A roulette puzzle. There's a roulette wheel with two outcomes: "reincarnate" (you escape) or "stay trapped in purgatory" (you stay another year, and then must spin again). You're forced to spin at least once. After that, you can stop only by drawing "reincarnate" , refusing to spin when required means you die (bad ending). The wheel is rigged so that "stay trapped" takes up a larger slice every spin: Spin 1: P(trapped) = 1/2 Spin 2: P(trapped) = 3/4 Spin 3: P(trapped) = 4/5 Spin 4: P(trapped) = 5/6 ... Spin k (for k ≥ 2): P(trapped) = (k+1)/(k+2) Each "stay trapped" outcome costs you exactly one year in purgatory. Let T be the total number of years you spend trapped before escaping. Question: What is the expected value of T? (Bonus: what's the probability you escape eventually? What's the median value of T?) submitted by /u/sbsw66 [link] [comments]