China DOS Union

The probability that you choose correctly for the first time is 1/3.

Therefore, the probability that the car is in the other two doors is 2/3.

The host points out a door. If you initially chose incorrectly (with a probability of 2/3), then the remaining door definitely has the car.

If you initially chose correctly (with a probability of 1/3), the remaining door definitely has no car.

So after the host's prompt, if you don't switch, the correct probability is 1/3 * 100% + 2/3 * 0 = 1/3.

If you switch, the correct probability is 1/3 * 0 + 2/3 * 100% = 2/3.

This depends on how the host is deliberately and with what mentality.

The host originally thought, there are 1000 doors, no one can choose the right one. This activity is just a facade. The boss has already said that this program has no money at all. Holding a car-drawing activity is just to increase a little popularity.
Every time the activity is, after someone chooses a door, immediately open the door where the car is hidden (actually the car is just a model).
Then announce "Sorry, your luck is still a little short, I hope you win next time. Okay, dear viewers, this episode of the program is over here. See you next time for the lucky car-drawing activity!"

But I didn't expect that I forgot to burn incense for the God of Wealth when I went out today. You just happened to choose the car. What should I do?
The host's face turned white with anxiety, but still forced a smile, and quickly thought in his heart: "Fortunately, the door hasn't been opened yet. I have to think of a way quickly, maybe there is still a way."

Suddenly remembered that when I was wandering on水木BBS, I seemed to see a theory that if a door with no car is opened, you should change your choice. The reason is also forgotten. Anyway, I didn't understand it at that time, and it seemed to say that no matter what the host thinks, you should change. If this person also saw this question or just couldn't figure it out, then there might be a chance. Alas, there's no way, just do it.
So the host opened 998 empty doors tremblingly, and then said to you: "Dude, give everyone another chance. You see I opened 998 doors, none of which are cars. Your luck is quite good. Now there are two doors left. I'll give you a chance to change. Do you want to change?"

If the host is ko, I won't change it.

That makes sense!
The host is really unfair!
I really want to give him a good beating!