The 1/e-strategy is the unique optimal strategy for the best-choice problem under no information
F. Thomas Bruss · arXiv (Cornell University) · 2020
This paper answers a long-standing open question (Bruss (1984)) concerning the optimality of the $1/e$-strategy for the problem of best choice under no information on the number of options. We give the background of this open problem and explain why the no-information hypothesis has intriguing aspects, suggesting that the problem may be ill-posed. Moreover, we will explain why these aspects had distracted for a long time from the essence of the problem. Then comes the main contribution of this paper. We show that the open problem is well-posed and then prove that the $1/e$-strategy is indeed optimal, and even the only optimal strategy. The main tools for the affirmative answer are generalized versions of the Odds-Theorem which we prove first, and, in particular, the ageless beautiful theorem of relative ranks of Renyi (1962).