ODD-MANNING WITH THE DEVIL. Marginal Revolution comments on a Crooked Timber post (with some very good comments) on the optimal time to take the Devil up on an offer to release you from Hell, if in a series of N flips of a fair coin (that's why I recommend the comments; why in Hell would there be a fair coin, and what is your soul doing there in te first place?) at least one of the flips comes up "heads." The Devil offers one flip on the first day, two flips on the second day, three flips ... with the proviso that your soul gets only one chance to play: if in N flips no heads come up, there will be no further offers forever thereafter.

There are some parallels between the coin flip from Hell problem and the St. Petersburg paradox, which Will at Crescat Sententia has comments on here and here. (Let me offer one brief explanation for the use of logarithmic valuation functions as a way of defanging the St. Petersburg paradox, which may or may not be less abstruse than those offered here, depending on your investments in human capital. In economics, it's often useful to think about the proportionate effect of a change in a variable, which introduces something called an elasticity. Natural logarithmic functions produce effortless elasticities.)