Bob wrote: "In this case, is it better to take the guaranteed $50 or spin for the prize with a bigger average (but a significant probability for a smaller result)? To my way of thinking, whether we get the opportunity once or 400 times is not an important distinction. I believe spinning is correct in either case."
It's important to realize that this is "your way of thinking". This is the "one step at a time" approach and its solution is the Kelly criterion. Alternatively, one could solve for groups, such as 400 spins, and avoid making decisions (tactics) that lead down paths you don't want to risk going down.
Bob wrote: "If the numbers were "large" (which is personally defined), then it can certainly make sense to take the "bird in the hand". For example, if we were guaranteed $5 million or could spin the wheel and get an average of $6 million, I would take the $5 million in a heartbeat. Even though the math is the same, $5 million is such a potentially life-changing amount that there is no way I can feel comfortable gambling with it. But $50? For me that's pocket change and I'm going with the math."
If you're "going with the math", there is a mathematical solution to this quandry of when to gamble as a function of your "gambling bankroll" and the approximation is known as the Certainty Equivalent:
CE = EV - Variance/Bankroll/2
If you remember your high school algebra class, that formula can be rearranged as:
Bankroll = Variance/(EV-CE)/2
If your current gambling bankroll is less than this amount, taking the gamble is mathematically not worth it, even though the gamble is positive longterm or on average. You simply don't have enough gambling bankroll to chase the edge (EV-CE) or "gamble with the edge" in that case. Almost 20 years ago, Jazbo published Kelly bankroll numbers (which are approximately double the CE bankroll numbers) for some common video poker games:
http://www.jazbo.com/videopoker/kelly.html
Posted by: nightoftheiguana2000@yahoo.com
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