As I understand it, FDT says that you go with the algorithm that maximizes your expected utility. That algorithm is the one that bets on 1:2 odds, using the fact that you will bet twice, with the same outcome each time, if the coin comes up tails.
I agree with that description of FDT. And looking at the experiment from the outside, betting at 1:2 odds is the algorithm that maximizes utility, since heads and tails have equal probabilities. But once you’re in the experiment, tails have twice the probability of heads (according to your updating procedure) and FDT cares twice as much about the worlds in which tails happens, thus recommending 1:4 odds.
As I understand it, FDT says that you go with the algorithm that maximizes your expected utility. That algorithm is the one that bets on 1:2 odds, using the fact that you will bet twice, with the same outcome each time, if the coin comes up tails.
I agree with that description of FDT. And looking at the experiment from the outside, betting at 1:2 odds is the algorithm that maximizes utility, since heads and tails have equal probabilities. But once you’re in the experiment, tails have twice the probability of heads (according to your updating procedure) and FDT cares twice as much about the worlds in which tails happens, thus recommending 1:4 odds.