“Another example: You flip a coin ten times and see the sequence HHTTH:TTTTH. Maybe you started out thinking there was a 1% chance this coin was fixed. Doesn’t the hypothesis “This coin is fixed to produce HHTTH:TTTTH” assign a thousand times the likelihood mass to the observed outcome, compared to the fair coin hypothesis? Yes. Don’t the posterior odds that the coin is fixed go to 10:1? No. The 1% prior probability that “the coin is fixed” has to cover every possible kind of fixed coin—a coin fixed to produce HHTTH:TTTTH, a coin fixed to produce TTHHT:HHHHT, etc. The prior probability the coin is fixed to produce HHTTH:TTTTH is not 1%, but a thousandth of one percent. Afterward, the posterior probability the coin is fixed to produce HHTTH:TTTTH is one percent. Which is to say: You thought the coin was probably fair but had a one percent chance of being fixed to some random sequence; you flipped the coin; the coin produced a random-looking sequence; and that doesn’t tell you anything about whether the coin is fair or fixed. It does tell you, if the coin is fixed, which sequence it is fixed to.” (Eliezer Yudkowsky, Rationality)

Fairly interesting point about how to intuitively manage Bayesian updating