相关论文: How to Beat Capablanca

This article discusses in detail the rating system that won the kaggle competition "Chess Ratings: Elo vs the rest of the world". The competition provided a historical dataset of outcomes for chess games, and aimed to discover whether novel…

Given a tree $T=(V,E)$ on $n$ vertices, we consider the $(1 : q)$ Maker-Breaker tree embedding game ${\mathcal T}_n$. The board of this game is the edge set of the complete graph on $n$ vertices. Maker wins ${\mathcal T}_n$ if and only if…

We prove that king chasing problem in Chinese Chess is NP-hard when generalized to $n\times n$ boards. `King chasing' is a frequently-used strategy in Chinese Chess, which means that the player has to continuously check the opponent in…

Using mostly elementary considerations, we find out who wins the game of Domineering on all rectangular boards of width 2, 3, 5, and 7. We obtain bounds on other boards as well, and prove the existence of polynomial-time strategies for…

We propose a class of chess variants, Multimove Chess (i,j), in which White gets i moves per turn and Black gets j moves per turn. One side is said to win when it takes the opponent's king. All other rules of chess apply. We prove that if…

Gauss proposed the problem of how to enumerate the number of solutions for placing $N$ queens on an $N\times N$ chess board, so no two queens attack each other. The N-queen problem is a classic problem in combinatorics. We describe a…

We show that, in John Conway's board game Phutball (or Philosopher's Football), it is NP-complete to determine whether the current player has a move that immediately wins the game. In contrast, the similar problems of determining whether…

This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…

The usual $n$-in-a-row game is a positional game in which two player alternately claim points in $\bb{Z}^2$ with the winner being the first player to claim $n$ consecutive points in a line. We consider a variant of the game, suggested by…

Dice odds in the board game RISK were first investigated by Tan, fixed by Osbourne, and extended by Blatt. We generalized dice odds further, varying the number of sides and the number of dice used in a single battle. We show that the…

In the natural generalization of tic-tac-toe to an $n \times n \times n$ board where $n \in \mathbb{N}$, it is known that the first player has a winning strategy if $n \leq 4$ and that either player can force a draw if $n \geq 8$. The…

This paper proposes \emph{knowledge-based paraonoia search} (KBPS) to find forced wins during trick-taking in the card game Skat; for some one of the most interesting card games for three players. It combines efficient partial information…

Deck building is a crucial component in playing Collectible Card Games (CCGs). The goal of deck building is to choose a fixed-sized subset of cards from a large card pool, so that they work well together in-game against specific opponents.…

We describe a preliminary investigation into learning a Chess player's style from game records. The method is based on attempting to learn features of a player's individual evaluation function using the method of temporal differences, with…

A famous (and hard) chess problem asks what is the maximum number of safe squares possible in placing $n$ queens on an $n\times n$ board. We examine related problems from placing $n$ rooks. We prove that as $n\to\infty$, the probability…

We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on chess.com. The standard version of the game is played on a regular 8 x 8 chessboard by a single player, with only white pieces, using…

We introduce variants of the Maker-Breaker and Waiter-Client games, which we call \emph{stotting}, in which a player grants a slight advantage to the opponent. We prove that a winning strategy in either stotting variant yields winning…

We analyze misere play of impartial tic-tac-toe---a game suggested by Bob Koca in which both players make X's on the board, and the first player to complete three-in-a-row loses. This game was recently discussed on mathoverflow.net in a…

The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…

The Queen's Domination problem, studied for over 160 years, poses the following question: What is the least number of queens that can be arranged on a $m \times n$ chessboard so that they either attack or occupy every cell? We propose a…