Sleeping Beauty is put to sleep on Sunday. A fair coin is flipped.
Heads: she wakes Monday only.
Tails: she wakes Monday AND Tuesday (memory erased between).
When she wakes, what should her credence in Heads be? Thirders: 3 possible awakenings, only 1 is Heads, so P(H) = 1/3. Halfers: The coin is fair, nothing changes that, so P(H) = 1/2.
This is one of the most debated problems in modern philosophy of probability.