a coin is flipped until it comes up head, on the nth flip. You are then paid 2n dollars. How much are you willing to pay to participate in this game?

Depends. Do I get to participate on a regular basis, like one does in a lottery?

one's desire for money isn't linear in the amount of money involved

Yes, I know about the law of diminishing returns, but that's actually another argument against buying lottery tickets, because it further decreases the value of a chance at winning. There are additional factors as well that decrease it even further -- taxes, as I briefly mentioned, the tendency of most lottery winners to end up with nothing to show for it five or ten years later, and so on. I didn't feel the need to bring these things up because just calculating the expected return is convincing enough in itself, except for the people who aren't going to be convinced regardless.

$;=sub{$/};@;=map{my($a,$b)=($_,$;);$;=sub{$a.$b->()}}
split//,".rekcah lreP rehtona tsuJ";$\=$ ;->();print$/
[download]