a permutation $\pi$, define the [**$i$th prefix flattening**]{}, denoted ${\pi|_{[i]}}$, to be the permutation obtained by flattening the sequence $\pi_1, \pi_2, \ldots, \pi_i$. In the [**game of best choice**]{} some $\pi \in {\mathfrak{S}}_N$ is chosen randomly, with probability $f(\pi)$, and each prefix flattening ${\pi|_{[1]}}, {\pi|_{[2]}}, \ldots$ is presented sequentially to the player. If the player stops at value $N$, they win; otherwise, they lose.

In this work, we are primarily interested in probability distributions obtained from weighting by some statistic $c : {\mathfrak{S}}_N \rightarrow {\mathbb{N}}$ and a positive real number $\theta$ via $$f(\pi) = \frac{ \theta^{c(\pi)} }{ \sum_{\pi \in {\mathfrak{S}}_N} \theta^{c(\pi)} }.$$ For example, we may take $c(\pi)$ to be the number of left-to-right maxima in $\pi$, obtaining the [**Ewens distribution**]{}; if $c(\pi)$ is the number of inversions then we obtain the [**Mallows distribution**]{}. When $\theta = 1$, we recover the [**complete uniform distribution**]{}.

A [**strike strategy**]{} for a game of best choice is defined by a collection of prefixes from $\bigcup_{i=1}^N {\mathfrak{S}}_i$ that we call the [**strike set**]{}. To play the strategy on a particular interview ordering $\pi$, compare prefix flattenings to the strike set at each step. As soon as the $i$th prefix flattening occurs in the strike 