Lower Bounds for Bruss' Odds Problem with Multiple Stoppings

This paper deals with Bruss’ odds problem with multiple stopping chances. A decision maker observes sequentially a sequence of independent 0/1 (failure/success) random variables with the objective to predict the last success correctly with multiple stopping chances. First, we give a nontrivial lower bound of the probability of win (obtaining the last success) for the problem with m-stoppings. Next, we show that the asymptotic value for each classical secretary problem with multiple stoppings attains our lower bound. Finally, we prove a conjecture on the classical secretary problem, which gives a connection between the probability of win and the threshold values of the optimal stopping strategy.