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Hi Strange Famous,
I do love this problem. The way I try to explain it is to ask you to think of Monty as a gardener or a goat weeder to be more precise.
The original garden of possibilities has the following configuration;
goat – goat – car
goat – car – goat
car – goat – goat
or 6 goats to 2 cars.
If you fence away box 1 possibilities from Monty by picking it first he can't weed out any goats from it. He is left with boxes 2 and 3.
In them he has the following possibilities;
Goat – Car
Car – Goat
Goat – Goat
or 4 goats to 2 cars, but then he gets to work. Because he has to weed out a goat each game (by opening a goat door), in the above grid he has to remove 3 goats leaving car – car – goat or 2 to 1 chances of a car.
So the question becomes do you stay in your unweeded patch or jump the fence into Monty's weeded one? Answer is simple, jump every time.
Don't get too stressed if it doesn't come to you right away as I have read an autobiography of the great mathematician Paul Eros and he too got it wrong initially.
Could be a little too much weed in the above explanation but hey.
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