Abstract
The odds theorem gives a unified answer to a class of stopping problems on sequences of independent indicator functions. The success probability of the optimal rule is known to be larger than $Re^{-R}$, where R defined in the theorem satisfies $R\ge 1$ in the more interesting case. The following findings strengthen this result by showing that $1/e$ is then a lower bound. Knowing that this is the best possible uniform lower bound motivates this addendum.
Citation
F. Thomas Bruss. "A note on bounds for the odds theorem of optimal stopping." Ann. Probab. 31 (4) 1859 - 1961, October 2003. https://doi.org/10.1214/aop/1068646368
Information