You wake up with no idea if it's day one or two — what are the odds?
Sleeping Beauty agrees to an experiment: she's put to sleep, and a fair coin is flipped. On heads, she's woken once, on Monday. On tails, she's woken twice, once on Monday and once on Tuesday, with a memory-wiping drug between wakings so she can't tell which day it is either time. Each time she wakes, she's asked: what's the probability the coin landed heads?
Reveal the answer
There are two defensible answers, and philosophers still argue over which is correct. 'Halfers' say the coin is fair and she's learned nothing new, so it must be 1/2. 'Thirders', following Adam Elga's influential 2000 paper, argue that since tails produces twice as many waking-moments as heads, and she can't distinguish them, the correct answer from her perspective is 1/3. The puzzle exposes a real, unresolved fault line in how probability should handle self-locating uncertainty.
— Adam Elga, Self-locating belief and the Sleeping Beauty problem — Analysis, 2000