I'm saying that if Sleeping Beauty's goal is to better understand the world, by performing a Bayesian update on evidence, then I think this is a form of "payoff" that gives Thirder results.

From If a tree falls on Sleeping Beauty...:

Each interview consists of one question, “What is your credence now for the proposition that our coin landed heads?”, and the answer given will be scored according to a logarithmic scoring rule, with the aggregate result corresponding to the number of utilons (converted to dollars, let’s say) she will be penalized after the experiment.

In this case it is optimal to bet 1/3 that the coin came up heads, 2/3 that it came up tails: [snip table]