The problem with the 1/3ers is they mix up probabilities from the experimenter's perspective with SB's perspective. Yes, from outside, MH, MT, and TT each occur 50% of the time. But I don't think you can just assume that the probabilities from the outside perspective carry over to the waking-up perspective. MH, MT, and TT are not 3 separate universes, they are 2 universes: one with one observer, and one with two observers.
The two universes are equally likely, but the 3 observers are not. SB knows when she wakes up that she will be an observer chosen from { MH } 50% of the time and from { MT, TT } 50% of the time. What is wrong with this logic?
Quote:
Similarly, take the dude from Memento (5 min memory). If coin lands heads, he will be woken up for 10 minutes. If it lands tails, he will be woken up for 10 hours. He is only woken up once in each case.
What's the probability of a fair coin? : 50/50
What's more likely to have been flipped for this experiment? : I'm awake, therefore tails.
Same logic again.
You can't just ignore time because "durdle, durdle, coins are 50/50". Time is a relevant piece of info here.
The problem here is that the guy doesn't remember how long he's been awake for. Time would be relevant info, if he knew it, but he doesn't. Dividing up each timespan into 5 minute chunks, he is 50% to be any of two observers, and 50% to be any of 120 observers.