Heh, this problem is working as intended 
.
Personally, I'd gamble for the big money in scenario 1 and gamble for keeping the most in scenario 2.
The "expected values" for both options in both games are the same.
-Zap
It must be badly phrased because they don't seem to be the same thing.
I give you $1000. Then I give you a choice: we flip a coin for a chance at an extra $1000, or I just give you an extra $500. Which do you choose?
I give you $1000, but, since I'm not nice, I then give you another choice: we flip a coin to decide whether I take it all away, or you just give me $500. Which do you choose?
Is that what it's supposed to mean?
If not,
1- You're given 1000, no conditions. Then given a choice for either a 50/50 chance at 1000 extra, or 500 no conditions. So here it's 1000+(1000 or 0; or 500). A choice between a scenario leading to either 1000 or 2000, and another that leads to 1500.
2- You're given 1000, then given a choice for either a 50/50 chance at -1000, or -500. Here it's 1000+(0 or -1000; or -500). So the choice is between a scenario that gambles equally between 0 or 1000, and another that leads to 500 everytime.
So the two situations are apples and oranges, the way I understand them. The way I see it, you've got money magically without any working for it. An extra 50% in the first one is enough to outweigh risking 50% on top of the first sum for the possibility of 33% more than what you get with the no-conditions choice. In the second scenario, again money out of thin air with a choice between either a 50/50 chance at 100% of the sum, or a no-conditions choice for 50% of the sum. It'd depend on the circumstances, but in the abstract I'd take the guaranteed 50% choice unless the sum was negligible enough.
