If my first choice happens to be a door with a goat behind it (which will be two times out of every three, on average), then Monty will reveal the other goat, leaving the door with the car behind it which I can get by switching.

If my first choice is the door with the car behind it (one time in three), then switching loses whichever goat Monty reveals.

So switching wins two times out of every three, on average.

I used three coins to represent the goats and the car and pretended to be Monty - it all became clear very quickly!

LFF