pawn sacrifices).ДЇrom a game-theoretical perspective, it is well known that in variable-sum games the actions of others can affect your optimal decisions. A plan gets executed quicker, thus being worth more positionally than materially (a.k.a. The Gambit itself is giving up a material advantage, a self-limiting policy, enabling speed and initiative in future play. Our theory of Gambits has Schelling's feature. Schelling views the strategy of conflict as a bargaining problem and provides numerous conflict situations in which an un-intuitive and often self-limiting move helps you win. Even the threat of a Gambit can have a psychological effect on the other player. Schelling's theory applies to a wide range of applications such as defender-attacker relationships to surprise attacks. Our work is closely related to the theory of conflict and negotiation, 6, 7 game theory, 3 and Coase's theorem on bargaining. Third, we advocate a new environment, chess, as a way to study behavioral economics. Second, we propose a method of ranking Gambits based on a player's preference for skew and risk. First, we utilize Bellman's principle of optimality and Q $$ Q $$-learning together with the latest chess engine, Stockfish 14.1, to determine, in a concrete way, the rationality of Gambits. The paper focuses on Gambits in chess, when a player offers a material advantage of a pawn (suboptimal play) for dynamic play in the continuation of the game. 5 Behavioral decision-making seeks to catalogue all the вЂњanomaliesвЂќ in human decision-making. This principle is central to the theory of maximum (subjective) expected utility which is prevalent in economic theory, see von Neumann and Morgenstern, 3 Savage, 4 and Edwards et al. Rational decision-making under uncertainty has a long history dating back to Ramsey 1 and de Finetti's 2 original discussion of previsions and the avoidance of sure loss (a.k.a. Our goal is to provide a theory of Gambits. Gambits are central to human decision-making. We conclude with directions for future research. We build on research in human decision-making by proving an irrational skewness preference within agents in chess. BodenвЂ“KieretskyвЂ“Morphy) Gambit and other common ones including the SmithвЂ“Morra, Goring, Danish and Halloween Gambits. Our methodology is applied to the popular Stafford and reverse Stafford (a.k.a. This then allows us to test whether the Gambiteer is following the optimal path in his decision-making. To test whether Bellman's equation holds in play, we estimate the transition probabilities to the next board state via a database of expert human play.

Our analysis uses Stockfish 14.1 to calculate the optimal Bellman Q $$ Q $$-values, which fundamentally measures if a position is winning or losing. policy) after the Gambit has been accepted.

This is a natural setting as chess Gambits require a sequential assessment of a set of moves (a.k.a. On the empirical side, we study the effectiveness of a number of popular chess Gambits. This allows us to calculate the Q $$ Q $$-values of a Gambit where material (usually a pawn) is sacrificed for dynamic play. Our theory is based on the Bellman optimality path for sequential decision-making. Chess provides an environment to study gambits and behavioral game theory. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play.

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