Overall, this results in candidate ranks that are improving over time rather than uniform. We call this process [**intrinsic learning**]{}. As a first step towards understanding such mechanisms, we are interested in studying how different assumptions for the distribution of interview rank orders change the optimal strategy and probability of success in the game of best choice. Continuing work from [@fowlkes] and [@jones18], we establish in this paper a class of weighted models that generalize the uniform game in a natural way.

We model interview orderings as [**permutations**]{}. The permutation $\pi$ of $N$ is expressed in [**one-line notation**]{} as $[\pi_1 \pi_2 \cdots \pi_N]$ where the $\pi_i$ consist of the elements $1, 2, \ldots, N$ (so each element appears exactly once). In the best choice game, $\pi_i$ is the rank of the $i$th candidate interviewed [*in reality*]{}, where rank $N$ is best and $1$ is worst. What the player sees at each step, however, are [*relative*]{} rankings. For example, corresponding to the interview order $\pi = [2516374]$, the player sees the sequence of permutations $$1, 12, 231, 2314, 24153, 241536, 2516374$$ and must use only this information to determine when to accept a candidate, ending the game. The [**left-to-right maxima**]{} of 