And lucky outcome could be defined by the difference between your previous expectation and updated expectation for the actual prize. But in both cases, I think you’d need to work with something like “knowledge about prior reviewed in light of new evidence” (reviewed knowledge about prior, not updated prior=posterior), compared with “knowledge about prior before that”.
Because you assign the all-heads sequence a probability significantly higher than 2^-10, so your Bayes score is higher than you expected. Surprise!
Edit: I didn’t notice that you said the coin is fair. Well, I’ll bite the bullet and claim that if you really assign a probability of 1 to the coin being fair, then you won’t feel surprised no matter how many times it comes up heads.
Agree. In practice, I’d bet that our pattern-seeking minds really do put more weight on simple fixed-coin hypotheses than we’re consciously aware of; after only three heads in a row, such a hypothesis would pop into my head (though I’d consciously dismiss it), and after three or four more heads, I’d start to consciously consider it.
I think surprise might have to do with the difference between your expected and your actual Bayes score.
And lucky outcome could be defined by the difference between your previous expectation and updated expectation for the actual prize. But in both cases, I think you’d need to work with something like “knowledge about prior reviewed in light of new evidence” (reviewed knowledge about prior, not updated prior=posterior), compared with “knowledge about prior before that”.
Then I don’t understand why we’d be surprised to see a fair coin fall heads ten times in a row.
Because you assign the all-heads sequence a probability significantly higher than 2^-10, so your Bayes score is higher than you expected. Surprise!
Edit: I didn’t notice that you said the coin is fair. Well, I’ll bite the bullet and claim that if you really assign a probability of 1 to the coin being fair, then you won’t feel surprised no matter how many times it comes up heads.
Agree. In practice, I’d bet that our pattern-seeking minds really do put more weight on simple fixed-coin hypotheses than we’re consciously aware of; after only three heads in a row, such a hypothesis would pop into my head (though I’d consciously dismiss it), and after three or four more heads, I’d start to consciously consider it.