Nigel Parsons had it right.

Taking the original Car/Goat/Goat scenario, remember that Monty knows where the car is. There are three equally likely sequences of events if you switch.

1) You choose the Car. Monty shows a Goat. You switch and get the other Goat.
2) You choose Goat 1. Monty shows a Goat. You switch and get the Car.
3) You choose Goat 2. Monty shows a Goat. You switch and get the Car.

So 2 out of 3, you get the car.

If you don't switch, there are another three equally likely sequences of events.

1) You choose the Car. Monty shows a Goat. You don't switch and get the Car.
2) You choose Goat 1. Monty shows a Goat. You don't switch and get the Goat.
3) You choose Goat 2. Monty shows a Goat. You don't switch and get the Goat.

So 2 out of 3, you get a goat.