Optimal Betting Strategy with Uncertain Payout and Opportunity Limits

Abstract

This paper was inspired by "Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin" (Haghani, Victor and Dewey, Richard, https://ssrn.com/abstract=2856963). It derives optimal strategy for a game with known payouts and probability, but uncertain limits on total payout and number of betting opportunities. It further develops some general gambling principles applicable to practical risk taking situations in which all parameters are uncertain and robust approximate simple solutions are required.

Keywords: Kelly criterion, gambling, betting, optimal strategy, risk, uncertainty

JEL Classification: C61, D01, C73, D81