No. 04
😴Sleeping Beauty
Is it 1/2 or 1/3? Philosophers still argue
The setup
- 1Beauty is put to sleep on Sunday and a fair coin is tossed.
- 2Heads: she's woken once (Monday). Tails: she's woken twice (Monday and Tuesday), with her memory of Monday erased.
- 3Each time she wakes, she's asked: what's the probability the coin came up Heads?
🤔 Intuition says: The coin is fair, so the answer is obviously 1/2 — isn't it?
🪙 Run one experiment
Flip the coin. Heads wakes Beauty once; Tails wakes her twice. Keep going and watch how often an awakening happens in a Heads world.
😴Sunday
→❔Coin
→❔Monday
📊 Let the server run thousands
Why it's a paradox
Halfers say no new information arrives on waking, so P(Heads) = 1/2.
Thirders count waking moments: across many runs there are twice as many Tails awakenings as Heads ones.
If Beauty bets on the coin every time she wakes, betting Tails wins twice as often — supporting the 1/3 answer.
💡 Key insight: Self-locating uncertainty splits 'probability of the coin' from 'probability given that you're awake right now.'
Further reading on Wikipedia →