This isn't a very enticing wager--it seems like I have a lot more to lose than to gain. If I set n at, say, $1M, then I might win $1M, which would be nice, or I could end up with basically nothing, which would be devastating. You might have a more interesting wager if $5000 were changed to something more substantial, like $250k.
Oh, that's true. Still, I think the wager is too scary for most people to accept for large values of n. Even if I set n=1M and have 10M when I'm 55, gaining the extra 10 million will make significantly less of a difference to my life than losing all but $5k will.
Dfranke, adhering to the constraints given shouldn't the correct answer should be a very large negative value for n? There's no upside to increasing the value of n; you're only putting yourself further at risk.
It's only a confounding factor to the extent that the shape of the curve varies across cultures. The only reason that comes to mind for any such variation would be the availability of charitable handouts or government welfare, and that's objective enough to easily factor out.
This isn't a very enticing wager--it seems like I have a lot more to lose than to gain. If I set n at, say, $1M, then I might win $1M, which would be nice, or I could end up with basically nothing, which would be devastating. You might have a more interesting wager if $5000 were changed to something more substantial, like $250k.