Like the last posting, this example is reasonably well known in maths type circles.
There is a quiz show on TV. In this quiz show there is a quiz show host, a contestant and 3 doors.
The doors are closed and the contestant cannot see what is behind them. But the contestant knows that behind 2 of the doors is a goat, and behind one of the doors is $1,000,000
The quiz show host asks the contestant to choose one of the doors by standing in front of it. The door that the contestant thinks has the prize behind it.
After suitable bla bla and building up the tension the quiz show host opens one of the other 2 doors to reveal a goat.
The quiz show host then tells the contestant he has a “special offer”, he has a choice, he can stick with the door he is at – Or he can swap to the other unopened door.
Massive tension…
After the contestant makes his decision – the door he has chosen is opened – and he gets whatever is behind it – be it a goat or the $1,000,000
Now here is the question, when the quiz show host asks the contestant if he wants to stick with the door he’s already selected or swap to the other unopened door – What should he do??
- He should stick
- He should swap
- It makes no difference
Don’t read further unless you want the answer.
Don’t read further unless you want the answer.
He should always swap. The odds of winning the $1,000,000 are much higher if he swaps.
Yet not a single person I have ever told this to has initially realised it.
Every one (including nuclear physics Phds) have insisted (sometimes for hours!) that it’s 50/50 – And it doesn’t make any difference if he sticks or swaps.
I said exactly the same the first time someone asked me.
Me too, alas.
This is actually explained in a book I have on investing, as an example of how most people (which I guess includes me!) misunderstand statistics, and hence how those who study it in detail tend to do better at investing. (Although why they would then tell the rest of us this, I don't follow!!!) (I can't find the book, but effectively you have a 2 in 3 chance of winning by swapping and a 1 in 3 chance by sticking.)