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Morendil comments on Updating, part 1: When can you change your mind? The binary model - Less Wrong
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What matters isn't so much finding the right answer, as having the right approach.
At least as far as I'm concerned, that's the main reason to spend much time here. I don't care whether the answer to Sleeping Beauty is 1/2 or 1/3, that's a mere curio.
I care about the general process whereby you can take a vague verbal description like that, map it into a formal expression that preserves the properties that matter, and use that form to check my intuitions. That's of rather more value, since I might learn how my intuitions could mislead me in situations where that matters.
The purpose of this post is to ask how you intend that to improve your accuracy. You plan to check your calculations against your intuitions. But the disagreements we have on Sleeping Beauty are disagreements of intuitions, that cause people to perform different calculations. There's no way comparing your intuitions to your calculations can make progress in that situation.
Well, I plan to improve my accuracy by learning to perform, not just any old calculation that happens to be suggested by my intuitions, but the calculations which reflect the structure of the situation. Some of our intuitions about what calculations are appropriate could well be wrong.
The calculations are secondary; as I sometimes tell my kids, the nice thing about math is that you're guaranteed to get a correct answer by performing the operations mechanically, as long as you've posed the question properly to start with. How to pose the question properly in the language of math is what I'd like to learn more of.
Someone may have gotten the right answer to Sleeping Beauty by following a flawed argument: I want to be able to check their calculations, and be able to find the answer myself in similar but different problems.