Odds theorem with multiple selection chances

Katsunori Ano, Hideo Kakinuma, Naoto Miyoshi

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We study the multi-selection version of the so-called odds theorem by Bruss (2000). We observe a finite number of independent 0/1 (failure/success) random variables sequentially and want to select the last success. We derive the optimal selection rule when m (≥ 1) selection chances are given and find that the optimal rule has the form of a combination of multiple odds-sums. We provide a formula for computing the maximum probability of selecting the last success when we havemselection chances and also provide closed-form formulae for m = 2 and 3. For m = 2, we further give the bounds for the maximum probability of selecting the last success and derive its limit as the number of observations goes to ∞. An interesting implication of our result is that the limit of the maximum probability of selecting the last success for m = 2 is consistent with the corresponding limit for the classical secretary problem with two selection chances.

Original languageEnglish
Pages (from-to)1093-1104
Number of pages12
JournalJournal of Applied Probability
Issue number4
Publication statusPublished - 2010 Dec


  • Multiple selection chances
  • Optimal stopping
  • Selecting the last success

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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