Given the above formulation, the inference is not the same. P(H) = 1⁄2, but after information about W or not W is given, then P(H | W) = 1⁄3 or P(H | not W) = 1. The math doesn’t care, you just aren’t awake to perform your update process. When precommitting, you are not manipulating P(H), you are manipulating P(H |W) by changing W, so there’s no issue.
P(A) = 1⁄2, P(B) = 0 is still the only way I can see to get P(H | W) = 1⁄2. In which case, I can’t find any non-artificial framing for why Heads Tuesday does not exist (and Heads Monday exists twice as much as Tails Monday).
Given the above formulation, the inference is not the same. P(H) = 1⁄2, but after information about W or not W is given, then P(H | W) = 1⁄3 or P(H | not W) = 1. The math doesn’t care, you just aren’t awake to perform your update process. When precommitting, you are not manipulating P(H), you are manipulating P(H |W) by changing W, so there’s no issue.
P(A) = 1⁄2, P(B) = 0 is still the only way I can see to get P(H | W) = 1⁄2. In which case, I can’t find any non-artificial framing for why Heads Tuesday does not exist (and Heads Monday exists twice as much as Tails Monday).