  The game of best choice, also known as the secretary problem, is a model for
sequential decision making with many variations in the literature. Notably, the
classical setup assumes that the sequence of candidate rankings is uniformly
distributed over time and that there is no expense associated with the
candidate interviews. Here, we weight each ranking permutation according to the
position of the best candidate in order to model costs incurred from conducting
interviews with candidates that are ultimately not hired. We compare our
weighted model with the classical (uniform) model via a limiting process. It
turns out that imposing even infinitesimal costs on the interviews results in a
probability of success that is about 28%, as opposed to 1/e (about 37%) in the
classical case.
