3 ms·

I agree on the 0:1 case, but say it's even 1:100000000. Before you go to sleep, you're asked "what do you think the result of the coin flip will be?", and then

by daxfohl 11y ago

I agree on the 0:1 case, but say it's even 1:100000000. Before you go to sleep, you're asked "what do you think the result of the coin flip will be?", and then you wake up and are asked "what do you think the coin flip was?" What new information have you received that changed your mind?

nightcracker 11y ago
The new 'information' is the number of times you're being woken up. Even though this information is not being told to you, you can implicitly use it by using the same strategy every time. You should see it from the perspective of every awakening. Imagine this. The experiment is repeated 10 times. On average the coin will have landed 5 times on heads, and 5 times on tails. This means that you'll be woken up 5 times while the coin landed on heads. However, you'll be woken up 500000005 (!) times while the coin landed on tails. Knowing this, when you're woken up only in 5/500000010 of the scenarios the coin landed on heads.
PeterisP 11y ago
The fact that no new information was gained does not mean that your answer to "what do you think the coin flip was?" will neccessarily be equal to "what do you think the result of the coin flip will be?" All it means is that you can already, before going to sleep, make an unconditonal strategy "when woken up, I'll say this". And your knowledge can easily lead you to a statement "right now, I believe the coin flip will be 50/50, but when I wake up I'll bet on tails". The coin flip does change the probabilities significantly after you get awakened - e.g. in the 0:1 chance you know that being awakened implies that it must be that particular result, and the 1:100000000 scenario implies that if you're awakened then it either was tails or something extremely unlikely happened. The "no new information" clause simply means that you get already informed about this probability before going to sleep, not after the coin flip.

by daxfohl 11y ago

nightcracker 11y ago

The new 'information' is the number of times you're being woken up. Even though this information is not being told to you, you can implicitly use it by using the same strategy every time. You should see it from the perspective of every awakening. Imagine this. The experiment is repeated 10 times. On average the coin will have landed 5 times on heads, and 5 times on tails. This means that you'll be woken up 5 times while the coin landed on heads. However, you'll be woken up 500000005 (!) times while the coin landed on tails. Knowing this, when you're woken up only in 5/500000010 of the scenarios the coin landed on heads.

PeterisP 11y ago

The fact that no new information was gained does not mean that your answer to "what do you think the coin flip was?" will neccessarily be equal to "what do you think the result of the coin flip will be?" All it means is that you can already, before going to sleep, make an unconditonal strategy "when woken up, I'll say this". And your knowledge can easily lead you to a statement "right now, I believe the coin flip will be 50/50, but when I wake up I'll bet on tails". The coin flip does change the probabilities significantly after you get awakened - e.g. in the 0:1 chance you know that being awakened implies that it must be that particular result, and the 1:100000000 scenario implies that if you're awakened then it either was tails or something extremely unlikely happened. The "no new information" clause simply means that you get already informed about this probability before going to sleep, not after the coin flip.