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I appreciate that you're trying to steelman the halfer position, but that's a really artificial construction. In fact, in this framing, the payout is 1/2 regardless of what she answers (as long as she's consistent). That's what happens when you try to sidestep the obvious way to bet (where even the Wikipedia article admits she should wager 1/3 on heads - and then somehow fails to definitively end the article there).
Nice, I think I'd encountered it before (I've unfortunately read a lot of "Ape in the coat"'s voluminous but misguided Sleeping Beauty posts), but I didn't specifically remember that one. Commit to betting only if the room is red. Then of the four equal-weight possibilities (Monday is red/blue) x (heads/tails), you win in red/tails and blue/tails, you lose in red/heads, and you don't bet in blue/heads. Expected payout per experiment is 1/4*(200+200-300) = 25.
He does seem to be wrong about "for reference, in regular Sleeping Beauty problem utility neutral betting odds for once per experiment bet are 1:1", because if you have any source of randomness yourself, you can actually get better odds (by ensuring that you'll "take the bet" more often when you have two chances at it). I see you actually posted a really nice analysis of the problem yourself in the link. It's fun that there's a distinction between an external source of randomness (where the results on Monday/Tuesday are dependent) and an internal source (where the results on Monday/Tuesday must be independent).
It sure is. That's kind of the point, I left a comment in more depth elsewhere in the thread.
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