You are Here: Home

# general formula for the optimium banker's offer for the n box DoND game? Tweet

Discussion, revision, exam and homework help from KS3 to degree level including engineering, construction, design and technology, agriculture, PE and sports science.

Announcements Posted on
Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 21-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
1. general formula for the optimium banker's offer for the n box DoND game?
Is there a general formula for the optimum banker's offer for the 5 box and 8 box game of deal or no deal in terms of the box values in the game?

Several formulae have been suggested based on fitting curves to the empirical data of offers the banker made. But none has shown why the banker made those particular offers. Is there a mathematical argument which leads to an expression for the best (optimum) offer the banker could make on the average for a particular n box game; an offer which minimises the banker payout for that game?

(By the way, it is not just the average value of the boxes remaining! - a common mistake in discussions of this problem).
Last edited by nixbits; 30-07-2012 at 10:18. Reason: typo
2. Re: general formula for the optimium banker's offer for the n box DoND game?
You'd have to collate a study of a) all bankers offers with b) all revealed boxes at the time, over a fairly large dataset.

Then, you can study the banker's offer distribution and attempt to plot a couple of linear regressions between bankers offers and average value of unrevealed boxes. Assuming of course, the banker's offer isn't actually cheating and made with the knowledge of what's in the box.

You could also add in other factors such as the range of values of unrevealed boxes (people may 'play it safe' instead of getting £10) and how far along the game it is.
Last edited by SunderX; 30-07-2012 at 10:23.
3. Re: general formula for the optimium banker's offer for the n box DoND game?
You won't be able to do find it with maths because it all depends on how risk adverse the player is. The best offer is just the lowest that the player will accept but the banker doesn't know what amount that is. The banker must just try and judge by the person's behaviour how risk adverse they are.
4. Re: general formula for the optimium banker's offer for the n box DoND game?
But given a particular set of box values {a b c d e f g h } for say the 8 box; is there an optimum value in terms of a b c etc which minimises the pay out on the average?... imagine a population of players all with the same 8 box so the banker, on the average, would seek to make this optimum payout. Is there an analysis which gives this optimum value?