You're right, this algorithm optimizes for "1 point for picking the best option, 0 for anything else", not knowing the distribution. If you do know the distrib

You're right, this algorithm optimizes for "1 point for picking the best option, 0 for anything else", not knowing the distribution. If you do know the distribution, and have some objective function, and samples are "free", you get a different model that you can solve inductively backwards from the case of "the last sample". A different model is that your objective function is still on order, but it gives some points for "closer to best". Maybe you score minus n for picking the nth best sample. In that case the model need not have a known distribution (It's different if you do or don't.) And the strategy us different: if the 99th sample out of 100 is the second best you've seen so far, you should take it. (Which can't possibly be optimal in the original model.)