and [@jones18] for the $321$-avoiding model.

Once we know by Theorem \[t:main\] that [*some*]{} positional strategy is optimal for each value of $\theta$, we can define the [**strategy function**]{} ${\kappa}_N(\theta)$ for a weighted game of best choice to be the number of candidates that we initially reject in the optimal strategy for value $\theta$. Hence, ${\kappa}_N$ is some function from $\mathbb{R}_{> 0}$ to $\{0, 1, \cdots,
N-1\}$. In Corollary \[c:ewensmain\], we describe this function precisely for the Ewens model.

When we perform the asymptotic analysis for the Ewens model, we find that the optimal strategy depends on ${\theta}$ with the optimal number of initial rejections being $k = N/e^{1/{\theta}}$. Remarkably though, the probability of success is always $1/e$, independent of ${\theta}$, neither better nor worse than the classical case.

The Mallows model is more subtle. When ${\theta}< 1$, the optimal strategy is to reject all but the last $j = \max(-1/(\ln {\theta}), 1)$ candidates and select the next left-to-right maximum thereafter. This “right-justified” strategy succeeds with probability $j {\theta}^{j-1} (1-{\theta})$. When ${\theta}> 1$, the optimal strategy is “left-justified,” rejecting the first $k$ candidates for some $k$ depending on ${\theta}$ but independent of $N$. Consequently, this shows that the classical model 