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        riddles >> general problem-solving / chatting / whatever >> Deal or No Deal strategy?
        
(Message started by: mfirmata on Mar 7^th, 2006, 9:25am)

Title: Deal or No Deal strategy?
Post by mfirmata on Mar 7^th, 2006, 9:25am

Is there any strategy to the game show "Deal or No Deal"?

I understand the probabilities and associated expected values of the prizes (within the remaining suitcases after a number of known valued case have been removed) can be calculated, but when it comes down the final suitcases, is it better to keep the original choice, choose the other suitcase, or take the deal (which is likely to be calculated to be less than the expected value of the original suitcase.)

I'm thinking of the Monty Hall Problem here and wondering if it applies in any way to Deal or No Deal.

Title: Re: Deal or No Deal strategy?
Post by JocK on Mar 7^th, 2006, 10:06am

Can you explain this game show "Deal or No Deal" in a bit more detail?

Title: Re: Deal or No Deal strategy?
Post by rmsgrey on Mar 8^th, 2006, 5:12am

You have 22 boxes, each containing a different sum of money, one of which is randomly assigned to the contestant. The contestant then opens the other boxes one by one to eliminate possible sums of money from his box.

The process is complicated by a hostile banker, whose stated aim is to minimise his losses, who attempts to buy the contestant's still unopened box from him at certain points - after the first 5 boxes are opened, then after every third box after that. Once the contestant takes an offer, that ends the game, but they play on to see what would have happened (and fill the time). The banker's offer is always below the expected value of the remaining boxes, with the precise shortfall varying depending on his mood, the distribution of unrevealed values, and his judgement of the contestant. For instance, yesterday's show here in UK had the last two boxes containing a quarter million and one pound, which attracted an offer from the banker of 75 thousand, which the contestant took (and then was revealed to have been holding the quarter million all along)

From memory, the sums of money are:

1p
10p
50p
£1
£5
£10
£50
£100
£250
£500
£750
£1,000
£3,000
£5,000
£10,000
£15,000
£20,000
£35,000
£50,000
£75,000
£100,000
£250,000

Title: Re: Deal or No Deal strategy?
Post by towr on Mar 8^th, 2006, 5:37am

If the bankers offer is always lower than the expected value of what you hold, then the rational solution is to keep what you have.
Of course this is more of a utility than probability problem. A guaranteed dollar is worth more than an expected dollar. The question then is, what does your utility curve look like?

Title: Re: Deal or No Deal strategy?
Post by SMQ on Mar 8^th, 2006, 7:51am

As to the end game, it's not a Monte Hall problem as the gameplay reveals nothing about the contents of the case you're holding vs. the case you're not holding. It is strictly a matter of whether you prefer a known payoff or a 50/50 chance at more than that. (See the Wikipedia (http://en.wikipedia.org/wiki/Deal_or_No_Deal) article for more details.)

Think of it this way; if you already had the Banker's offer in your pocket, would you wager the difference between that and the high amount on the board on a coin toss? If so, go for it; if not, take the deal. For instance, if (in the US version) the $500K and $750K cases are the two remaining and the deal is $620K, you might be willing to wager ~$130K on a fair coin toss if you already had $620K in your pocket, so play for it. If, however, the two remaining cases were $1K and $500K with an offer of $220K, if you already had the $220K in your pocket you probably wouldn't be willing to wager it all on a coin toss, so take the deal.

That same general mode of thought can be extended back earlier in the game, but as the odds get more complicated it becomes more and more about your own risk/reward and utility functions and less about the statistics.

--SMQ

Title: Re: Deal or No Deal strategy?
Post by mfirmata on Mar 8^th, 2006, 9:05am

SMQ,
That Wikipedia article explained things well.

Thanks

Title: Re: Deal or No Deal strategy?
Post by rmsgrey on Mar 8^th, 2006, 10:58am

on 03/08/06 at 05:37:28, towr wrote:

From the banker's viewpoint, it's obviously worst case for him if the contestant works from the expected value. On the other hand, each contestant has just the one shot at the game, so it's fairly sensible to just look at your chances of getting a sum of money that's more than the offer - your chances of "winning", regardless of the size of the "win"

It does appear that contestants are more risk averse when the sums of money are large - 2 contestants have left with 1p, while 5 have had the quarter million in their box and sold it...

Title: Re: Deal or No Deal strategy?
Post by Roy42 on Jul 13^th, 2006, 5:23am

Here in Australia the highest amount is only $200K but my brother's and my strategy is: for him, take the first offer he sees above 10K, for me, take either the very first offer, the first above 10K, or play to the end, after all, getting so close to winning the highest sum and then not getting it out of a matter of luck and immense greed if you live in U.S or U.K, it doesn't mean you actually lost that amount of money, does it? ??? :P ::) 8) :o :( >:( ;D :D ;)

P.S i think the offer amount is based on the remaining sum of money in all cases including yours, divided by the # of unopened cases(that's an average, right? sorry, really tired) because i once had the board game of deal or no deal and it said to do that to get an offer amount e.g, for aus. when 200K and 50c are left the offer is 100K so-so.

Title: Re: Deal or No Deal strategy?
Post by rmsgrey on Jul 15^th, 2006, 8:55am

There have actually been a few games in recent weeks where the banker has offered the expected value when down to the last two boxes - with boxes that are relatively close in value.