Correct, but there’s a one line argument :)
Your expected payoff should be 0, so p*100 + (1-p)*0 = 7 => p = 7/100

@Arthur, Mathematica is telling me the answer is 7/100. http://dreev.es/rsolve

Do you differentiate between saving towards a bequest versus over saving without such an end in mind?

And I see that one person so far claims in the straw poll there that I convinced them to save *more*. :)

If a positive singularity indeed occurs in the next couple decades, then the fraction of your life you spent saving too much money will be infinitesimal compared to the astronomical lifespan you will enjoy. Similarly, the loss of utility would be trivial compared to the wealth you would enjoy.

So “the singularity is near” argument implies that maybe your savings won’t matter, but it also implies that in that not saving doesn’t matter much either. The singularity makes everything moot.

Singularitarian arguments aside, I don’t think people in the US suffer from too much savings. If anything, the saving rate in the US is one of the lowest in the world. This means you’re living in a country where people heavily discount the future, which should give you a strong incentive to save (though manipulation of the interest rate complicates matters).

Sure, there is such a thing as saving too much, but compare the US’s meager 5% saving rate to Singapore’s 50%. It’s much more likely US citizens save too little.

@Manoel, thanks! That’s really nice to hear!

As to the bonus puzzle, I think Arthur has nailed it again. It’s not true that you’ll always go broke. If the random walk is biased towards saving then you might never go broke. The probability depends on how biased the random walk is. If the walk is biased in the other direction (towards spending) then you’re right that you’ll definitely eventually go broke.

And the bonus puzzle is the classical random walking class example (gambler’s ruin). It’s pretty obvius that with p = 50% or higher, the person will go broke.

In fact, I think this was one of the questions in a test I take in a stochastic process class. But I can’t remember the answer to the general case for any value of p.

But I guess that you will go broke for sure for any value of p higher than zero. That’s because no matter how unlikley, there will be a sequence of spendings that will make you spend all of your money. More formally, denoting a spending event as success, and the amount of money you have at time t by k, the probability of k success after time t (with no failure) approachs 1 as time goes to infinity.

I pasted the solution here
http://paste.ubuntu.com/680100/