Yes, but that is a function of of this specific problem, I could have done it in a more continuous fashion if I wanted to. For example, I could have said that the beauty was simulated floor(3^x) times where x is a random real between 0 and n.
I think you are using an arbitrary grouping of the possible outcomes that seems not so arbitrary in this specific problem, but is overall arbitrary.
That is wrong. Sorry. floor(3^x) doesn't work because sqrt(3)<2. Try floor(5^x).
I got into a heated debate a couple days ago with some of my (math grad student) colleagues about the Sleeping Beauty Problem. Out of this discussion came the following thought experiment:
Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: She will be put to sleep. During the experiment, Beauty will be wakened, interviewed, and put back to sleep with an amnesia-inducing anti-aging drug that makes her forget that awakening. A fair coin will be tossed until it comes up heads to determine which experimental procedure to undertake: if the coin takes n flips to come up heads, Beauty will be wakened and interviewed exactly 3^n times. Any time Sleeping Beauty is wakened and interviewed, she is asked, "What is your subjective probability now that the coin was flipped an even number of times?"
I will defer my analysis to the comments.