Gambits: Theory and Evidence

 

Abstract of the article "Gambits: Theory and Evidence" by Shiva Maharaj, Nick Polson, Christian Turk, published in Applied Stochastic Models in Business and Industry,Volume 38, Issue 4, July 2022 

Gambits are central to human decision making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study Gambits and behavioral economics. Our theory is based on the Bellman optimality path for sequential decision making. This allows us to calculate the Q values of a Gambit where material (usually a pawn) is sacrificed for dynamic play. On the empirical side, we study the effectiveness of a number of popular chess Gambits. This is a natural setting as chess Gambits require a sequential assessment of a set of moves (a.k.a. policy) after the Gambit has been accepted. Our analysis uses Stockfish 14 to calculate the optimal Bellman Q values. 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. This then allows us to test whether the Gambiteer is following the optimal path in his decision making. Our methodology is applied to the popular Stafford, Reverse Stafford (a.k.a. Boden-Kieretsky-Morphy), Smith-Morra, Goring, Danish, and Halloween Gambits. We conclude with directions for future 

From the Discussion

 On the one hand, a Gambit policy is not rational; the Gambit leaves open one state of the world where the opponent can win with certainty. On the other hand, the Gambit leads the Gambiteer to advantage with any sub-optimal play from the opponent.