# Deal or No Deal

### #31

Posted Dec 20, 2005 @ 8:44 AM

### #32

Posted Dec 20, 2005 @ 9:36 AM

I also thought that the woman contestant should have followed her own instincts and quit and not listen to her husband - he was quite dramatic, wasn't he?

### #33

Posted Dec 20, 2005 @ 10:03 AM

I'm sure Howie's got an earpiece with the model info and banker info being piped in to him.

Lame, but I got nothing else to do this week. So, I'll probably still watch it.

### #34

Posted Dec 20, 2005 @ 11:00 AM

It all looked a little too staged to me. The snappy answers from the first woman, "You make the decisions at home...but we're not at home," to the dancing Dad and the well-scrubbed faces of the kids. Mom didn't play the odds well at all.

Word on that. I totally thought the first contestants were staged and rehearsed. It was all a little too...

*something.*Hubby was obnoxiously "hip/cool" and the mom had all the "right" lines.

Boooooorrrrrring.

### #35

Posted Dec 20, 2005 @ 11:44 AM

I haven't been following Howie Mandel's career since he left St Elsewhere (actually never really followed his career, just watched the show), but what happened to his hair? Is his baldness a choice, cancer or natural hair loss? Just being nosy.

Does the baldness have anything to do with his famous germaphobia? Perhaps he is freaked out by dirt getting stuck in his hair, so he figures being bald is more clean? Just a guess. He did hug the contestant--I thought there was going to be a "don't touch Howie" rule (I mean, come on, the guy played

*Celebrity Poker Showdown*with latex gloves on), but evidently not.

I thought the game was fun. I set the DVR to tape it and will watch the rest of the week...it definitely is a show to watch with a fast forward button!

**Edited by OhTara, Dec 20, 2005 @ 1:34 PM.**

### #36

Posted Dec 20, 2005 @ 11:47 AM

I'm pretty sure the first family was coached to behave extravagantly because when you get down to it, that's all this show has. It's a person picking numbers; it requires flashy contestants to keep things interesting.

### #37

Posted Dec 20, 2005 @ 12:00 PM

The show exploits a very tricky "Let's Make A Deal"-type brain teaser re: odds of a particular event occurring, and is patently dishonest to the players about the percentages they really face.While I'm sure her family was comfortable, she expressed an interest in buying a house. $140k, $90k, $80k, they would go a lot farther to making that a reality than a 20% chance of winning $500k. If you cannot afford to take chances, you *shouldn't* be taking chances.

In this situation, the woman

*did not*have a 20% chance of winning 500K (or whatever odds they were quoting at various stages of the game). Her original case selection was made from 26 cases, meaning she had a 1 in 26 chance of picking $500K. Those odds don't change because cases not having the $500K are revealed. The odds of her case having $500K were 1 in 26 at every single point during the process. I'm amazed that the the show can get away with this deception.

It may have been a good risk to not take the $138K when it was offered, because a non-$500K reveal probably would have resulted in the bank upping the offer. But if she or anyone in her entourage really believed they had decent odds of getting the big money in their case, they were idiots.

### #38

Posted Dec 20, 2005 @ 12:30 PM

In this situation, the woman did not have a 20% chance of winning 500K (or whatever odds they were quoting at various stages of the game). Her original case selection was made from 26 cases, meaning she had a 1 in 26 chance of picking $500K. Those odds don't change because cases not having the $500K are revealed. The odds of her case having $500K were 1 in 26 at every single point during the process.

With all due respect, that analysis is not correct. While the original odds were 1 in 26, once 21 other briefcases were opened, there were five cases left, one of which had $500K in it. The odds were therefore

*at that point*1 in 5 that any one case had the $500K.

I missed the first night but will check this out once or twice this week. My feeling is that the concept here is more intriguing than any execution of it could be. But it is a hit in other parts of the world....

### #39

Posted Dec 20, 2005 @ 12:45 PM

### #40

Posted Dec 20, 2005 @ 1:03 PM

The family kept saying they had a vibe about case #8 - idiots you are supposed to pick the cases that you don't have a good vibe about!

I picked 8 at the very beginning, so I guess I would have won $500K. ;)

Every time they would say no deal, Howie was like "Okay, but we have to open 5 more suitcases!" like that was some horrible thing. Now granted, your next offer could go down depending on what suitcases get opened, but it is not like it affects the case you already chose.

This show is just so easy though. I mean as long as you don't act too stubborn and ultimately take a deal at some point, you're pretty much guaranteed to win a good amount of money.

They really should have added another element, like another case that has a red stopper in it, and if you open that case, it ends the game and you have to take what is in your case and go home. You really have no disincentive to keep opening cases other than uncovering all the big ticket prices and lowering the bank's offer.

### #41

Posted Dec 20, 2005 @ 1:07 PM

With all due respect, that analysis is not correct. While the original odds were 1 in 26, once 21 other briefcases were opened, there were five cases left, one of which had $500K in it. The odds were therefore at that point 1 in 5 that any one case had the $500K.

**EaglesNest**is correct. The events are not independent, so while the odds of any one case holding a particular amount is 1 in 26, the odds of it being so

*given that*you know the contents of other cases is considerably higher. To put it another way, if there are only 5 cases, one has to have it so each has 20%.

They could add a "switch" option in. In fact, the much-ado-about-nothing method would be to give them a "Trade Card" at the beginning, so each round they could have the tension of deciding whether or not to use it. And thus gloriously drag out the show while adding absolutely nothing.

Absolutely nothing, I should emphasize. As long as every choice is random (made by the contestant), there's no difference between the case you put by your side, and a case on the floor you've simply decided not to open.

On a different issue, I'm wondering if variance is a component of their offer. Most people make an implicit assessment in that area, and those of us who've studied risk management would probably do it more directly. For example, if you're down to two cases, the $100k and $.01 would have a mean of $50k. So would the $25k and the $75k. But the first pairing has much more variance, much more risk. So if they don't adjust the offer for that, it's a calculable method for deciding when to take an offer.

(Yes, I'm an incredibly boring person to take to a casino.)

He did it a number of years ago, so far as I know it was just a choice. I'm sure it makes blowing up a surgical glove with your head that much easier.I haven't been following Howie Mandel's career since he left St Elsewhere (actually never really followed his career, just watched the show), but what happened to his hair? Is his baldness a choice, cancer or natural hair loss? Just being nosy.

### #42

Posted Dec 20, 2005 @ 1:11 PM

### #43

Posted Dec 20, 2005 @ 1:19 PM

There's only suspense as long as there's big money still in one of the cases. Too much fnur and banker b.s. Just not enough to this game to keep it interesting.

I guess this is the real life incarnation of the "Network Time Killer" made famous by Hal Gurnee on the Late Show with David Letterman during his NBC days.

Edited because it

*is*Network Time Killer

**Edited by jblues, Dec 21, 2005 @ 12:18 PM.**

### #44

Posted Dec 20, 2005 @ 1:20 PM

ETA: I think that was "Network Time Killer"

**Edited by FreeperDave, Dec 20, 2005 @ 1:21 PM.**

### #45

Posted Dec 20, 2005 @ 1:32 PM

For example, at one point, Howie points out that only 2 of the 8 cases had more than the $77,000 that was being offered. While that's true thet the banker was offering far more than the MEDIAN case amount, he was offering far less than the MEAN case amount. For one of the 2 cases left was the $500,000 case, and that is over $400,000 more than the offer, while the smallest amount was only about $77,000 less than the offer.

I followed the first episode with an excel spreadsheet, and the offers were (as a percentage of Expected Value) approximately 20%, 40%, 75%, 65%, 90%, 101%, 100%, and 99%. It's pretty boring that the early offers are so clearly no deals that you might as well fast forward halfway through the show to the interesting decisions.

### #46

Posted Dec 20, 2005 @ 1:38 PM

**Toonces**just beat me to this point. I played a couple of rounds with the on-line game, and early on it is clear that the banker is offering an amount to encourage people to proceed. That is, the bank may offer your around $40,000 when there are seven values remaining that are higher than that amount and thirteen values remaining that are lower than that amount. The odds dramatically are in your favor if you open four more cases, since you are favored to pick (eliminate) more cases that are lower than the offer amount. Even if you unluckily pick more cases that are higher than the offer amount, the fact that there are fewer remaining cases means your next offer is still likely to be higher.

So I think it is the MEDIAN rather than the MEAN that is the key to good game theory here.

### #47

Posted Dec 20, 2005 @ 1:53 PM

With all due respect, that analysis is not correct. While the original odds were 1 in 26, once 21 other briefcases were opened, there were five cases left, one of which had $500K in it. The odds were therefore at that point 1 in 5 that any one case had the $500K.

This is wrong, although it's easy to understand how this confuses folks. The original selection was based on 26 cases, and the odds of the case selected containing a given specified amount doesn't increase just because some cases are revealed. The 20% odds only come in to play if, once it's down to five cases, the dollar amounts are mixed, and the contestant gets to re-select a new case.The events are not independent, so while the odds of any one case holding a particular amount is 1 in 26, the odds of it being so given that you know the contents of other cases is considerably higher. To put it another way, if there are only 5 cases, one has to have it so each has 20%.

I'm linking to the related brain teaser here. This explains the concept in detail.

