User talk:Martin Hogbin/Monty

Car hidden behind Door 1		Car hidden behind Door 2	Car hidden behind Door 3
Player initially picks Door 1
Host opens either goat door		Host must open Door 3	Host must open Door 2
Switching loses with probability 1/6	Switching loses with probability 1/6	Switching wins with probability 1/3	Switching wins with probability 1/3
Switching loses with probability 1/3		Switching wins with probability 2/3

Solution

Say you initially pick either of the goats, the host must open the other door with a goat behind it in order to reveal a goat. So you have one door with a goat behind it and the host has opened the other door which also has a goat behind it. The remaining door therefore must have the car behind it. So if you swap, you get a car.

If you initially pick the car, it makes no difference which door the host opens, any other door has a goat behind it. so if you swap, you get a goat.

Player has picked a goat	Player has picked a car
	Player has picked Door 1 and the car is behind Door 2
The host opens the other goat door	The host opens the either goat door
Players who chose a goat and switch must get a car	Players who chose a car and switch must get a goat