Deal or No Deal

[JackT]

You've seen the show. I was watching it the other day and was wondering if anyone had any thoughts as to what optimal strategy would be....

Here are the rules, briefly explained:
There are 26 briefcases, each containing a different amount of money. (the values are all displayed on a big board, ranging from $.01 to $1,000,000. Not knowing the sum of money in each case, the contestant CHOOSES one case at the outset and it stays closed until the end. He then opens the remaining cases, one by one, revealing the money they contained. At predetermined intervals the contestant receives an offer from The Bank to purchase the originally chosen case from the contestant, the offer being based on the money values that are in the cases that have yet to be opened. The contestant must then decide whether to take the deal from the bank, or to continue opening briefcases. If he decides No Deal and continues to open cases with low values, then the next bank offer will be higher (as the contestant's case is proven not to contain these low values, and may contain a high one). Alternatively, the contestant risks revealing higher value cases, which would lower future offers from The Bank.

Usually the Bank will offer significantly less than the average of the remaining cases.

But still I would think that optimal strategy would depend on the contestant's risk tolerance. I mean, to some, the CHANCE that you could walk away with (say) $.01 is not worth risking (say) $150,000 guaranteed on the 50% chance one will win $1,000,000.


Another question crossed my mind...

Because the contestant chooses HIS case at the outset (and The Bank would obviously know how much is in that case), does the bank make its offers using the information that it knows about what the ACTUAL VALUE inside the contestant's case, or is it strictly based on all remaining cases? If the former, can the game be exploited?

 

[DoNotDisturb]

NO ONE knows the contents of the suitcases. If a suitcase is 'accidently' opened during the taping. Everthing is stopped, the suitcases/amounts are shuffled again and they start from scratch.

The BANK makes the offers based on what $$ amounts are left and the probabilty of the contestant holding a LARGE $$ - if there are a lot of HIGH $ amounts, the BANK offers more to keep from having to pay the largest amount available. If there are more lesser amount, the BANK has the law of probability on it's side, so the offer amount is less.

They can't risk any hint of 'rigging' not with the game show scandal of the 1950's? (or 60's)

 

[JackT]

While you're certainly right that they can't risk the hint of 'rigging', it is not clear to me that The Bank (the man behind the phone) knowing the amounts in all of the cases ahead of time would be 'rigging'... as long as Howie (the gameshow host) or the women holding the cases don't know.

Anyway, paragraph 4 of this link provides a better (and more "official") explanation of the game than I did above: http://www.nbc.com/Deal_or_No_Deal/playwin/rules.shtml

Any thoughts on what the best strategy would be? Or what YOUR strategy would be?

 

[Boywonder2]

The odds of picking the million, 3/4 million or 1/2 million out of 26 cases is relatively low. So the game is more on whether or not someone can make a rational decision whether to keep going or take the deal based on the offer. Most people go on the game with the excitement of the million dollars when in reality the chances are really low. So based on the remaining cases if a good deal comes in people need to be disiplined and take it.

 

[richman10]

you guys may be retarded - even the makers of the show admitted to Howie Mandel when they pitched it to him that its a game show about Nothing

All it is is luck -
HERE IS THE STRATEGY
Keep picking cases and do not take any deal as long as the million is still on the board. Even if you know that you do not have the million in your case, as long as it is still out there, the banker will keep increasing the amounts he offers you
That is the whole game
If you open the million dollar case, go home
If not, keep opening up
DUH!!!

 

[justme]

But still I would think that optimal strategy would depend on the contestant's risk tolerance.

Because the contestant chooses HIS case at the outset (and The Bank would obviously know how much is in that case), does the bank make its offers using the information that it knows about what the ACTUAL VALUE inside the contestant's case, or is it strictly based on all remaining cases? If the former, can the game be exploited?

1. You are exactly right. If I were better at economics, I could probably ask you a few dozen questions about your prefrences over lotteries and then tell you what your optimal strategy given your revealed preferences.

2. I don't think the bank would be allowed to know the contents. It would make the game dull because if the person chose the $.01 case the bank would never have an incentive to deal.

 

[Slinky Bender]

Hint to JackT: think if it was blackjack and you were using an elementary card counting system with + and - depending on what had been burned.

