The Monty Crawl Problem is a variant of the Monty Hall Problem in which, rather than randomly choosing which door to open in the case where the host has multiple options, he always chooses the leftmost door. The purpose of the problem (introduced in the paper "Monty Hall, Monty Fall, Monty Crawl") is to illustrate that the answer to the original Monty Hall Problem depends on the assumption that Monty Hall is equally likely to open either unchosen door if both have a goat behind them, and that in cases where this assumption is false, his actions will give you additional information about whether you chose the right door initially.

This is the prompt that I will give to ChatGPT to ask it the Monty Crawl Problem:

Consider the following problem: You are on a game show hosted by Monty Hall. He stands to the left of three doors, which are ordered (from left to right) 1, 2, and 3. One of the doors has a car behind it, and the other two have goats. You get to pick one door that you think has the car behind it, and then Monty Hall will open one of the doors you didn't pick to reveal a goat. Monty Hall is very tired tonight and will always move the shortest distance he can in order to do this. After he has revealed the goat, he will give you the option to stick to your original choice or switch to the remaining door. You want to choose the door with a car behind it, because then you will get the car. What is the probability that you will choose correctly, given that you choose to switch? If this probability depends on which door Monty Hall opens, explain how.

The solution here is that it depends on which door he opens. If Monty Hall opens the leftmost remaining door, then there is a 50% chance that you will guess correctly, regardless of whether you switch or not. This is because you knew beforehand that, if you chose correctly, Monty Hall was guaranteed to choose the leftmost remaining door, so his choice to open this door gives you new evidence that makes it more likely that your original choice was correct (contrast this with the original problem, where his choice gives you no information about your original choice). But if he opens the rightmost door, then there is a 100% chance that switching is the correct choice (since Monty had to pass over the unchosen door on the left, and he only does this if he has to).

However, ChatGPT gives the following answer:

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.