I’ve always thought this an interesting problem.. not least for the amount of discussion and disbelief that always entails.

‘Suppose you’re on a game show and you’re given the choice of three doors. Behind one is a car, behind each of the others is a goat. You pick a door, say door A, and the host, who knows what’s behind the other doors, opens another door, say B, which has a goat. He then says : “Do you want to switch to door C?” Is it to your advantage to take the switch?’

I’ll put the answer in the 1st comment. Keep in mind the solution is somewhat counter-intuitive and has been very controversial in the past!

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on 26 May 2005 at 7:52 pm |cfgYou should always switch.

(although this is not intuitive!)

Check out this website for some discussion of the problem and a better explanation than I will give you.

http://www.math.toronto.edu/mathnet/games/monty.html

In essence: “If you adopt the non-switching strategy, you will win whenever your original guess was correct (which has a 1/3 probability of happening), and lose otherwise. If you adopt the switching strategy, you will lose whenever your original guess was correct, but you will win whenever your original guess was wrong (which has a 2/3 probability of happening).”

on 27 May 2005 at 12:56 am |ChrisWow, is that what it’s called?!

I wrote a little online game to test it a couple of months ago, although using a ball and three cups rather than cars and donkeys. Here.

My explanation is not very good, but it collects the statistics for every game played, and it’s working out as expected (or rather not expected).