You just took me back to my randomized algorithms class.  That was the hardest class ever. To this day, I find probability and combinatorics to be really really hard, but the Monty Hall problem is really a classic simple tool that people can use in their daily lives.

Monty Hall was asked about the "Monty Hall" problem once. He pointed out that on the actual show once a contestant turned down a choice they were never offered it again -- so after choosing door 1, 2, or 3, they would never be asked if they wanted to switch to a door they turned down.

The puzzle's a classic, and sounds very much like the show, but it wouldn't actually happen on the show.

Warbo, the middle door being chosen the most often is NOT the reason for this seeming paradox. In fact, I would venture to guess the web interface with the screenshot in the blog posting selects a door randomly for the money. That is certainly the assumption in the puzzle.

The KEY to this puzzle is that the game show host is aware of what is behind each door.

Warbo, if the game show host was unaware of what is behind each door and selects a door at random, it happens to have a goat behind it, and he asks you if you want to switch, then yes, you have a 50% chance of having the money behind your door.

But run that scenario a few times. 33% of the time, the game show host will select a door and the money will be behind it! AND THAT NEVER HAPPENS IN THIS SCENARIO. THE HOST WILL SELECT A GOAT 100% OF THE TIME BECAUSE HE KNOWS WHAT IS BEHIND THE DOORS.

THAT is why your door has a 33% chance of having the money behind it.

Think of it like this - instead of 3 doors, there are 100 doors. You select one door. The game show host opens 98 other doors and each has a goat behind it. He asks you if you want to switch.

Now, what's more likely - you selected the right door the first time? Or is it more likely that the game show host knowingly opened all the other doors except the one with the money in it? You had a 1% chance of being right the first time. And that does not change throughout the puzzle.

In this scenario there is just a 1% chance you have the right door - and a 99% chance that if you switch you win!

Regardless of what you pick, its still more than you left the house with in the morning-- even if its a goat.

Granted, big money is always nicer, but there is no evil in a year supply of Rice a Roni (frequently given as a parting gift back in the 70's from gameshows).

its 67% chance of winning because the host has knowledge of which door had the winning prize behind it and which had the dud and is forced to open the door with the dud.

Consider this. After your first decision there are only three possible outcomes.

You chose the prize right the first time.

You chose dud 1.

You chose dud 2.

Since a dud must be removed by the host. Its easy to see that by switching you increase your chances of winning (the only way you could switch and lose is if you picked the prize the first time, if you chose either dud the first time you'd be better off switching)

The following is a list of all possible outcomes of the game
D = first choice is dud
P = first choice is prize
S = switch
NS = no switch
W = win
L = loss

D-S-W (first dud)
D-S-W (second dud)
P-S-L
D-NS-L (first dud)
D-NS-L (second dud)
P-NS-W

As you can see, by switching, you attain a 67% chance of winning the game.