Is Deal or No Deal an example of Monty Hall?

[Rhys Benjamin]

Something came up today which I thought I'd float here:

Does the Monty Hall problem applies to Deal or No Deal?

At the beginning of the game you have picked a box at random (from 22). At the end of the game, if you have rejected all offers along the way, you have two boxes left - the one you started with and one other. Let us say, for argument's sake, that the boxes contain £1,000 and £100,000. You reject the banker's final offer, and he then offers you the chance to swap the boxes.

Surely this is a bit Monty Hall-ish? At the start of the game you had a 1/22 chance of picking the £100,000 box, and yet now you have a 1/2 chance of picking it if you swapped?

[Innis Carson]

No, otherwise exactly the same reasoning could be applied to the other box, and you would reach the opposite conclusion. The Monty Hall effect only arises because, in the classic Monty Hall scenario, the rules of the game make a clear distinction between the grand prize door and the other doors (the distinction being that host specifically avoids opening the grand prize door, but can open the other ones). In Deal or No Deal, all of the boxes are completely interchangeable as far as the mechanics of the game are concerned.

[Gavin Chipper]

And that's the thread.