 

[Ozzy]

There is no strategy... you just have to calculate risk vs reward as you go along.

I've learned from the two or three times I seen parts of it that most idiots on this show have no ability to calculate odds or risk factors.

 

[Ozzy]

2. I don't think the bank would be allowed to know the contents. It would make the game dull because if the person chose the $.01 case the bank would never have an incentive to deal.

They know exactly where the million and every other $ amount is.... its all calculated mathemtically as they go along on a +/- like Benders blackjack example. There is no banker actually dealing, risking or enticing anyone or anything. It's pretty easy to figure out within a few % (5-10%). You of all people would be able to calculate it exact.

Didn't anyone here ever watch Lets Make Deal.... This is the same thing with the ante upped a bit. Monty always knew yet he offered various gifts and duds. I thought Monty Hall was one of the greatest host because of his ability to do this and never give the secret of the deal away.

This show could care less if it gave away a million a night.. they probably would prefer a few people win it. It cost virtually nothing to produce and its at the top of the ratings. Thats why TV loves reality shows... low budget and big revenue. It's because of shit like this you'll probably never see a Seinfeld or Friends type success again cause networks would sooner give us reality bull shit for near nothing production costs than pay a cast of 5 or 6 a million per episode plus residuals for life.

 

[justme]

It's easy to calculate the expected value of the remaining suitcases. But there's a difference between expected value which is a random variable and actual value which is a deterministic variable.

The bank, I'm guessing, makes an offer based on it's (set) preferences. I don't doubt there's incentive to 'sell' the excitement of the game. But all of that could be included in the bank's preference relation.

What's interesting, theoretically anyways, is how the people's risk tolerance factors in.

What's really interesting, I'm sure, is the ways in which the player's behavior departs from rational economic behavior. A friend tells me that he was discussing this show with an economics professor the other day. The prof was certain that 'several' papers and disertations in behavioral economics would come from this show.

 

[Slinky Bender]

Shouldn't there be? In fact, how about this: I'll bet someone, if they studied very carefully, can use the behavioural information from this game to model the irrational behaviour of people in other markets where the behaviour isn't so easily filtered out/factored in, and thus too hard to analyze by studying those markets directly.

But something you may not be considering: perhaps the Bank isn't making offers based on what appears to be an optimal strategy of how to spend the least amount of money, but based on another factor: how to make the game interesting/exciting to those watching. And if that is the case, the Bank may be doing some "poker playing", that is, "playing the man, not the cards". In other words, the Bank may make offers based on what it's perception of what the player is going to do, rather than based strictly on the odds. There may be some bluffing on the part of the bank, or "feeler betting", or other gambling tactics that aren't odds based, but behaviour based.

 

[Slinky Bender]

Does anyone know if there's a website with just the summary moves made by the bank and the players on the show? I'd love to see how this thing plays, without having to watch the BS for the hour.

 

[Slinky Bender]

If you have some time to kill:

http://www.people.fas.harvard.edu/~trebbi/BT_17nov2005.pdf

http://www.tinbergen.nl/discussionpapers/06009.pdf

 

[BigMadM]

After watching the game for a few episodes, this is my feelings.

Odd of you getting down to 4 boxes, 2 being small amounts, and 2 being lets say 400 thou, and 1 million, the banker is going to figure a 25% chance of One mill, and a 50 % chance of 400 thou or more. So, hed offer around 225 thou, or within 15 grand of that.
So out of 26 picks, you have 2 left with big amounts, thats a 1 in 13 chance, if you get down to the final 4, if youre lucky, and then its about an 8% chance of that, so since the odds are 91% favor against that happenning, anyone who does better or close to that, and is offered anything over 200 thou, should take it and leave. Odds of getting money are just too small.

 

[BigMadM]

but Im far from a statitician, so what do I know

 

[justme]

Slinky - Thanks for the links. I read the first few pages of the Hah-vahd paper and it looks good. I'll print it out and read the rest.

BMM - it's not simply a matter of acurately being able to determine the probabilities (expected values and variances). It's also a matter of personal preference over what economists call lotteries.

Let me give you a simple example.

