It’s easy to construct alternate examples of the Monty Fall problem that clearly weren’t in the training data. For example, from my experience GPT-4 and Bing Chat in all modes always get this prompt wrong:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You know that the car is always behind door number 1. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
Notably, if you tell it to think step by step it gets the question right and answers with:
This problem is known as the Monty Hall problem. In the original problem, the car is placed randomly behind one of the three doors, and the host always opens a door with a goat after you make your initial choice. However, in your variation, the car is always behind door number 1.
Let’s analyze your version step by step:
You initially choose door No. 1, which always has the car behind it.
The host, knowing what’s behind the doors, will always open one of the other two doors, revealing a goat. In this case, he opens door No. 3.
Now you are given the option to switch your choice to door No. 2.
In this version of the problem, it is NOT to your advantage to switch your choice, because the car is always behind door No. 1, and you have already chosen that door. If you switch to door No. 2, you will end up with a goat instead of the car.
This is honestly pretty similar to how humans behave most of the time. They pattern match and don’t really pay close attention. However, if you give cues that something is actually important, for example by putting them in an exam room and telling them a test will be graded, they can do somewhat better. Telling GPT-4 to think step by step does something similar.
It’s easy to construct alternate examples of the Monty Fall problem that clearly weren’t in the training data. For example, from my experience GPT-4 and Bing Chat in all modes always get this prompt wrong:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You know that the car is always behind door number 1. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
Notably, if you tell it to think step by step it gets the question right and answers with:
This problem is known as the Monty Hall problem. In the original problem, the car is placed randomly behind one of the three doors, and the host always opens a door with a goat after you make your initial choice. However, in your variation, the car is always behind door number 1.
Let’s analyze your version step by step:
You initially choose door No. 1, which always has the car behind it.
The host, knowing what’s behind the doors, will always open one of the other two doors, revealing a goat. In this case, he opens door No. 3.
Now you are given the option to switch your choice to door No. 2.
In this version of the problem, it is NOT to your advantage to switch your choice, because the car is always behind door No. 1, and you have already chosen that door. If you switch to door No. 2, you will end up with a goat instead of the car.
This is honestly pretty similar to how humans behave most of the time. They pattern match and don’t really pay close attention. However, if you give cues that something is actually important, for example by putting them in an exam room and telling them a test will be graded, they can do somewhat better. Telling GPT-4 to think step by step does something similar.
I’m not sure if I’m missing something. This is first try after reading your comment: