According my log, since the dubloon change, I’d never had more than 8 runs between drops of some kind before. I don’t run a huge number of islands, but I would like to reach a couple of goals before I quit them entirely.
( on my 26th run, I got a pet drop … alas, a duplicate going on the AH for 1/50th the price of the last one I need for the “I’m just here for the pets” achievement )