I've yet to share this with anybody who didn't initially make the same common mistake (I made it myself, and took a long time to be convinced I was wrong).

This show is making the same error, and deceiving people into thinking that their odds are better than they really are.

ETA: Another link with a lot of vigorous discussion on the nuances of this brain teaser. Even though I've long since been convinced about the correct answer, the debate is still fascinating.

**Edited by cggb, Dec 20, 2005 @ 2:15 PM.**

### #48

Posted Dec 20, 2005 @ 1:55 PM

### #49

Posted Dec 20, 2005 @ 2:17 PM

I'm linking to the related brain teaser here. This explains the concept in detail.

I believe the difference between the brain teaser linked to above and the situation in deal/no deal is that the opening of the cases in deal/no deal is completely random (the contestant does not know the value of any of the cases) and the brain teaser involved the INFORMED opening of a door. Therefore, every time a new case is opened the probability is readjusted (so you have a 20% chance of winning the 500K if there are 5 cases left).

*Explained in much better detail below.*

**Edited by AngryKim, Dec 20, 2005 @ 2:19 PM.**

### #50

Posted Dec 20, 2005 @ 2:17 PM

**cggb**, we will have to agree to disagree; I'm not going try to convince you that you're wrong, but I'll try to convince others reading!;)

In the Deal or no Deal example with the $500K case, each of the events leading to the 1 in 5 cases scenario was random -- the initial selection of the player's case, and the other 20 cases eliminated. The player knew nothing about the contents of any of the cases. She was left with five cases (or was it six including here?), one of which held the value of $500K. Therefore the odds that any one case held $500K (or hers) was 1 in 5 (or 6). Because each event was random, the probablity was adjusted every time new information was gained.

In the Monty Hall example, by contrast, Monty KNOWS where the big prize is, and he is intentionally revealing information to alter the odds/increase the tension. Take the extreme example in the website link where there are 1000 doors, one of which has a big prize, and the other 999 have booby prizes. If you select one of these doors at random, your odds of getting the prize are 1 in 1000. If other doors are then opened one at a time AT RANDOM, your odds of having chosen the prize will increase with each door that reveals a booby prize. If somehow you get all the way down to two doors AT RANDOM, then the odds that the prize is behind your door is 1 in 2.

In the Monty case, however, he knows where the prize is and he SELECTS 998 booby prizes to be eliminated, leaving you with a choice between a door you chose at random at 1 in 1000 odds and a door that has a 999/1000 chance of having the prize. Damn right, you ought to switch. But that says nothing about shifting odds in a truly random setting.

### #51

Posted Dec 20, 2005 @ 2:25 PM

This is wrong, although it's easy to understand how this confuses folks. <snip> The 20% odds only come in to play if, once it's down to five cases, the dollar amounts are mixed, and the contestant gets to re-select a new case

Not to belabor it, since I already gave a fairly rigorous answer previously, but this is definitely

*not*the Monty Hall problem described in that link, which I mentioned myself a few pages ago. They key to the Monty Hall problem is that the show was making the decision, based on their own knowledge. In Deal, every choice is made by the contestent, i.e. random, and thus the Monty Hall parallel does not arise.

That's easily disproved. If you don't like the 1-in-5 scenario, let's continue the process. Eventually there's only unopened case left and only one number on the board. The odds of that number being in the case are definitely better than 1/26. They're 100%.The original selection was based on 26 cases, and the odds of the case selected containing a given specified amount doesn't increase just because some cases are revealed.

### #52

Posted Dec 20, 2005 @ 2:26 PM

When initially selected, the case has a 1 in 26 chance of having the $1 million prize, right?

Now, does the random unveiling of the other 25 change the chances the one selected case has of containing the $1 million?

If we get down to 5 cases, does each have a 20% chance of containing the prize?

If the $1 million prize is unveiled elsewhere, does the unopened case, initially selected

**still**have a 1-in-26 of having $1 million in it? No, it doesn't. Once the prize is revealed in another case, the chances of it being in our selected case are zero.

So, we know that the random unveling of the other cases can reduce the probablity of the selected case from 1-in-26 to 0. So why would this not work the other way around?

### #53

Posted Dec 20, 2005 @ 2:30 PM

### #54

Posted Dec 20, 2005 @ 2:34 PM

In DoND, it is true that the probability of choosing the $500K briefcase is 1 in 26, as is the probability of choosing the $1M briefcase. But let's say the $1M briefcase is revealed by the contestant in her first alternate pick. The probability that the initially chose the $1M briefcase drops to 0% (it is now an impossibility). It was 1/26 at the time she made the pick, but given further information, it is now 0%.

