At first I was thinking of something along those lines, averages. I'm not a math guy so I was thinking there was more to it since I didn't know other aspects of the situation; such as my limit, the other guy's limit, and so on.

I think my answer would have been, especially without more data, to not play the game. After living in Vegas for a number of years I know that even though the house often provides favorable percentages, the house always wins in the end.

But with some more wording, this could be a clever brain teaser. Thanks for bringing it up.

And to continue the questioning, if you have one reroll, and we assume you reroll a 1-3, then the expected value is (3.5 + 3.5 + 3.5 + 4 + 5 + 6) / 6.

I'll take that hedge fund job now.

Isn't $1 a valid answer?

I'm willing to pay $1, because the lowest amount I can win is $1, and I'd have a net loss of 0.