# plantains and coupon collecting

I must have stochastic processes on the mind after wrapping up another semester.  I will admit that this is a rather silly post. I was sauteing a couple of plantains last night.  I cut the plantains into thin slices and then saute them in a little olive oil in a cast iron skillet until they are browned.  It’s hard to flip plantain slices over, and only a few slices can come into contact with the skillet.  As a result, it’s hard to evenly cook the slices.

As I was cooking, I starting to mentally model how I would estimate how long it would take to brown all of the plantain slices.  Since I flip plantains at semi-regular intervals (about once every minute or two), it provides a discrete-time structure to the problem.  The more flips have occurred, the lower the probability that any unbrowned plantain comes into contact with the skillet (since it becomes more likely that already-browned slices come in contact with the skillet).  This is not unlike the coupon collecting problem, where there is a set of n coupons from which coupons are collected one at a time with replacement.  The set of n coupons is my set of plantain slices, plantain slices are collected when they come in contact with the skillet, and plantain slices can come into contact with the skillet more than once.  I do not collect coupons one by one, but rather I collect a subset of coupons at each flip–the number of plantain slices that can come in contact with the skillet.  The bottom line is that it takes an increasingly long time to brown each additional plantain slice.

Of course, I could always game the system and manually exchange browned plantain slices with unbrowned plantain slices to sleep along the cooking process and encourage uniformity.  But (a) I don’t have the time to devote to manually flipping with two kids to feed and (b) that’s a little obsessive.

So that leaves me with the solution to the coupon collecting problem: the plantains would burn before they would all be browned. I suppose I’ll have to work on my plantain-turning technique and accept a few undercooked plantains.

What algorithm do you use for skillet cooking?  How do you cook plantains? (I love ’em, but I’m a plantain novice. I’d love some new recipes).