> Game 2: If you guess correctly then you get $10 by the end of the experiment.
The question is clear you get a reward each time you awaken, not at the end of the game.
The reward is correctness (Humans like being correct = reward, else things like 'should believe' becomes meaningless hence the question becomes meaningless Q.E.D. it's not meaningless and correctness is a reward)
"When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?"
This fits with my understanding of what's happening here. The SO discussion is a bit unclear as you go down the page, but the initial statement of problem up top clearly claims that you're questioned each time you awaken.
I think you're quite right to point out that being correct is the only fair heuristic for this question. Several of the defenses of a 'halfer' belief amount to "you ought to believe this so that your beliefs obey this type of decision theory". Actively believing something with a (reliably) worse payout to conform to a rule about belief seems like a terrible form of epistemology.
On a related note, are you familiar with Newcomb's Paradox and the LessWrong debates over it? They get to a similar idea of "correctness above all".
The question is clear you get a reward each time you awaken, not at the end of the game.
The reward is correctness (Humans like being correct = reward, else things like 'should believe' becomes meaningless hence the question becomes meaningless Q.E.D. it's not meaningless and correctness is a reward)
"When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?"