set, accept the candidate at position $i$ and end the game. Otherwise, the strike strategy rejects the candidate at position $i$ to continue playing. It follows directly from the definitions that any strategy (including the optimal strategy) for a game of best choice can be represented as a strike strategy because the player has only the relative ranking information captured in the prefix flattenings to guide them as they play. We can visualize the set of all possible prefixes as a tree, partially ordered by containment of prefix flattening, which we call the [**prefix tree**]{}. See Figure \[f:treeex\] for a small example.

To find the optimal strike set, we define several conditional probabilities. For brevity, we say that $\pi \in {\mathfrak{S}}_N$ is [**$p$-prefixed**]{} if it contains $p$ as a prefix flattening, and we say that $\pi$ is [**$p$-winnable**]{} if including $p$ in the strike set would win the interview order $\pi$. Explicitly for $p = p_1 p_2 \cdots p_k$, we have that $\pi$ is $p$-winnable if $\pi$ is $p$-prefixed and $\pi_k = N$. For each prefix $p$, the [**strike probability**]{} ${\mathcal{S}}(p)$ is the probability of winning the game if the prefix $p$ is included in the strike set restricted to 