Monty Hall problem

This is the popular math problem in an American TV show. They are panic because of the strange result. This is probability. We still don't understand in the AI era.

There are 3 doors. When you open the one of three, there is the gold. Two doors are empty.

You think that the probability is 1/3. However, you have the second chance. You can see where the empty door is.

Therefore, you have 50% chance to get the gold.

You are in front of the 3 door. This is zero, but you don't know yet. You have 1/3 probability. You can change your decision.

You got the gold. When you change the door, you increase the probability. This is 2/3 which is about 67%>50%. Each door has 1/3 probability, so (1)+(3)=2/3.

E(X) is expectation. Xi is the gold and Pi is probability.

AI is getting smarter because they have more chance for better solution. AlphaGo is well known.