Gardner's Minichess Variant is solved

A 5x5 board is the smallest board on which one can set up all kind of chess pieces as a start position. We consider Gardner's minichess variant in which all pieces are set as in a standard chessboard (from Rook to King). This game has roughly 9x10^{18} legal positions and is comparable in this respect with checkers. We weakly solve this game, that is we prove its game-theoretic value and give a strategy to draw against best play for White and Black sides. Our approach requires surprisingly small computing power. We give a human readable proof. The way the result is obtained is generic and could be generalized to bigger chess settings or to other games

TCEC15: the 15th Top Chess Engine Championship

TCEC15 was the 15th season of the Top Chess Engine Championship and ran from March 5th to May 28th, 2019. TCEC has become the largest Open Computer Chess Championship. It attracts the best engines in the field and provides an opportunity for absolute and comparative analysis of the participating engines in a computational experiment. Once again, the final offered a contrast of playing styles between neural-network engine LEELA CHESS ZERO and STOCKFISH. This time, the ‘new architecture’ LC0 won, 53½-46½, making their ‘TCEC Sufi’ score 103-97 to LC0. Again, KOMODO was third. The attached files at http://centaur.reading.ac.uk/83156/ provide the 808 games with engine PVs, the detail on them and some summary statistics. The decisive games of Divisions 1 and P, and of the Superfinal have been played out by FRITZ17 at depth 24 to mate to enable and benchmark endgame practice

Statistical Feature Combination for the Evaluation of Game Positions

This article describes an application of three well-known statistical methods in the field of game-tree search: using a large number of classified Othello positions, feature weights for evaluation functions with a game-phase-independent meaning are estimated by means of logistic regression, Fisher's linear discriminant, and the quadratic discriminant function for normally distributed features. Thereafter, the playing strengths are compared by means of tournaments between the resulting versions of a world-class Othello program. In this application, logistic regression - which is used here for the first time in the context of game playing - leads to better results than the other approaches.Comment: See http://www.jair.org/ for any accompanying file

Game Solving with Online Fine-Tuning

Game solving is a similar, yet more difficult task than mastering a game. Solving a game typically means to find the game-theoretic value (outcome given optimal play), and optionally a full strategy to follow in order to achieve that outcome. The AlphaZero algorithm has demonstrated super-human level play, and its powerful policy and value predictions have also served as heuristics in game solving. However, to solve a game and obtain a full strategy, a winning response must be found for all possible moves by the losing player. This includes very poor lines of play from the losing side, for which the AlphaZero self-play process will not encounter. AlphaZero-based heuristics can be highly inaccurate when evaluating these out-of-distribution positions, which occur throughout the entire search. To address this issue, this paper investigates applying online fine-tuning while searching and proposes two methods to learn tailor-designed heuristics for game solving. Our experiments show that using online fine-tuning can solve a series of challenging 7x7 Killall-Go problems, using only 23.54% of computation time compared to the baseline without online fine-tuning. Results suggest that the savings scale with problem size. Our method can further be extended to any tree search algorithm for problem solving. Our code is available at https://rlg.iis.sinica.edu.tw/papers/neurips2023-online-fine-tuning-solver.Comment: Accepted by the 37th Conference on Neural Information Processing Systems (NeurIPS 2023

A MATHEMATICAL ANALYSIS OF THE GAME OF CHESS

This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first player to lose the queen. Ultimately, it is shown that mathematics exists inherently in chess. Therefore math can be used to improve, but not perfect, chess skills

Gender, competition and performance: evidence from chess players

This paper studies gender differences in performance in a male‐dominated competitive environment chess tournaments. We find that the gender composition of chess games affects the behaviors of both men and women in ways that worsen the outcomes for women. Using a unique measure of within‐game quality of play, we show that women make more mistakes when playing against men. Men, however, play equally well against male and female opponents. We also find that men persist longer before losing to women. Our results shed some light on the behavioral changes that lead to differential outcomes when the gender composition of competitions varies