A coin is tossed without the result being shown to you. If it's heads, you are put in a sensory deprivation chamber for 61 minutes. If it's tails, you are put in it for 121 minutes. Data from your past sensory deprivation chamber visits shows that after about a minute, you will lose all track of how long you've been in the chamber. So now you find yourself in the chamber, and realize that you've lost track of how long you've been there. What should your credence be that the coin landed heads?
Why is this a Sleeping Beauty case? Well, take the following discretized version. If it's heads, you get woken up 1,001,000 times and if's tails, you get woken up 2,001,000 times. There is no memory wiping, but empirical data from past experiments shows that you completely stop keeping track of wake-up counts after you've been woken up a thousand times. So now you've been woken up, and you know you've stopped counting. What should your credence be? This is clearly a version of Sleeping Beauty, except that instead of memory-wiping we have a cessation of keeping count, which plays the same role of being a non-rational process disturbing normal rational processes.
Oddly, though, in the sensory deprivation chamber case, I have the intuition that you should go for 1/2, even though in the original Sleeping Beauty case I've argued for 1/3. I don't have much intuition about my discretized version of the sensory deprivation chamber case.
P.s. I was thinking of blogging another Sleeping Beauty case, but it looks like LessWrong has beaten me to essentially it. (There may be a published version somewhere, too.)