https://en.m.wikipedia.org/wiki/Sleeping_Beauty_problem

The Sleeping Beauty problem is a puzzle in decision theory in which whenever an ideally rational epistemic agent is awoken from sleep, they have no memory of whether they have been awoken before. Upon being told that they have been woken once or twice according to the toss of a coin, once if heads and twice if tails, they are asked their degree of belief for the coin having come up heads.

Resolves based on the consensus position of academic philosophers once a supermajority consensus is established. Close date extends until a consensus is reached.

I will use my best judgement to determine consensus. Therefore I will not bet in this market. I will be looking at published papers, encyclopedias, textbooks, etc, to judge consensus. Consensus does not require unanimity.

If the consensus answer is different for some combination of "credence", "degree of belief", "probability", I will use the answer for "degree of belief", as quoted above.

Similarly if the answer is different for an ideal instrumental agent vs an ideal epistemic agent, I will use the answer for an ideal epistemic agent, as quoted above.

If the answer depends on other factors, such as priors or axioms or definitions, so that it could be 1/3 or it could be something else, I reserve the right to resolve to, eg, 50%, or n/a. I hope to say more after reviewing papers in the comments.