graph radii and diameters induced by the $k$-dimensional versions of the well-known six international chess pieces on every finite $\{n \times n \times \dots \times n\} \subseteq \mathbb{Z}^k$ lattice since they…
Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad…
The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world…
Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge values comprise the comparison data. The basic idea is very…
This paper introduces the first deep neural network-based estimation metric for the jigsaw puzzle problem. Given two puzzle piece edges, the neural network predicts whether or not they should be adjacent in the correct assembly of the…
The paper suggests a family of paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the challenges of ranking in Swiss system, the features of individual and team…
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…
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…
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…
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…
We apply to the $n\times n$ chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I showed that the number of ways to place $q$ identical…
The paper aims at analyzing the least squares ranking method for generalized tournaments with possible missing and multiple paired comparisons. The bilateral relationships may reflect the outcomes of a sport competition, product…
We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude…
Two straightforward methods to extend an assessment of individual elements to groups are to sum individual assessments or to treat the group as a single merged element and assess it accordingly. In this work, we analyze another natural…
In this paper we investigate the value of a social network with respect to the probability mechanism underlying its structure. Specifically, we compute the value for small world and scale free networks. We provide evidence in support of the…
We derive recurrences and closed-form expressions for counting nonattacking placements of two types of chess pieces with unbounded straight-line moves, namely the bishop (two diagonal moves) and the anassa (one horizontal or vertical move…
This paper contributes a new way to evaluate AI. Much as one might evaluate a machine in terms of its performance at chess, this approach involves evaluating a machine in terms of its performance at a game called "MAD Chairs". At the time…
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…