Monty Got a Raw Deal

“Monty this seems strange to me
The movies had that movie thing,
But nonsense has a welcome ring”
— Monty Got a Raw Deal, R.E.M. (1992)

Short of writing about the war in Iraq or Alan Greenspan, the best guaranteed debate-starter online is the so-called Monty Hall problem. I mentioned it in passing a week ago, and a spirited discussion immediately followed.

Columnist John Kay of the Financial Times, to whose column I was referring when I first wrote about the issue, followed up this week by shaking his head at the number of Monty-confused people who wrote in. The trouble is, as someone who posted elsewhere on my site has said, columnist Kay is confused himself.

Here is what Kay wrote in his latest column on the subject:

Contestants on the Monty Hall show choose from three closed boxes, one of which contains the keys to a car. After you have made your choice, Monty opens one of the two remaining boxes, which is empty. Should you alter your choice? The answer is yes. He might have spoiled the game by opening a box that contained the car keys, but he didn’t. Monty might have been blind drunk and could as easily have opened your box by mistake – but he didn’t. It does not matter what Monty knows, or is thinking. All you need know is that the box Monty opens is empty. [Emphasis added.]

Is columnist Kay correct? No. The key to the Monty Hall problem — and one reason that how you state it is crucial to people coming up with the correct answer — is that Hall a) knows where the car is, and b) his choice of doors is not random. (There is a good roulette-based explanation of this here.) It seems that letter-writers to the FT aren’t the only people who have trouble with the problem.


  1. One thing that the FT seems to have left out of their analysis:
    If he opens your box by mistake and it’s empty, you should almost certainly change your mind.

  2. I think misunderstanding the Monty Hall problem should be sufficient grounds for disqualification from jury duty.

  3. Videlicet says: