Deal or No Deal - a mathematicians's perspective.

Well, given it's not linear, what is it instead? Is there perhaps a cutoff point for a given person, at which the bird in the hand is worth too much to live with having thrown away? Some fraction of net worth or current salary, perhaps - i.e. you have to put the game in wider context?

I had some thoughts about that. I decided it was an individually dependent function of effort and time. For simple things, I use the "windscreen washing" rule of thumb - how much money would you make if you spent that time washing windscreens at a stop-light. Perhaps I should have a secondary measure based on selling second hand computer equipment.

What I'm really trying to do is make some theoretical link between the nonlinearity and the fact that the game is non-iterated, rather than to choose an explicit (and sociologically derived) function for an individual.

But is there actually a different optimal strategy for a non-iterated game? I think it's just a continuum of risk levels - you're willing to accept up to some point on the curve, and your choice in practice is going to be affected by factors outside of the game itself. If you were already a billionaire and didn't care, you'd play till the end.

Yes. If it's iterated, you hit the expectation bang on the nose every time to maximize your long term winnings.

Is this a form of martingale? Like in gambling situations?

Yes, it is.

And here is some analysis I've just found, but don't have time to read now.

It's the philosophy behind the saying, "A bird in the hand is worth two in the bush. " Quiz shows exploit the uncertainty many people feel when they are not quite sure whether to go with a maximax strategy or a maximin one: "Okay, Mrs.

I was repairing a computer at the house of a friend of mine, and he happened to have it on...
Now, because his computer has been on the fritz for a while I've been round there quite a lot recently. (He has this *I'll try and fix it until it is so broken I have to get Hunter out to make it work again* attitude...) I saw some geezer called *Bunny*, who was one of the box holders, and he was singing at people...
On the last occasion, he was the contestant, and...hey, he is an annoying bugger, embarassing to the point of wanting to throw things at the TV. Every time he yelled *No Deal!* and jumped up and down like a stock-broker on a pogo stick I had to be restrained from throwing the mouse through the screen...and yet he was...I dunno...charismatic? Entertaining? Someone upon which to hang all your pent up frustrations?
His formula seemed, in the end, to be based on the dream and the fortune teller...and it earned him a hundred grand...and to be fair to him, he even predicted correctly where the quarter-mill was going to be...
Trouble is, I can't help feeling that A) He was under the impression that he was the star of the show, and B) Someone at Channel 4 will offer him a presenters job...

*singger* I think watching it three times has been enough for me, but that doesn't stop the mathematics from going around and around in my head.

I did a course on this kind of thing at Durham - it's called decision theory. The examples we worked with generally involved cake, and you'd be given a problem generally involving cake.

Assume that tea shops in Durham only sell three types of cake - chocolate cake, ginger cake, and fruit cake. All three kinds of cake cost the same, but you're unlikely to like them all equally. So we assign them utility values. Suppose you really love chocolate cake, quite like ginger cake, and don't like fruit cake all that much. Utility values might go like this:

Chocolate: 10
Ginger: 7
Fruit: 1

You're in tea shop A, where they only have ginger cake. You know that next door is tea shop B, where they will either have chocolate cake or fruit cake, but if you leave shop A, the last piece of ginger cake will be sold. If the probability of there being chocolate cake in shop B is 0.5, will you risk changing shops?

The expected utility value (EUV) of the cake in shop A is 7. The EUV of the cake in shop B is 0.5 + 10*0.5 = 5.5

So you stay put.

If there's a 2/3 chance of there being chocolate, the EUV of shop B is also 7. At this point, psychology comes in. Are you risk-prone or risk-averse? The risk-prone person is more likely to take the chance on the chocolate cake. They're also more likely to say 'no deal' and therefore need a bigger offer to tempt them to deal. So part of the game is convincing the banker that you're risk-prone to encourage him to make higher offers.

I had a brief essay I wrote on this subject but I don't know where I left it. But decision theory was one of my favourite maths courses, even if I did leave every lecture desperate for cake.

Slightly O/T.

An old school friend was on it. I heard on the rumour mill that the producer tells everyone to act up. If you are smiling looking cute (as my school friend was), that's not enough, he told her to get up and dance!

Anyways, I was wondering about the maths, but I couldn't be bothered to figure it out. I *did* however thing "Hmm, if shevek was on that program, he would definately have a statistical method for determining when to deal or not" :P

I like it when they win 1p !!!

I personally think they get toooo greedy on deal or no deal and sometimes even 10k would change their lives but they still have a £50k box up
there and they continue to gamble and lose. Anyway I am building my very own deal or no deal game soon via joomla and it will be hosted
at joomla tutorial