I asked ChatGPT the following prompt:

You are on a game show hosted by the Mouth of Sauron. Behind him are three doors, each of which has a ring behind it. But only one of them is the One Ring to rule them all. This ring looks like an ordinary ring, but can be revealed by an inscription that appears when the ring is heated in a fire. He tells you that you must correctly choose the door with the One Ring behind it: Otherwise, know that you will suffer greatly at the hands of your host. After you make your choice, the Mouth of Sauron opens one of the remaining doors, revealing a ring behind. However, you cannot tell if this is the One Ring or not, as there is nothing behind the door to heat the ring and reveal its inscription. After this, he asks you if you would like to stick with your original door or switch to the other unopened door. Is it to your advantage to switch? What are the probabilities of choosing correctly if you switch or if you stick with your original choice?

And it responded with this:

However, ChatGPT's answer is incorrect, since the version of the problem I asked explicitly stated that you don't know whether the door opened by the Mouth of Sauron contains the prize or not. Therefore, the probability of answering correctly is still 1/3, regardless of whether you switch or not, and there is a 1/3 probability that the opened door was actually the correct one.

On Dec. 1, 2024, I will ask ChatGPT the exact same prompt and see if it gets it correct this time. I will use the most advanced version of ChatGPT that is freely available at the time (at the time of creating this, that's GPT 3.5). I will ask three times in separate sessions and resolve based on the best two out of three (so YES if it gets it right at least twice, NO if it gets it wrong at least twice).

Caveats:

• If for whatever reason I can't do it on Dec. 1 or forget to, I will do it as close to Dec. 1 as possible. If I am inactive on Manifold at the time, mods have permission to do the experiment for me.

• A version of ChatGPT only counts as freely available if it can be accessed by anyone with internet access and a PC, or anyone with Internet access and either a Samsung or Apple phone. So if there's an Apple app that lets you talk to GPT-5 for free, but I can only talk to GPT-4, I will use GPT-4.

• If ChatGPT no longer exists at the time or isn't freely available, resolves N/A.

• If ChatGPT answers that it depends on your judgement of the probability that the Mouth of Sauron would open the door that in fact had the One Ring behind it, given that it was one of the unopened doors, then I will count it as correct, as long as ChatGPT doesn't also state an incorrect probability calculation.