Lower Bounds for Bruss' Odds Problem with Multiple Stoppings

We give asymptotic lower bounds of the value for Bruss' optimal stopping problem with multiple stopping chances. It interestingly consists of the asymptotic threshold values in the optimal multiple stopping strategy. Another interesting implication of the result is that the asymptotic value for each secretary problem with multiple stoppings is in fact a typical lower bound in a much more general class of multiple stopping problems as modifications of odds problem.