I believe that, due to Monty's knowledge of which door conceals the car, your best bet is to switch doors. An explanation (a lengthy, not entirely coherent explanation) is below.
My understanding of this problem is as follows:
Monty chooses one door which to open. The other two are similar in that they are not chosen by him, but they are dissimilar in why they are not chosen by him. The unchosen door which you first select is unchosen simply because it is the door which you selected (and Monty cannot reveal to you whether your first selection was correct or there is no question of whether to switch doors). The remaining unchosen door was not chosen because the chosen door had a goat behind it. To put it another way, by not choosing this door, Monty wasn't forced to show you the car (although, it is possible that he wouldn't have been forced to show you the car, even if he'd not chosen the chosen door instead of this one).
So Monty not choosing the door you initially selected gave you no new information about what's behind it (as he would have done it regardless of the location of the car). However, Monty not choosing the other door does give you new information: namely, that not choosing it didn't result in you seeing the car through the chosen door. (If one of the two doors which you didn't initially select is randomly eliminated -- equivalent to your random selection of a door when the game began --, it cannot, likewise, be said that Monty not choosing the door which you selected will result in Monty not revealing the location of the car. That is, if you initially select a goat door, and the other goat door is randomly eliminated, Monty not choosing your door does result in Monty revealing the location of the car.)
Mathematically, your first selection is from three doors, one of which contains a car -- hence, there is a one-in-three chance that you'll select the door behind which is the car. Monty's choice of which door to open is between the remaining two. When making this decision, he may be faced with three car-goat arrangements (for simplicity, I'm just going to call the remaining doors "left" and "right," since there must be one of each): car left, goat right; goat left, car right; or goat left, goat right. Each of these is equally probable. In either of the first two, Monty must select the one door behind which is the goat, which means that the door not chosen must be the car; this is the case in two thirds of the possible arrangements. In the remaining case, Monty can select either goat door and the remaining door is also a goat. So in two of the three arrangements (or two thirds of them) the door not chosen based on Monty's knowledge of the location of the car actually conceals the car. The other one third of the time, Monty's knowledge is not needed and your first selection is, in fact, the correct one.
2/3 + 1/3 = 1, so the car is still behind one and only one of the doors. But it is twice as likely to be behind the door which you didn't initially select. Monty tells you that by always selecting a non-car door to open. (If Monty selected a door at random, one third of the time he would select the car door and you'd have no chance of winning; two thirds of the time he'd select a goat door and then both doors would possess fifty-fifty odds. [0 + 1/2 + 1/2] / 3 = 1/3, so each door would have a one-in-three chance before he opened one of them and a one-in-two chance after he opened a non-goat door. That is the situation which you described.)
The whole idea here is that you have more information about the door which you didn't initially select.
Slashdot Mirror
Did anybody notice that the "30" is vertically symmetric? So was the correct answer, "8 is the only one which is doubly symmetric?"
Wrong again, Mensa.
My understanding of this problem is as follows: Monty chooses one door which to open. The other two are similar in that they are not chosen by him, but they are dissimilar in why they are not chosen by him. The unchosen door which you first select is unchosen simply because it is the door which you selected (and Monty cannot reveal to you whether your first selection was correct or there is no question of whether to switch doors). The remaining unchosen door was not chosen because the chosen door had a goat behind it. To put it another way, by not choosing this door, Monty wasn't forced to show you the car (although, it is possible that he wouldn't have been forced to show you the car, even if he'd not chosen the chosen door instead of this one).
So Monty not choosing the door you initially selected gave you no new information about what's behind it (as he would have done it regardless of the location of the car). However, Monty not choosing the other door does give you new information: namely, that not choosing it didn't result in you seeing the car through the chosen door. (If one of the two doors which you didn't initially select is randomly eliminated -- equivalent to your random selection of a door when the game began --, it cannot, likewise, be said that Monty not choosing the door which you selected will result in Monty not revealing the location of the car. That is, if you initially select a goat door, and the other goat door is randomly eliminated, Monty not choosing your door does result in Monty revealing the location of the car.)
Mathematically, your first selection is from three doors, one of which contains a car -- hence, there is a one-in-three chance that you'll select the door behind which is the car. Monty's choice of which door to open is between the remaining two. When making this decision, he may be faced with three car-goat arrangements (for simplicity, I'm just going to call the remaining doors "left" and "right," since there must be one of each): car left, goat right; goat left, car right; or goat left, goat right. Each of these is equally probable. In either of the first two, Monty must select the one door behind which is the goat, which means that the door not chosen must be the car; this is the case in two thirds of the possible arrangements. In the remaining case, Monty can select either goat door and the remaining door is also a goat. So in two of the three arrangements (or two thirds of them) the door not chosen based on Monty's knowledge of the location of the car actually conceals the car. The other one third of the time, Monty's knowledge is not needed and your first selection is, in fact, the correct one.
2/3 + 1/3 = 1, so the car is still behind one and only one of the doors. But it is twice as likely to be behind the door which you didn't initially select. Monty tells you that by always selecting a non-car door to open. (If Monty selected a door at random, one third of the time he would select the car door and you'd have no chance of winning; two thirds of the time he'd select a goat door and then both doors would possess fifty-fifty odds. [0 + 1/2 + 1/2] / 3 = 1/3, so each door would have a one-in-three chance before he opened one of them and a one-in-two chance after he opened a non-goat door. That is the situation which you described.)
The whole idea here is that you have more information about the door which you didn't initially select.