The Three Door Dilemma (also called the Monty Hall Dilemma)

Remember Monty Hall and the TV show Let’s Make a Deal? Monty offers you the contents behind one of three doors (only one door hides something valuable). After you make your choice, Monty will show you the contents of one of the two remaining doors, which was always a dud prize (like a goat). Then he will ask you whether you want to keep your original door choice, or switch to the other closed door. That is the big dilemma: is it better to keep your first choice, switch to the other door, or doesn’t it matter (because the odds are 50/50 with two doors remaining)?

Note: In this game, Monty always shows an empty door (goat) after you make your first choice, and then you are always offered a choice of keeping your first choice or to switch to the other door.

What do you think is the best strategy?

Always switch
Never switch
Does not matter (it’s 50/50)

How confident are you in your strategy?


Try to determine what the best strategy is by playing the game at least 20 times with each strategy. Are you surprised by the results? Check our explanation after you’ve played for a while.