switchStrategy openingGambit DoorA DoorB DoorC

Monty Hall has hidden a prize behind one of these doors.

Monty invites you to choose one of the doors but won't let you open it just yet.

Monty opens one of the other doors to reveal - a goat!

He then asks you if you would like to change your mind or to stick with the door you originally chose. It's time to make your mind up, which door are you going to open?

Bad luck! When you opened your chosen door it also revealed a goat.

Congratulations! When you opened your chosen door it revealed a fantastic prize that you are now free to take home.

 The Red Door An open door - this door is now open revealing a goat! An open door - this door is now open revealing a fantastic prize! The Green Door An open door - this door is now open revealing a goat! An open door - this door is now open revealing a fantastic prize! The Blue Door An open door - this door is now open revealing a goat! An open door - this door is now open revealing a fantastic prize!

Well, whether or not you won the prize did you make your decision by guesswork or logical reasoning? The question is, if we allowed you to play this game repeatedly what strategy should you adopt?

Always stick to the first door you chose. Always switch to the other closed door when Monty offers you the chance. It really doesn't matter whether you stick or switch - the outcome's the same. incomplete openingGambit DoorA DoorB DoorC DoorB DoorA DoorC DoorA DoorB tempter tempter 0 goat 1 prize poser poser 2 completed No. Initially, the probability of the prize being behind each door is 1/3. Opening a losing door can't possibly make this go down for the remaining closed one! In fact you should never stick to your original decision. Yes, you should always switch doors when offered the chance. Congratulations, perhaps you should think about a career as a TV game show contestant?

No, you should infact always switch doors. This problem has fooled many mathematicians since it was first posed in an American magazine article and continues to present a seemingly paradoxical answer!

The probability of your first choice door hiding the prize is 1/3 and this can't change. But, 2/3 of the time you'll be wrong with your first choice and, by revealing a goat, Monty is effectively telling you which door the prize is behind the remaining 2/3 of the time! So by switching doors, your chances of getting the prize go up to 2/3!