Fowlkes, Aaron; Jones, Brant Positional strategies in games of best choice. (English) Zbl 1417.91147 Involve 12, No. 4, 647-658 (2019). Summary: We study a variation of the game of best choice (also known as the secretary problem or game of googol) under an additional assumption that the ranks of interview candidates are restricted using permutation pattern-avoidance. We describe the optimal positional strategies and develop formulas for the probability of winning. Cited in 6 Documents MSC: 91A60 Probabilistic games; gambling 05A05 Permutations, words, matrices Keywords:secretary problem; random permutation; permutation pattern PDFBibTeX XMLCite \textit{A. Fowlkes} and \textit{B. Jones}, Involve 12, No. 4, 647--658 (2019; Zbl 1417.91147) Full Text: DOI arXiv References: [1] 10.1201/b12210 · Zbl 1255.05001 · doi:10.1201/b12210 [2] ; Deutsch, Electron. J. Combin., 9 (2002/03) [3] ; Firro, Electron. J. Combin., 14 (2007) [4] 10.1080/01621459.1966.10502008 · doi:10.1080/01621459.1966.10502008 [5] ; Kadison, Exposition. Math., 12, 125 (1994) [6] 10.1002/rsa.20601 · Zbl 1349.05006 · doi:10.1002/rsa.20601 [7] 10.1016/j.aam.2013.12.004 · Zbl 1300.05032 · doi:10.1016/j.aam.2013.12.004 [8] 10.1016/S0012-365X(01)00362-4 · Zbl 1003.60015 · doi:10.1016/S0012-365X(01)00362-4 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.