To me adding a bet fundamentally changes the question. Canonically, the question is phrased based on credence, maximizing a bet isn't the same as being rational about reality. Asking for a bet (odds) is not the same as asking for probability of the coin flip(credence).
For the same reason that I know that I may die in the next 5 years but simultaneously be unwilling to take that as a nontransferable bet at even the most generous odds, Sleeping Beauty should believe that the coin flip was 50/50 but be unwilling take a bet of the same odds.
So, using deductive reasoning to answer the question: A fair coin has a 50/50 value, a... (read more)
To me adding a bet fundamentally changes the question. Canonically, the question is phrased based on credence, maximizing a bet isn't the same as being rational about reality. Asking for a bet (odds) is not the same as asking for probability of the coin flip(credence).
For the same reason that I know that I may die in the next 5 years but simultaneously be unwilling to take that as a nontransferable bet at even the most generous odds, Sleeping Beauty should believe that the coin flip was 50/50 but be unwilling take a bet of the same odds.
So, using deductive reasoning to answer the question: A fair coin has a 50/50 value, a... (read more)