I have a game in which you flip a coin. Heads you get nothing, tails you get $1,000. How much would you pay to play the game? The expected value of the game is clearly $500. Anyone who will play the game for $500 and no more is referred to as risk nuetral. A person that is willing to pay more than $500 is called risk seeking. A person that will not pay $500 is called risk averse.

Niether risk averse nor risk seeking behavior is economically irrational per se. Risk aversion is (thought to be and probably is) a function of a given person's utility function. That is, for some people the money over $500 is worth more than the first five hundred dollars. Maybe someone gets a five hundred dollar bonus, but they really want to buy a flat screen TV for $1,000. For them the $500 won't buy anything they want. The $500 is useless, but the $1,000 has very high utility. So they're willing to pay more than $500 for the chance at the big screen. This guy is risk seeking.

On the other hand, some people are risk averse. Let's change the numbers around. Supposed instead that we give you the option of flipping the coin. This time, however, tails means you lose everything and are left penniless. With heads your net worth is doubled exactly. It's the same game as before with the new cost scaled to be exactly your net worth. But where you might be willing to play the first game, the second game is far less attractive. The idea of being completely destitute at the end of a coin flip is too frightening to even contemplate. So in this case the first (whatever it is, say $500,000) is worth much more to you than the next $500,000). So if you avoided this game we'd say you were risk averse.

As the utility of money changes, people exhibit all kinds of risk behavior. What is irrational in the economic sense, however, is when a person makes choices that contradict his prior revealed risk preferences.

 

[Ozzy]

After watching the game for a few episodes, this is my feelings.

Odd of you getting down to 4 boxes, 2 being small amounts, and 2 being lets say 400 thou, and 1 million, the banker is going to figure a 25% chance of One mill, and a 50 % chance of 400 thou or more. So, hed offer around 225 thou, or within 15 grand of that.
So out of 26 picks, you have 2 left with big amounts, thats a 1 in 13 chance, if you get down to the final 4, if youre lucky, and then its about an 8% chance of that, so since the odds are 91% favor against that happenning, anyone who does better or close to that, and is offered anything over 200 thou, should take it and leave. Odds of getting money are just too small.

You're pretty much on the mark... But I think it would be a touch hight because of the 400 still in play. If it's one in four chance of a million and the other three are low amounts (under 100,000)... The offer you would think would will be 25% (250), but they tend to offer a bit less, probably in the 225 range. With the 400 in play your chances of winning at least that much is 50% and the million offsets that even higher. So the risk isn't as great so the offer goes up a bit.. probably 260-270.

I think the person who figures this shit out has bookmaking experience cause there seems to be a vig price figured into all the offers I've seen so the house always has a slight advantage on the offer. So you're never getting the true odds. For example, for two suitcases... one has a mil and the other has one dollar, the offer you would think should be 500, but it would prob be closer to 475-490. I don't thnk you'll ever see an offer go above 500 unless the last two suitcases are both very high numbers with one being a million.

 

[Ozzy]

What I want to know is why any fool would play three card monty when the usual payoff is $20 with a bet of $20 (least the ones I've seen).... and your chances of winning (assuming it was on the up and up) were still only one in three?

Talk about fixing the game from al angles.

 

[Ozzy]

Let me give you a simple example.

I have a game in which you flip a coin. Heads you get nothing, tails you get $1,000. How much would you pay to play the game? The expected value of the game is clearly $500. Anyone who will play the game for $500 and no more is referred to as risk nuetral. A person that is willing to pay more than $500 is called risk seeking. A person that will not pay $500 is called risk averse.

Consider the coin flip odds every year at the super bowl. Makes no difference what you play... you are always laying odds.

Last year for example to win the toss it was Sea -$1.35 Pitt -$1.15 You're risking that much for a dollar. The odds on heads or tails was 6/5 regardless of which way you went.

And people wonder how the house always wins.

 

[beadman]

I have been watching DORND since it started and can offer this opionion.
When a offer is made by the banker. say 5 cases left 100,000 200,000
$5 $1 and 500,000 and the offer is 130,000. I would say add the total cases 800,006 and divide by 5 = 160,001 and if the sum is greater then offer you can take it if it is lower you should never take it. If you feel greedy then play on. Only when there is one big amount left do you have to stop because you could bust out and leave with $5 like some lady did not long ago.