The Doomsday Scenario.....one of those sayings I never analyzed because I thought it was self evident. But no, there actually is a Doomsday formula, and I'm indebted to Paul Kedrosky for the goods.....

Imagine two urns, one containing 10 balls numbered 1 thru 10; and a second urn containing a million balls, numbered 1 thru 1,000,000. If you pull a ball at random from one of the urns and you obtain a "3", the likelihood, according to Bayesian prior/posterior probabilities, is much higher that you have pulled from the 10-ball urn than the 1,000,000-ball urn.

The argument is ordinarily used to posit that we are closer to Doomsday than we know. After all, if we assume that humans are spread randomly through history, and you are here now making the observation -- sixty thousand years and fifty billion humans into our collective existence -- then what is the likelihood that we are closer to Doom, as opposed to being further away? Well, to think in urn-ish terms, you are either in a small urn -- there will never be more than 100-billion humans alive -- or we will go on to populate the multiverse -- thus there eventually being hundreds of billions of people alive. Given that you are "merely" number 50-billion, the likelihood is that we are in the smaller urn (by the (loose) Bayesian reasoning above), so Doomsday is closer than any of us think.