### Abstract

In this note we present a bound of the optimal maximum probability for the multiplicative odds theorem of optimal stopping theory. We deal with an optimal stopping problem that maximizes the probability of stopping on any of the last m successes of a sequence of independent Bernoulli trials of length N, where m and N are predetermined integers satisfying 1 < m < N. This problem is an extension of Bruss' (2000) odds problem. In a previouswork, Tamaki (2010) derived an optimal stopping rule. We present a lower bound of the optimal probability. Interestingly, our lower bound is attained using a variation of the well-known secretary problem, which is a special case of the odds problem..

Original language | English |
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Pages (from-to) | 885-889 |

Number of pages | 5 |

Journal | Journal of Applied Probability |

Volume | 51 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2014 Sep 1 |

### Keywords

- Lower bound
- Maclaurin's inequality
- Odd problem
- Optimal stopping
- Secretary problem

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of Applied Probability*,

*51*(3), 885-889. https://doi.org/10.1239/jap/1409932681