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.
I'm not sure whether you're understanding the wager correctly. If you win, you double your entire savings, not just gain $n.