The answer is pretty clear with Bayes’ Theorem. The world in which the coin lands heads and you get the card has probability 0.0000000005, and the world in which the coin lands tails has probability 0.5. Thus you live a world with a prior probability of 0.5000000005, so the probability of the coin being heads is 0.0000000005/0.5000000005, or a little under 1 in a billion.
Given that the worst case scenario of losing the bet is saying you can’t pay it and losing credibility, you and Adam should take the bet. If you want to (or have to) actually commit to paying, then you have to decide whether you would completely screw over 1 alternate self so that a billion selves can have a bit more money. Given that $100 would not really make a difference to my life in the long run, I think I would not take the bet in this scenario.
Surprised at that level of risk aversion. I would definitely take the bet given the “pure” thought experiment, though in reality the odds would be a lot lower given the probability that some information would have leaked by day 9, or e.g. the different possibilities listed by Dagon.
His level of risk aversion is absurd and likely not maintained in other situations leading to not transitive preferences. Or more realistically he’s just bad at intuitively thinking about numbers so he can’t give meaningful answers.
The answer is pretty clear with Bayes’ Theorem. The world in which the coin lands heads and you get the card has probability 0.0000000005, and the world in which the coin lands tails has probability 0.5. Thus you live a world with a prior probability of 0.5000000005, so the probability of the coin being heads is 0.0000000005/0.5000000005, or a little under 1 in a billion.
Given that the worst case scenario of losing the bet is saying you can’t pay it and losing credibility, you and Adam should take the bet. If you want to (or have to) actually commit to paying, then you have to decide whether you would completely screw over 1 alternate self so that a billion selves can have a bit more money. Given that $100 would not really make a difference to my life in the long run, I think I would not take the bet in this scenario.
Surprised at that level of risk aversion. I would definitely take the bet given the “pure” thought experiment, though in reality the odds would be a lot lower given the probability that some information would have leaked by day 9, or e.g. the different possibilities listed by Dagon.
His level of risk aversion is absurd and likely not maintained in other situations leading to not transitive preferences. Or more realistically he’s just bad at intuitively thinking about numbers so he can’t give meaningful answers.