Sleeping Kelly

arXiv:2510.15911v3 Announce Type: replace-cross Abstract: The Sleeping Beauty problem is a problem of imperfect recall that has received considerable attention. One approach to solving the Sleeping Beauty problem is to allow Sleeping Beauty to make decisions based on her beliefs, and then characterize what it takes for her decisions to be "rational". In particular, she can be allowed to make monetary bets based on her beliefs, with the assumption that she wants to gain wealth rather than lose it. However, this approach is often coupled with the erroneous assumption that Sleeping Beauty should maximize the expected value of her bets. Here, we infer probabilities when Sleeping Beauty maximizes the expected growth rate of her wealth using the Kelly Criterion, to show that Sleeping Kelly is an ex ante Halfer and de se Thirder and impervious diachronic Dutch Books.