The question of how you change your expectations, though, boils down to asking &quot;how do I think the person chose?&quot;<p>Interestingly, I think that given any particular choice of maximum entropy distribution, the recommendations boil down to &quot;there is a value above which you should stick and below which you should switch.&quot;  Since I don&#x27;t think - from the question alone - there is any particular reason to favor a specific distribution, I think it amounts to a free choice of that number.  If you have some idea of, say, the bankroll of the game runners (or, at worst, the total amount of money in circulation) you should be able to do better, of course.