Fiddler: Optimal Baseball Lineup

Solution to this weeks fiddler. I must admit I am not too happy with this solution, which involves simply using monte carlo simulations of all possible slugger starting positions and calculating the one with the best score.

Empirical Answer: The slugger should be ranked 4th, when the pure hitters take a single with probability \(p=1/3\) and the sluggers hit home runs with probability \(q=1/10\). If the pure hitters took singles with \(p=2/3\) instead, then surprisingly the optimal position is 9th.