When you wake up, you don't know which awakening it is. You claim the probability of heads is 50%.
Now, you are told it is the first awakening. The probability of learning that if heads is twice as much as the probability of learning that if tails, so your Bayes factor is 2:1. You therefore cannot still believe that the probability of heads is 50%.
Now, you are told it is the first awakening. The probability of learning that if heads is twice as much as the probability of learning that if tails, so your Bayes factor is 2:1. You therefore cannot still believe that the probability of heads is 50%.