>>12974091After reading that article
If you need to make a decision which optimizes over all iterations, it's 1/3.
If you need to make a decision which is only based on the initial coin flip, it's 1/2.
So I guess the difference is how we understand the question posed to the sleeper in the original question. So if it's about her credence, then answering 1/3 is most correct over many trials.