There is a lot going on here. 1. The part about the red-haired and green-haired people is more or less the Sleeping Beauty problem[1]. The LessWrong community

There is a lot going on here. 1. The part about the red-haired and green-haired people is more or less the Sleeping Beauty problem[1]. The LessWrong community (who are Bayesians) has concluded that this problem is under-specified and doesn't say what it's asking, and has two different valid answers.[2] EDIT: Actually it's a bit different. I wouldn't assume the two problems should have the same answer. 2. The dice room / madman experiment is ill-defined. It only works if you have an infinite population to take people from (if there is a bound on the number of rounds you can do, the effect vanishes), and it implicitly assumes that every person is equally likely to be chosen. This is nonsense, because there is no uniform distribution on the natural numbers. Taking a closer look, put the die results in a grid, where columns are the total length of the experiment, and there's one row for each round: len=1 len=2 len=3 round 1 snake round 2 normal snake round 3 normal normal snake Here are the probabilities of these results: len=1 len=2 len=3 round 1 1/36 round 2 35/36 1/36 round 3 35/36 35/36 1/36 If you take the product of each row, that gives the probability that the experiment ends in that particular round. If you sum up these probabilities, you get 1, as you'd hope. (It converges slowly.) Here are the number of people involved in each die roll, with a * if they are killed: len=1 len=2 len=3 round 1 1* round 2 100 100* round 3 10000 10000 10000* The reason this experiment is unintuitive is because you can calculate the probability that someone will die (i) by column, assuming that the length of the experiment is known, or (ii) by row, assuming that the round you were selected in is known, and these give different answers. (Try it.) This is because infinite sums are not commutative. 3. There's no trouble with the doomsday argument, because SIA is correct :-). [1] https://en.wikipedia.org/wiki/Sleeping_Beauty_problem https://en.wikipedia.org/wiki/Sleeping_Beauty_problem [2] http://lesswrong.com/lw/32o/if_a_tree_falls_on_sleeping_beauty/ http://lesswrong.com/lw/32o/if_a_tree_falls_on_sleeping_beau...