The Monte Hall problem

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?

Wikipedia says it is to your advantage to switch the door!!!

http://en.wikipedia.org/wiki/Monty_Hall_problem

But I agree with another reader who says that Wiki is wrong here:

Here's the example given by the reader:

When you flip a coin, the odds of it coming up HEADS is 1 in 2. {I know you all knew that.}
What are the odds of flipping a coin 8 times and getting all HEADS? 1 in 256.
Okay, so you flip a coin 7 times and get 7 HEADS. What are the odds that the next flip will come up HEADS?

1 in 2 of course. That's because previous results have no influence on future probability.

That's where the Monte Hall "puzzle" falls down. The previous action of Monte removing one of the doors has NO EFFECT on the future probability of which door the car is behind. There are 2 doors, so the odds are 1 in 2 that they already have the right door, and 1 in 2 that switching will get them the car.