Quote Originally Posted by dsaxton
I posted the link to point out that the fact that a gamble has positive expectation is not sufficient in showing that it is a "good" gamble. If it were, then it would be a good gamble to pay $3 million to play the St. Petersburg game, where you only win $2 half the time.
That problem is flawed because it does not take into account all the variables. Its really just a bankroll question IMO. If you have a trillion bazillion dollar bankroll then you probably would come out ahead betting $100 a time to play the St. Petersberg game. If you only had say $1000 then youre more likely to bust and "when youre broke youre done" so playing this game on a short bankroll is likely to bust you.

Its exactly the same as the adjustments youd make to play poker in a tournament. You have to consider your tournament "cash" EV not just your chip EV. If someone who covers you pushes and shows you even a 55/45 flip in your favor it is often correct to fold since folding gives you the most real money EV. In a cash game youd correctly call it every time with a large bankroll.

In a similar problem say you sit at a $100NL table with a bankroll of $2000. You run a little hot and work up to $2000 in the course of an hour.
You are now playing $100NL with a $4000 bankroll. You look over at the $200NL tables and see that the players are at least as bad over there as they are here and decide you will finish this hand and then move over to 200NL to double your longterm hourly rate. Someone ahead of you who also has $2000 pushes allin and shows you a 51/49 flip in your favour. The EV of a call is +$40 but the (almost) half the time you lose you wont be able to move up to 200NL so it is probably even more longterm +EV to just fold it and secure your winnings and move up to $200NL right now.