Mystery solved! The answer to your OP is that the reason anyone can trust ChatGPT for code is that they use a much better model than the one you're using! GPT-3.5 is ancient and way behind GPT-4. In fact, there are now tens of organisations who have developed model classes way ahead of GPT-3.5.
ChatGPT is just the brand. I guess you're using GPT-4, but if you're using the default model (GPT-3.5) that would certainly explain below-expectation results.
I don't think there's a contradiction between being something that just generates text and being something that does have thought processes and intention.
Not logical. It doesn't follow from the assumption that the host would not pose the question "Hey, here's the car, wanna switch?" that the contestant would automatically lose. You could just as well speculate that if the host opened the door to the car the contestant would automatically win the car.
If the format of the game allows him to show the car to the player, how could his personality not enter into it? In every case where the player picks a goat-door, the host will be presented the option to either reveal the car or the goat. I mean, one can imagine various complicated scenarios in which the host might reveal the car exactly 50% of the time in such cases, but none seem like they can be reasonably arrived at.
I don't think your interpretation of the sentence is sensible. The sentence mentions that the host knows what's behind the doors. So, if he is allowed to open the door with the car, the problem would become insoluble and would just be about speculating on the host's personality. And it definitely doesn't support the conclusion that the probabilities become 50/50.
It's simple. To begin with it's 1/3 your pick is right. You know that a goat will be revealed. So it's absurd to suppose that the fact that a goat is revealed has increased the probability of your initial guess being correct.
Which door is opened to reveal a goat is totally irrelevant, as either would (under the absurd supposition) increase the probability of the initial guess to 50%. In other words, an increase to 50% would be guaranteed from the very beginning. So a contradiction is reached with the obvious fact that initial prob is 1/3.