Bingo. I read the code to be sure there wasn't a factor to model this. The answer should depend on the relative probability of choosing a whole pill or a half pill. The code assumes equal odds, with no state dependence on the remaining ratio.

I was startled by the formula, though. It's the same as the Gilbert-Shannon-Reeds model for card shuffling, where the probability of a card falling from each packet scales to the number of cards left in each packet. (I wrote the "seven shuffles" paper with Persi Diaconis.)