## April 12, 2006

### A mathematical query

On Deal or No Deal, if you get all the way to the end without dealing you get the option to swap your box for the last remaining box. Query is, should you?
Is it the same as the two goats and a car game show principle? (Three doors, behind two are goats, and behind one is a car. You choose a door, the gameshow host opens one of the other doors to reveal a goat. He gives you the option to change doors. In this situation you should change (assuming you want to find the car!).) Or is it slightly different somehow? Assume we have got right to the end and the banker's final offer has been rejected.

### 8 comments by 5 or more people

1. #### Helen Ryan

I'd quite like to win a goat.

12 Apr 2006, 17:19

2. That's what everyone says when they're given this problem! I think the game show industry may be missing a trick in not giving away goats as prizes.

12 Apr 2006, 17:31

3. #### David Kelly

I would say that it would depend on which two values are contained in the two boxes.

12 Apr 2006, 18:02

4. #### Colin Thomas

As a maths student taking a break from revision, I reckon that it doesn't matter especially whether or not you switch. If the two remaining prizes are £A and £B, then the expectation for your box is £(A+B)/2, and the expectation of the other box is also £(A+B)/2. The fundamental difference with the goats/car thing is that the gameshow host knows where the car is, so always opens a door with a goat behind it. In Noel's case, he doesn't know which box contains which amount of money… and doesn't do anything that could affect the expectation, anyhow. So basically, change boxes if you're feeling lucky.

12 Apr 2006, 18:55

5. Well, assume you want the higher of whichever boxes are left.

12 Apr 2006, 18:55

6. Regardless, as I'm not a mathematical person (by any stretch of the imagination) isn't Deal or No Deal great? Fantastic procrastination TV!

Also, the Banker will only offer swap if it makes good TV and usually if the two figures left have quite a large differential. (I didn't see this evening's though- so I may now be proved wrong.)

After sitting and watching with Andy on numerous occasions (plus trying to introduce it to Neil) the mathematical aspect of the programme seems quite topsy-turvy. While the Banker appears to offer the rough average of the remaining numbers, there is the other aspects of a) making watchable TV, and b) ensuring the programme doesn't lose too much money.

12 Apr 2006, 19:55

7. It's a different dealy… in the first the chances are 2 to 1 that you started with the goat, so if you really want to get the car you should swap. However, in DOND (I think it deserves an acronym) the boxes are all independant and therefore, it makes no difference.

Sometimes the people on the show annoy me though. A guy the other day started going really quick and when he hit a high number decided he should slow it down… seriously, it makes noooooo difference!

12 Apr 2006, 21:17

8. #### James Miles

Doesn't it?

DOESN'T IT?

Yes, you're right. It doesn't.

06 May 2006, 15:39

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