I think if we change the nature of the problem but keep the game principle the same we have an more intuitive answer:
Imagine someone tosses a fair coin and asks you to determine the probability of whether it’s heads. They tell you have not tampered with it and will show you the actual result, and even toss the coin in front of you.
You would naturally say 1/2 . They show you the result (heads or tails) and write it down as the last result on their log. [This is effectively what happens when sleeping beauty wakes up]
Afterwards they show you the log for every flip you made in the past. Secretly they... (read more)
I think if we change the nature of the problem but keep the game principle the same we have an more intuitive answer:
Imagine someone tosses a fair coin and asks you to determine the probability of whether it’s heads. They tell you have not tampered with it and will show you the actual result, and even toss the coin in front of you.
You would naturally say 1/2 . They show you the result (heads or tails) and write it down as the last result on their log. [This is effectively what happens when sleeping beauty wakes up]
Afterwards they show you the log for every flip you made in the past. Secretly they... (read more)