In "Sleeping Beauty and Self-Location: A Hybrid Model", Bostrom comes up with a way to have Beauty believe that P(Tails) = 1/2, both before and after learning that it's Monday. The idea is to treat the situation as five separate possible cases: three cases before learning it's Monday (Heads^Mon_1, Tails^Mon_1, Tails^Tue_1) and then two cases after learning it's Monday (Heads^Mon_2, Tails^Mon_2). Once Beauty learns that it's Monday she's now in a new reference class, and since each world contributes exactly one observer moment, she ends up back at P(Tails) ... (read more)
In "Sleeping Beauty and Self-Location: A Hybrid Model", Bostrom comes up with a way to have Beauty believe that P(Tails) = 1/2, both before and after learning that it's Monday. The idea is to treat the situation as five separate possible cases: three cases before learning it's Monday (Heads^Mon_1, Tails^Mon_1, Tails^Tue_1) and then two cases after learning it's Monday (Heads^Mon_2, Tails^Mon_2). Once Beauty learns that it's Monday she's now in a new reference class, and since each world contributes exactly one observer moment, she ends up back at P(Tails) ... (read more)