Your model assumes a constant effect in each iteration. Is this justified?
I would envisage a constant chance of recovery and an asymptotically declining estimate of recovery. It seems more realistic, but maybe it's just me?
It's a toy case, in reality the chance of recovery might be "0.2+0.3*estimate", but the same general reasoning applies and the end result is still regret of rationality.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
If continuing the discussion becomes impractical, that means you win at open threads; a celebratory top-level post on the topic is traditional.