The relevant number for the purpose of judging the “correctness” of predictions is the probability you should have had at the time of the prediction (ie. the epistemically correct prior). Whether the outcome of the coin flip is heads or tails, the correct prior odds are 1:1, because you had no evidence either way.
If royf bets that katydee will win a fencing bout, and in fact they lose fourteen touches in a row, only to win by forfeit, we should update towards suspecting that royf miscounted the evidence, since such a bad athlete should not have much strong evidence predicting their winning. We should believe that the correct prior probability of katydee winning (from royf’s point of view) is lower than royf thought it was.
The relevant number for the purpose of judging the “correctness” of predictions is the probability you should have had at the time of the prediction (ie. the epistemically correct prior). Whether the outcome of the coin flip is heads or tails, the correct prior odds are 1:1, because you had no evidence either way.
If royf bets that katydee will win a fencing bout, and in fact they lose fourteen touches in a row, only to win by forfeit, we should update towards suspecting that royf miscounted the evidence, since such a bad athlete should not have much strong evidence predicting their winning. We should believe that the correct prior probability of katydee winning (from royf’s point of view) is lower than royf thought it was.