I’d recommend distinguishing between the probability that the coin landed heads (which happens exactly once), and the probability that, if you were to plan to peak you would see heads (which would happen on average 250,000 times).
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!!!!”
I’d recommend distinguishing between the probability that the coin landed heads (which happens exactly once), and the probability that, if you were to plan to peak you would see heads (which would happen on average 250,000 times).
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!!!!”