Keeping with my comment to your previous post, the probability of the coin landing heads is a model for the frequency measurements that the Sleeping Beauty undertakes. (Also, you have some typos in the text, my favorite being “panthers in the data”). This frequency depends on how the measurement is made, and so is not an invariant. Specifically, if the SB in question checks the state of the dice each time it is woken up in your repeated SB setup, she measures the frequency approaching 1⁄3 for the heads, because of the double counting the same throw on Monday and Tuesday. While an outsider measures 1⁄2, since they don’t double count. So there is no conflict or contradiction, just different measurements and hence different hypotheses.
Keeping with my comment to your previous post, the probability of the coin landing heads is a model for the frequency measurements that the Sleeping Beauty undertakes. (Also, you have some typos in the text, my favorite being “panthers in the data”). This frequency depends on how the measurement is made, and so is not an invariant. Specifically, if the SB in question checks the state of the dice each time it is woken up in your repeated SB setup, she measures the frequency approaching 1⁄3 for the heads, because of the double counting the same throw on Monday and Tuesday. While an outsider measures 1⁄2, since they don’t double count. So there is no conflict or contradiction, just different measurements and hence different hypotheses.