This thing is really counter-intuitive. My original figuring was a toss up. Your odds of being right changed from 1 in 3 to 1 in 2 after Monty opens a door. Considering Steve Prevette chose this one, I feel much better. I found this puzzle and an interesting article with some interesting answers @:

.:: Dean's World: The Brainteaser That Changed My World ::.
Here’s a sample explanation:

Before the other door is opened, you have three alternate futures, all equally likely. Opening one door closes off one, but it equally consistent with the other two. That is why people thing, "hmmm, 50/50".

BUT, the door that stayed closed ONLY stays closed in half of the future where you have the right door. And the door that stayed closed stays closed in ALL of the futures where IT is the right door.

SO:

All the futures started out equally likely

ALL the futures with the prize behind the opened door are foreclosed

HALF the futures with the prize behind your door are foreclosed

ALL the futures with the prize behind the remaining closed door are open.

Try something simpler. Here are your possible combinations at the beginning with the (P)rize, Goat (B)ooby Prize, and Chickens (B)ooby Prize. I eliminated the possible permutations because they don’t really matter.

Door......1 2 3

Combo 1 P B B

Combo 2 B B P

Combo 3 B P B

If you choose door number 1 and don’t switch, your chances are 1 in 3 of getting this correct. The same goes for any other door choice. (Let's say you always choose #1.) Monty then ALWAYS reveals A SINGLE DOOR (x) with a booby prize leaving you:

Door......1 2 3

Combo 1 P B x

Combo 2 B x P

Combo 3 B P x

2 times out of 3, Monty has eliminated the remaining Booby Prize leaving only the Prize behind the door you did not pick. Remember, Monty does not know which door the prize is behind. However, HE DOES NOT OPEN A DOOR AT RANDOM. The lovely Carol Merill only opens a door that has a Goat or Chicken behind it. The online version of the game that Jim posted above bears out this conclusion: You should always switch, you'll be right more often.

Would the two Steve’s, Statistical and Prevette like to chime in? Cari, how about you?