Personal bests act as reference points. Examining 133 million chess games, we find that players exert effort to set new personal best ratings and quit once they have done so. Although specific and difficult goals have been shown to inspire greater motivation than vague pronouncements to "do your best," doing one's best can be a specific and difficult goal-and, as we show, motivates in a manner ...

are completely competitive, where whatever one player wins, the other loses. Examples of such games include chess, checkers, backgammon, etc. We will show that in such games: • An equilibrium always exists (although not necessarily a pure one); • All equilibrium points yield the same payoff for the players; • The set of equilibrium points is actually the cartesian product of independent sets of...

The aim of this study was to explore when experts trust their intuition. Take-The-First heuristic suggests that generate a few options based on option validity match the current situation and probably pick first one they generated. In chess, rated quality moves can be used analyze fast slow decisions. We provided players with strategic (long-term) tactical (short-term) situations asked for choi...

This paper explores the question, important to the theory of expert performance, of the nature and number of chunks that chess experts hold in memory. It examines how memory contents determine players' abilities to reconstruct (1) positions from games, (2) positions distorted in various ways, and (3) random positions. Comparison of a computer simulation with a human experiment supports the usua...

Chess is a deep and well-studied game with a wealth of content and data. Because of the relative simplistic nature of the game states, games themselves are relatively easy to record, and thus there are large databases of games, dating back to Francesco di Castellvi vs Narciso Vinyoles, 1475. The vast majority of published games are between masters and grandmasters, usually recorded by tournamen...

Contrary to a widely held belief, experts recall random material better than non-experts. This phenomenon, predicted by the CHREST computational model, was first established with chess players. Recently, it has been shown through a meta-analysis that it generalises to nearly all domains where the effect has been tested. In this paper, we carry out computer simulations to test whether the mechan...

In 2003, the first two authors proved that a chess-likes game has a Nash equilibrium (NE) in pure stationary strategies if (A) the number n of players is at most 2, or (B) the number p of terminals is at most 2 and (C) any infinite play is worse than each terminal for every player. In this paper we strengthen the bound in (B) replacing p ≤ 2 by p ≤ 3, provided (C) still holds. On the other hand...

The game of Hex is a two-player game with simple rules, a deep underlying mathematical beauty, and a strategic complexity comparable to that of Chess and Go. The massive game-tree search techniques developed mostly for Chess, and successfully used for Checkers, Othello, and a number of other games, become less useful for games with large branching factors like Go and Hex. We offer a new approac...

We suggest that AI can help decision-makers learn; specifically, it them learn strategic interactions by serving as artificial training partners and thus to overcome a bottleneck of scarce human partners. present evidence from chess computers, the first widespread incarnation AI. Leveraging staggered diffusion we find they did indeed players improve substitute for also illustrate computers were...