I don’t see why the problem is not solved. The probability of being at X depends directly on how I am deciding whether to turn. So I cannot possibly use that probability to decide whether to turn; I need to decide on how I will turn first, and then I can calculate the probability of being at X. This results in the original solution.
This also shows that Eliezer was mistaken in claiming that any algorithm involving randomness can be improved by making it deterministic.
I don’t see why the problem is not solved. The probability of being at X depends directly on how I am deciding whether to turn. So I cannot possibly use that probability to decide whether to turn; I need to decide on how I will turn first, and then I can calculate the probability of being at X. This results in the original solution.
This also shows that Eliezer was mistaken in claiming that any algorithm involving randomness can be improved by making it deterministic.