CapitalistImperialistPig

Once more into the breach: another statistics problem from The Burg: Suppose you’ve somehow found yourself in a game of Russian Roulette. Russian roulette is not, perhaps, the most rational of games to be playing in the first place, so let’s suppose you’ve been forced to play. Question 1: At the moment, there are two bullets in the six-shooter pointed at your head. How much would you pay to remove both bullets and play with an empty chamber? Question 2: At the moment, there are four bullets in the six-shooter. How much would you pay to remove one of them and play with a half-full chamber? The hardest part of this kind of problem is figuring exactly how to frame it. Suppose, for example, that objective here is to maximize your lifetime, and that your expected lifetime, should you survive the game, is a function of your remaining wealth W, say f(W). For question 1, then, without the payoff, your expected future lifetime becomes: L = (1/3)*0 + (2/3)*f(W) = (2/3)*f(W), and L = f(W-P) with ...

Let me depart for the moment from my traditional practice of abusing Steve Landsburg to note that I quite liked his post on countable and uncountable numbers. He briefly discussed the countability of the integers and rationals and presented Cantor's proof of the uncountability of the reals. One of his commenters asked the following: Imagine that you run the front desk at a hotel with a countably infinite number of rooms. Imagine further that all of the rooms are occupied. A man shows up in the lobby and asks for a room. Can you give him a room? The answer is yes of course, but it should keep your bell boys busy. Interestingly enough, it's hardly any more trouble to accomodate a countably infinite number more of guests. Still, you have to say that the manager who let this deplorable situation arise made a big mistake. How should he have run his hotel so that he didn't have to move an infinite number of people each time some more guests showed up? What if he had an unc...