That is a good example of how the optimizer's curse causes an overestimate of the maximum expected value, and even reliably causes a wrong choice to be associated with the maximum expected value. But how do I apply the correction mathematically, so I can know for which expected values on the high uncertainty boxes I should expect their best of them to be better or worse than the low uncertainty box? Even better, how can I deal with situations where the uncertainties of the expected values are not so conveniently categorized (and whose actual values aren't conveniently uniform)?