If you know this one already, don’t attempt to answer it because that spoils the fun.

You are on a gameshow and you have got to the final round where there are 3 doors. Behind 2 are goats and behind 1 is a car (the aim of the game is to choose the car). The gameshow host, who knows where the car is, asks you to pick a door. You pick door number 1. The gameshow host then opens door number 3 and shows you that there is a goat behind it. The host now offers you the chance of sticking with door number 1 or changing your mind to door number 2.

Is it worth changing your mind or should you stick with your original decision?

stick with it. because they will not want you to win the prize so you think that that door is useless so they will move the prize to there. they might be a step ahead of you and think you will do that and then not change the position of the prize.

My problem is, surely this puzzle is completely undecidable (?) unless you know whether or not the presenter would WANT the contestant to win the car? Are we assuming they DON’T want you to? Because on a lot of game shows they like you to win - for instance, on Who Wants To Be A Millionaire, they’ve made the questions fractionally easier, because people win more money and therefore you get better viewing figures.

All this shitty maths crap aside, surely that’s the major factor?

yeah, it would depend upon whether the production people wanted you to win, if they didn’t you are in a bad way, if they do then you are still in a bad way because they might change the car to there so you pick it but you change.

This is the problem with posing complex maths problems on a philosophy board. People start doing that annoying thing where you have to pick at the question and ask if the host has been married twice before and if he likes cabbage.

This is a maths problem. Assume that the host is not biased in anyway to the contestant. He merely is there to pick a door which he knows has a goat behind. He is not trying to make the contestant win or lose.

you should always change your mind because the probability that you will get the car is greater.

We are fooled into thinking that the first door you choose changes it’s probability when the third door is removed but this is logically untrue. The probability of a door being the car does not change just because you have eliminated one other door.

Another good way of explaining it is if you use the model of 1000 doors. Say you choose door number 1, probability of choosing the car is 1/1000. Say then that the host, who knows the car is behind door 468, removes ALL the doors except 468 and 1. Are you going to keep with 1 considering you chose it when the odds were 1/1000, or are you going to choose door 468 which the presenter has purposefully not opened? Obviously you are going to choose door 468 because it would be madness not too.

This is the same principle with 3 doors but we are fooled into thinking it is different because of the smaller scale.

Ben, I don’t belive that to be true. You’ve simply illustrated a case of bluff, double-bluff, or no bluff.

Yes, the fact that 998 doors have been cleared to leave the one you’ve picked (1) and another door (498) points towards the car being behind door 498; it stands out suspiciously. But all we know is that there is a car behind one of two doors. Mathematically, the probability is exactly the same. If, as you say, this is just a maths problem, there is equal expectation of winning whether you change your mind or stick with your original decision.

So how to solve the problem? You weigh up all the factors, and, as all probabilities are even, the only thing that will influence your decision is that suspicious door 498. Now, either it’s a game of chance as to whether the host is bluffing or not by highlighting that door, or you tell us whether the host is working in our favour or not.

[This message has been edited by rich (edited 23 February 2002).]

The trick lies in remembering that the presenter is not in favour or malicious towards the contestant, he KNOWS where the car is and simply chooses at random one of the doors which is not the car.

surely it should come down to the production crew as they can change the postion of the car. the host cann only open doors, while the crew can switch things, or the crew can just decide to not give you the car whether or not you get the correct door.

Why is it so difficult for people to understand the concept of a “fun maths puzzle”. It doesn’t MATTER what colour shoes the crew were wearing or what the presenter had for dinner last night, THIS ISN’T REAL LIFE. Monty Python really hit the nail on their head with the scene in Life of Brian when Brian is preaching a parable about two servants and someone from the crowd shouts “What were their names?”

Next time i’ll put a WARNING note for people who find it difficult to separate real life and quaint probability puzzles.

no, no, no, no, no. it still makes no difference. who CARES which door the presenter’s fannying around with? either way there’s two doors left, and if the presenter is unbiased, it makes no difference. I HATE THIS FRIGGING PUZZLE… you’re all gay

we have golden gurnseys, no i don’t live on a farm i live on a small holding, yes we have horses, no we don’t have sheep, yes we have peacocks, no we don’t have cows, etc etc