The problem is that you are counting frequencies, and I am not. It is true that if you run the experiment many times, my estimate will change, from the very moment that I know that the experiment will be run many times.
But if we are going to run the experiment only once, then even if I plan to peek, I would expect with 50% probability to see heads. That does not mean “per awakening” or any other method of counting. It means that if I saw heads, I would say, “Not surprising; that had a 50% chance of happening.” I would not say, “What an incredible coincidence!!!!”
The problem is that you are counting frequencies, and I am not. It is true that if you run the experiment many times, my estimate will change, from the very moment that I know that the experiment will be run many times.
But if we are going to run the experiment only once, then even if I plan to peek, I would expect with 50% probability to see heads. That does not mean “per awakening” or any other method of counting. It means that if I saw heads, I would say, “Not surprising; that had a 50% chance of happening.” I would not say, “What an incredible coincidence!!!!”