[stygiansonic]

Thanks for writing this.

Is this concept (dice room puzzle, doomsday argument) at all related to the st Petersburg paradox? https://en.m.wikipedia.org/wiki/St._Petersburg_paradox

[hbrav]

I think it's a little different. It's like asking "what is the probability that a given coin is in the round that the player wins?" But the St Petersburg paradox isn't about that, it's purely about how many coins the player wins. I suppose it runs into similar problems when you ask about prizes that are so large that the bank runs out of coins, but I think it remains interesting even if you cap it at some finite number of coin flips. It still has the small-probability-of-huge-payout property.

If you've ever looked at the Kelly Criterion, that seems related (and in fact is one of the articles linked to from that Wikipedia page). There you maximise expected log return at each round, and I think that tames the infinity in this case (though I have _not_ checked that).