Sleeping Beauty and ChatGPT
Here is the famous Sleeping Beauty problem.
Puzzle. Sleeping Beauty agrees to take part in an experiment. On Sunday, she is put to sleep, and a fair coin is tossed. If it lands heads, she is awakened on Monday only. If it lands tails, she is awakened on both Monday and Tuesday. After each awakening, she is put back to sleep and given a drug that erases her memory of that awakening. She knows the rules of the experiment, but during each awakening she cannot tell which day it is or whether she has been awakened before. Each time, she is asked: From her point of view, what is the probability that the coin landed heads?
The answer is 1/3. I won’t repeat the details here; explanations are easy to find. Yet plenty of people insist that the answer is 1/2. Apparently, if enough people argue with the correct answer, a problem gets promoted to a paradox.
I tried to convince the halfers. I wrote many essays, some of them with Alexey Radul. Here is the list in chronological order.
- The Sleeping Beauty Problem (with Alexey Radul) — August 25, 2011.
- Sleeping Beauty Meets Monty Hall — August 27, 2011.
- Sleeping Beauty and Mondays (with Alexey Radul) — August 27, 2011.
- Sleeping Beauty Wants the Prize Money (with Alexey Radul) — August 30, 2022.
- The Sleeping Beauty Problem Amplified — August 31, 2022.
- Sleeping Beauty and Tuesdays — September 1, 2022.
Eventually, I got tired and stopped fighting. I decided to wait, hoping that the correct answer would catch on.
More than 15 years have passed since I started advocating for the correct answer. Yesterday, I revisited the Wikipedia page. People are still arguing. So I asked ChatGPT Pro for the answer. It replied: 1/3. Is ChatGPT’s authority enough to turn the tide?
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Xing Xu:
I’ve gone back and forth on this one over the years, and honestly my gut still says 1/2 even though I know the math says 1/3. There’s something about waking up with no memory of prior awakenings that makes the coin feel untouched, like it shouldn’t matter how many times you’re asked. But the thirder argument about counting awakenings rather than experiments keeps nagging at me. I liked the bit about waiting for the correct answer to catch on. It made me laugh, but it’s also a little sad, fifteen years is a long time to argue about a coin flip. I’m curious whether ChatGPT said 1/3 because the training data finally tipped, or because the reasoning genuinely lands there now. Either way, I don’t think the halfers are going anywhere.
31 October 2026, 1:02 amIgor:
It’d be great to know which of many current ChatGPT models answered correctly (e.g. 1/3). I’m not sure it was always the case.
31 October 2026, 7:58 pm