Positional strategies in games of best choice
Aaron Fowlkes, Brant Jones
TL;DR
This paper explores a variation of the secretary problem where candidate ranks are restricted by permutation pattern-avoidance, deriving optimal strategies and formulas for success probabilities.
Contribution
It introduces a novel permutation pattern-avoidance constraint into the secretary problem and provides explicit formulas for optimal strategies and success probabilities.
Findings
Derived formulas for winning probabilities under pattern-avoidance constraints
Identified optimal positional strategies for the modified game
Extended classical secretary problem analysis with permutation restrictions
Abstract
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.
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