> The second person has NO choices.

In the setup I described, he does. That's just the point. There are two closed doors in front of him. He can choose either one.

The two people are not competing. Both see two closed doors. The first chooser, who has seen a goat and switched, now has a 2 in 3 chance of finding the car by guessing. The newcomer, who's just shown up and hasn't seen or done anything, has only a 1 in 2 chance. With the same two doors.

It sure feels paradoxical to me.

Recall DMcG's bowl of tickets. In that situation, knowing the color of the winning ticket ahead of time obviously increases your odds of picking it from a bowl with your eyes open. Your odds are dependent on your actual knowledge.

But in the case of the now-revealed goat, the chooser doesn't have to know or understand anything. Just switching increases his odds - accidentally. "Information" in the ordinary sense appears to be irrelevant. And the uninformed second chooser is stuck with 1 in 2 no matter what he does or thinks.

I envy anyone who thinks it's conceptually straightforward. Maybe it's all elementary, if you've had the right course.