Problem: EV++ and risk tolerance in a multiple decision scenario.

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Here is a problem that I sometime think about as a fun theoretical excercise. Sometime I pose it to others to find out how they think about EV and risk tolerance:

A rich person offers you $1000. You can have this money with no conditions and walk away. This same person than says:

"I will give you a 5 in 6 chance (roll of a die for example) of doubling your money. If you roll 2,3,4,5,6 you double your money. If you roll a 1, you lose and I get my money back - all of it. There are other no other conditions."

Do you take the offer? Of course you do - right? EV+ !

Let's say you take the offer and win. He then gives you the same offer. 5 in 6 chances of doubling up the new sum($2,000 this time) or losing ALL the money. Do you take it this time? Of course.... right? EV+ !

He then offers his offer over and over again, to the extent of his full wealth (billions of dollars - theoretical question remember). Also keep in mind that this game is a one time deal. Once it's over - i.e. you lose all your money or walk away - there are no replays.

The dilemna of this problem is that calculating cumulative probability shows that you have less than 50% of getting to $8000 and less than 20% of getting to a million and less than 3% to getting to a billion. But at no point is the individual EV decision 'wrong' to go on.

This question is clearly a question of risk tolerance, but I find it interesting from the perspective that it is sometime CORRECT to turn down a very high EV+ situation. And in this game it will become correct to turn down a very high EV+ at some point.