You have AA every hand . . . when do you quit?

I believe the paramount factor in this situation in not "expected value", but "expected utility" as a few people have hit on. The question has nothing to do with math, because anyone with any math skill would conclude that all-in with pocket aces vs two random cards is an easy call all day long, mathematically speaking. But how many people would risk $32,000.00 on the second to last hand of the deal for an 80% chance to double up, probably not the guy making $15/hr with a wife, kid, and $32,000.00 left on his mortgage, because the $32,000.00 he has would mean a lot more than the extra $32,000.00 he might expect to make if he won. Some may quit after doubling up only one or twice, if $2,000.00 is what they needed to make them happy, and risking that was not worth the extra $2,000.00 they would expect to make 4/5 times.


A more extreme example would be if you won $10,000,000.00 playing the lottery and that $10,000,000.00 constituted your entire worth. Afterwards you were given the option to place that $10,000,000.00 on the line to spin the "big wheel" that offered a 1/10 chance to win $10,000,000,000.00 more. Of course you are 10% to win but have a 1000/1 return on investment. Mathematically speaking that is a no brainer, but the relative value of the extra $10,000,000,000.00 vs. the 90% chance you will go broke is probably not worth the risk for any rationalt person. Keep the ten million and be set for life, take your chance and 10% of the time come out filthy rich with almost too much money to spend, and the other 90% be broke and back humping a 40/hr a week job. I guarentee everyone will people pick the first option.

The only person who might take the option to spin would be someone who was already extremely rich and $10,000,000.00 was not a significant increase in net worth whereas $10,000,000,000.00 would have would have a much larger relative value to him. A person like Bill Gates for example.

That is why people play slots, keno, the lottery, etc. Anyone with any knowledge knows they are not even a favorite to win or that they are even making a +EV decision, but it is not about "expected value", the "expected utility" of winning millions playing the lottery outweighs the relative value of that $5 they are almost certainly going to lose playing it.