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.
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.