Odds Theorem with Multiple Selection Chances

@article{Ano2010OddsTW,
  title={Odds Theorem with Multiple Selection Chances},
  author={Katsunori Ano and Hideo Kakinuma and Naoto Miyoshi},
  journal={Journal of Applied Probability},
  year={2010},
  volume={47},
  pages={1093 - 1104}
}
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 have m selection chances… 
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