How do we decide if your answer is correct? If you have all the power, you might as well just make up a random number between 0 and 1 and call it the answer. That's why the whole SSA vs SIA argument makes little sense.
Oops. You are right, what I said didn't make sense. I just edited the above post by changing "I tell you if you are right" to "I tell you how many times the coin was flipped"
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.