Once you agree to that, the probability of the other briefcases increase cannot all stay at 1/26, otherwise all possible outcomes do not add to 100%. In the Monty Hall problem where Monty avoids the car on purpose, the probability of the car being selected stays the same while the probability of the other booby prize rises to 2/3. In this case, there is no such bias, so the probability of all selections increase to 1/25.

-------------

In other secrets, there is a decent mental shortcut to learn the amount of a "Fair Deal" without a calculator or computer. If there are N briefcases remaining in the game (including the chosen briefcase), Divide each of the top valued briefcases (anything $5000+) by N, and add the results. The total is a good approximation of a fair deal.

Example: The 5 values left are $500,000; $100,000; $30,000; $400; $25. "A Fair Deal" is $100,000 + $20,000 + $6,000 = $126,000.

**Edited by toonces, Dec 20, 2005 @ 2:43 PM.**

### #55

Posted Dec 20, 2005 @ 2:39 PM

Still can't figure Howie Mandel's look - Dr. Evil with a Soul Patch? If hair freaks out his germ phobias, then how come the amount of potential much crap which must get stuck in that vagina under his lip doesn't?

**Edited by RevLovejoy, Dec 20, 2005 @ 2:42 PM.**

### #56

Posted Dec 20, 2005 @ 2:42 PM

The second link in my previous post talks a lot about the known/random nature of the picking. There's tons of point/counterpoint for anyone who cares about this sort of thing. I definitely subscribe to the notion that it is irrelevant to the overall probability whether the D or ND situation is random or known, but what appears to be a lot of intelligent minds are taking many different points of view on the subject. Regardless of who is right or wrong, the knowledge/random conundrum seems to be a reasonable subject of debate with respect to its applicability to the show.Not to belabor it, since I already gave a fairly rigorous answer previously, but this is definitely not the Monty Hall problem described in that link, which I mentioned myself a few pages ago. They key to the Monty Hall problem is that the show was making the decision, based on their own knowledge. In Deal, every choice is made by the contestent, i.e. random, and thus the Monty Hall parallel does not arise.

ETA:

**toonces**, based on the second link I reference above, there's plenty of debate on both sides of this issue. I definitely respect your point of view, but I think it would require more discussion than is appropriate for this site to conclude who is definitely right or wrong.

**Edited by cggb, Dec 20, 2005 @ 2:47 PM.**

### #57

Posted Dec 20, 2005 @ 3:00 PM

-----

Edited to add:

But just for fun, I'll try proving it one more time. We reduce DoND to 3 briefcases, with $1; $1,000; and $1,000,000. Contesant chooses briefcase #1. Then Howie asks you to choose a briefcase to eliminate. You choose #2. Howie's beauty opens it up to reveal $1,000.

Quiz Time! Given what you now know what is the probability that:

Briefcase #1 contains $1?

Briefcase #1 contains $1,000?

Briefcase #1 contains $1,000,000?

Be sure your answers add up to 100%.

Correct answers are below:

50%, 0%, and 50%

**Edited by toonces, Dec 20, 2005 @ 3:16 PM.**

### #58

Posted Dec 20, 2005 @ 3:27 PM

I picked 8 at the very beginning, so I guess I would have won $500K. ;)

So did I! What are the odds of that?

As for the odds problem, I agree the odds change with each revealed case. Yes, at the beginning the odds are 1 in 26 you picked the million dollar case. But once you've picked it, these odds are no longer relevant. You picked the right case, or you didn't. IOW, your chosen case now has a fixed amount. Each time a subsequent case is revealed, it gives you information about your case (you know it does not contain the amount revealed). You can then use this information to determine the likelihood your case contains a desired amount.

This show is about gambling, which people like to do. The smart player will take the money offered while there are still several cases with high amounts not revealed. It's practically a sure thing, that you can win about $100,000 this way.

I don't think the show is boring, but it certainly was a let down when they didn't win a big amount. And they have to keep playing while knowing they blew it. It borders on being cruel.

### #59

Posted Dec 20, 2005 @ 5:01 PM

It did amuse me to watch how the contestant's attitude changed. At first, she gets offered a low five-digit figure, and she's like "Mmm...that's alot of money but not enough". Then it gets up to 100K and she turns that down. Then, it's back down to 17K and she's like "screw it, who cares now, might as well have what's in the case".

Because, once you had a chance at 100K and blew it, what's 17K to you? <g>

### #60

Posted Dec 20, 2005 @ 5:37 PM

If you say so. I'll let you win and peacefully remove myself from the discussion.Actually, cggb, this is mathematics and there IS a correct answer. That you choose not to follow the incontrovertable proofs that everyone else who has posted here has given you above, and use as your only source of counter-proof a reference to other people being confused does not a controversy make.