c4countdown

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?

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.

And that's the thread.

Gavin Chipper wrote: ↑Sat Nov 09, 2019 7:27 am And that's the thread.

Not quite ... an alternative explanation:
The essence of the Monty Hall problem (& supposed paradox) is that the quiz master knows which box the prize is in. Once he reveals this knowledge (by opening doors) all boxes/doors are not equally likely any more.
However in "Deal or No Deal" Noel Edmonds literally knows nothing (hard to believe I know). So it's a straightforward probability problem - each of the unopened boxes is equally likely to hold the prize as any other. I.e. it's a literal game of pure chance! How anyone managed to drag a game show out of it beats the shit out of me, but hey-ho!

John Garcia wrote: ↑Tue May 24, 2022 6:58 pm

Gavin Chipper wrote: ↑Sat Nov 09, 2019 7:27 am And that's the thread.

Not quite ... an alternative explanation:
The essence of the Monty Hall problem (& supposed paradox) is that the quiz master knows which box the prize is in. Once he reveals this knowledge (by opening doors) all boxes/doors are not equally likely any more.
However in "Deal or No Deal" Noel Edmonds literally knows nothing (hard to believe I know). So it's a straightforward probability problem - each of the unopened boxes is equally likely to hold the prize as any other. I.e. it's a literal game of pure chance! How anyone managed to drag a game show out of it beats the shit out of me, but hey-ho!

I think that's what Innis said.