Optimal Doubling Strategy Against a Sub-Optimal Opponent
Konstantinos V. Katsikopoulos and Özgür Şimşek
Journal of Applied Probability, to appear.
For two-person, zero-sum games where the probability of each player winning is a continuous function of time and is known to both players, the mutually optimal strategy for proposing and accepting a doubling of the game value is known. We present an algorithm for deriving the optimal doubling strategy of a player who is aware of the sub-optimal strategy followed by the opponent. We also present numerical results about the magnitude of the benefits; the results support the claim that repeated application of the algorithm from both players leads to the mutually optimal strategy.