Yet Another Comment Not Answering Your Question .... [...] A lot depends on whether this "large sum of money" is more or less than five million dollars.

Playing the lottery was an irrational decision, but was the right choice. The outcome, as stated by moridinamael, is divorced from the decision making processes that went into it. Assuming an unambiguous result that can only either be good or bad, and the most rational choice based upon the evidence then at hand led to a bad outcome, one still made the best (most rational) decision - but, considering the bad result, 'twas the wrong choice. This classification if useful when determining the competency of a leader - they may have been an extremely rational decision maker but made nothing but wrong choices due to poor quality of information. I forget my source - as for the terms, fubarofusco's "Hindsight" fits well, while "Expected Value" does not.