Conclusion of our little quiz

Well, the answer is: You have to switch doors.

My first thought was as well that chances are similar but in fact they aren't. If you have chosen door 1 there are three possible outcomes:

• The car is behind door 1: If you stay you win / If you change the goat is yours.
• The car is behind door 2: If you stay you get the goar / If you choose to change you win the car.
• The car is behind door 3: The host had opened door 2 instead of door 3.
  

As you see the probability for you brand new car are 50% if you choose to change, wheareas they are 33% in the case that you stay with your first choice.

To put some maths in this conclusion one can read into the bayesian conditional probability. Well if you like to you are probably unique, once was enough for me :).