The Monty Hall problem goes like this.

Say you are a competitor on the game show "Let's Make a Deal" and legendary game show host Monty Hall has his classic choose which door contest.

Behind one is a new car, behind the other two are goats.

You choose one door.

Before that door is opened, Monty opens one of the remaining doors so you can see what is behind it.  And it's a goat.

Question:  Should you keep your first choice or switch to the last remaining door.

Answer: You should switch.  It is a definitive choice.  Switch.

The logic is that if you keep the door you have a fifty fifty chance but if you switch you have a 2/3 chance.  Because you are essentially choosing the 2 doors choice over the one door choice.

Don't believe me go here and try it out.

For a more detailed explanation go over here: wikipedia

here is a decision tree from that article.  Assuming the player chooses door 1 to begin with.