  The problem of mismatched guesswork considers the additional cost incurred by
using a guessing function which is optimal for a distribution $q$ when the
random variable to be guessed is actually distributed according to a different
distribution $p$. This problem has been well-studied from an asymptotic
perspective, but there has been little work on quantifying the difference in
guesswork between optimal and suboptimal strategies for a finite number of
symbols. In this non-asymptotic regime, we consider a definition for mismatched
guesswork which we show is equivalent to a variant of the Kendall tau
permutation distance applied to optimal guessing functions for the mismatched
distributions. We use this formulation to bound the cost of guesswork under
mismatch given a bound on the total variation distance between the two
distributions.
