Brain Teaser

You are a contestant on a game show, and are shown three doors. Let's call them Doors A, B, and C.

Behind two of the doors is absolutely nothing, but behind one is a vast cash prize.

To start off with you are told to pick a door. The game show host then opens one of the two doors you did not pick to show you there is nothing behind it.

You are then given the option of sticking with your first choice of door or changing you mind and picking the other un openned door. You then open the door you have picked in the hope you win the prize.

So say the cash was behind door A and I initially chose Door B the host would tell me that there was no money behind door C, and I would have the choice of openning door B (my first choice) or door A (changing my mind).

What is the best stategy for playing the game, sticking with your first choice, changing your mind, or doesn't it mattter?

with my luck I would be better off mugging the host. I think that actually in this instance it has been proven you are better off going with the other door.

changing your mind

You are both right,

if you change your mind you have a 2/3 change of winning.

Initially I thought it didn't matter as you always had to choose between two doors but then I thought about it some more!

This is a rehash of another thread, which had a goat behind two doors instead of nothing, and a worthwhile prize behind the third door.

It turns out that the fact that goats were offered as a consilitory prize actually
alters your probablility for picking the correct door.


Check the thread at : A Probability Puzzel by Slaine

Chuckle, who would want a goat as a consolation prize? :D :D

is there an explanation as to why changing your mind is better than sticking to your initial choice?

Yes, check the link a couple of posts up.

the short answer is this:

your first pick is based on two bad choices.
remove one bad one, and switching gives you a much better
choice, better than your first one, even though it seems that you've the same chance with the two doors, you don't because
of previous conditions changing.... okay there is no short answer.
but it is all explained, you just have to read a bit.

A quick analysis.

2/3 of the time your initial choice was wrong. Switch & win.
1/3 of the time your initial choice was right. Switch & lose.

Check the above: 2/3 of the time, switching is a good idea.