A cake is sliced roughly in half, the largest piece being chosen each time, the other pieces discarded. We will assume that a random cut creates pieces of proportions

P = {(2/3, 1/3) with probability 3/4
{(2/3, 3/5 with probability 1/4

Thus, for example, the first cut (and choice of the largest piece) may result in a piece of size 3/5​. Cutting and choosing from this piece might reduce it to size 3/5 2/3 at time 2, and so on. How large, to first order in the exponent, is the piece of cake after n cuts?