[542354234235]

> unless it is explicitly stated that Monty knows where the car is and that he deliberately opens a door with a goat.

That has been part of the explicit problem ever since it was first presented back in 1975.

"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 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?"

[jonsen]

It does not clearly say that it is Monty’s procedure to

- allways open a door

- allways open a door with a goat

- and not open a door at random

Often discussion of the solution reveals that this is not clear.

[542354234235]

There are three doors. You have picked one, leaving two other doors. It absolutely explicitly says he opens one door. The only options are a goat or a car. If it was a car, you would have lost already and so there is no problem. If it was random, you still get the same information (what is behind one of the unpicked doors).

[jonsen]

> If it was random, you still get the same information

No, if both you and Monty pick a door at random, there’s 1/3 chance of a car behind each door. If Monty’s door reveals a goat, it’s 50/50 for the remaining two doors. It’s mandatory to specify Monty’s procedure precisely.

[jibal]

This is goalpost moving that has nothing to do with the original point. If people misunderstand the conditions of the problem, that has nothing to do with intuitions about probability.

I won't respond further.

[jonsen]

> nothing to do with the original point.

Agree, but my point is that the Monty puzzle is a bad example to use educational if not careful.