# Odds theorem with multiple selection chances

Katsunori Ano, Hideo Kakinuma, Naoto Miyoshi

Research output: Contribution to journalArticle

7 Citations (Scopus)

### Abstract

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 language English 1093-1104 12 Journal of Applied Probability 47 4 https://doi.org/10.1239/jap/1294170522 Published - 2010 Dec Yes

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

Odds theorem with multiple selection chances. / Ano, Katsunori; Kakinuma, Hideo; Miyoshi, Naoto.

In: Journal of Applied Probability, Vol. 47, No. 4, 12.2010, p. 1093-1104.

Research output: Contribution to journalArticle

Ano, K, Kakinuma, H & Miyoshi, N 2010, 'Odds theorem with multiple selection chances', Journal of Applied Probability, vol. 47, no. 4, pp. 1093-1104. https://doi.org/10.1239/jap/1294170522
Ano, Katsunori ; Kakinuma, Hideo ; Miyoshi, Naoto. / Odds theorem with multiple selection chances. In: Journal of Applied Probability. 2010 ; Vol. 47, No. 4. pp. 1093-1104.
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