An Application of Machine Learning To Protect Against Sure Loss in Games of Chance
Matthew F. Doty, Varun Mazumdar · Digital Scholarship - UNLV (University of Nevada Reno) · 2019
We present novel techniques for protecting players of games of chance from sure loss. Since Ramsey (1926) decision theorists have known that players whose betting positions violate the laws of probability expose themselves to arbitrage. We regard such violations as simple mathematical errors to be rectified. No known techniques for correcting broken betting positions have been developed, so we introduce a technique. Given an incoherent set of bets, we characterize nearby coherent sets of bets and provide algorithms to compute them. Bets are compared using the L2-loss function commonly employed in linear regression. A machine learning algorithm based on AdaBoost from Freund et al. (1997) is presented which compute the closest consistent set of bets to a flawed set. We prove a lower bound on the worst case convergence rate of the algorithm introduced. We show how to use machine learned bets as the basis for other bets without fear of arbitrage. The tools developed are new defenses against costly mathematical errors. While the techniques developed here are suited to games of chance, they provide a non-parametric framework for machine learning any joint probability distribution from specified training data. The algorithms presented provide a novel safeguard to protect gamblers from exploitation.