Talk:Deal or No Deal/Archive 1

Theory
I can't recall the exact name but shouldn't there be a mention of the gameshow theory regarding mystery doors. Working on the basis that when the presenter offers the opportunity, after eliminating one of the three mystery doors, for the contestant to change their mind.

The theory would be hugely compatible with Deal Or No Deal as it is the central conceit. Any views on this?Crikeymikey 20:11, 28 December 2006 (UTC)

No, the Monty Hall paradox does not apply in this. 65.65.180.44 17:14, 13 June 2007 (UTC)

UK edition: Am I lising count?
According to Noel in today's episode (on-air as I type) yesterday, the contestant had the 250K in her box. I missed the episode, so I'm not completely sure, but does this make it 3 times now? -- Lardarse 16:51, 8 December 2005 (UTC)


 * Nope, she was left with a choice between £100,000 and £250,000 (but had dealed earlier on at £31,000) and the £100,000 was in her box. BillyH 20:42, 8 December 2005 (UTC)
 * She actually had the £100,000 in her box, and the £250,000 was in the other box. The offer "would have been" straight down the middle: £175,000. --Bonalaw 20:45, 8 December 2005 (UTC)
 * Ok, I changed back the edit I made yesterday, but my cookie expired without me realising it, so it doesn't appear as one of my edits. -- Lardarse 16:41, 9 December 2005 (UTC)

calculating odds
In the US version, I think we can all agree that there is a 3% (1:26) chance of any dollar value appearing in each of the individual cases. Something tells me that this is not accurate with regards to the player.

Is this right:  The player is hoping to select a box that contains a specific dollar amount (US$1m). Going back to the old Johnny Carson "someone in this room has my birthday" statistic issue, the odds that the player has selected the $1m box should be much, much less than 3%.

For those of you who don't know the Johnny Carson birthday game, it goes something like this: in any given crowd of people of x size, there is a 50% chance that two people in the group share the same birthday. When this fact was presented on The Tonight Show, Carson inadvertently embarrassed the mathmatician presenting this by asking if anyone in the audience shared a specific birthday (his own). The odds of two people in the room sharing a specific birthday are much lower than the odds of two people in a room sharing any day as their birthday. I believe this also applies to case selection -- any case containing any amount is at 3%, but a specific case containing the big prize is much, much lower. Comments? SpikeJones 02:59, 21 December 2005 (UTC)


 * The mathematics in Deal or No Deal have nothing to do with the Birthday paradox. The birthday paradox applies to cases where the random numbers are drawn in a way where duplicates are possible.  The linked-to article explains it much better than I could.


 * Deal or No Deal has 26 unique values in 26 unique cases. When the contestant picks his case, there is, of course, a 1 in 26 chance that it was the big money case. Vslashg 03:21, 21 December 2005 (UTC)


 * Agreed that there is a 1:26 chance that any case contains the big money, but once the game begins with a selected case where the focus is whether that specific case contains a specific amount of money, does that change the odds a la the birthday paradox? SpikeJones 04:18, 21 December 2005 (UTC)


 * No. The shift in "focus" on Carson's show only "changes" the probability because two completely different things were being measured.  Say for the sake of a simple example that there are 50 people in the room.  The odds are 97% that at least one pair of people present share a birthday.  But if one person speaks out and asks "does anyone share my birthday?", the odds drop to about 12.5%.  The change isn't really because we are focusing on one particular birthday, but rather because the first case is looking at all 1225 possible pairs of people in the room, while the second is looking at only 49 pairs.


 * No such change of focus happens on Deal or No Deal. We agree that each of the 26 cases has a 1-in-26 chance of containing the big money, correct?  When the contestant picks his case (let's say #7), absolutely nothing changes.  We have no new information, and the contestant's choice changes nothing about the situation.  Every case has a 1-in-26 chance of holding the big money, including case #7.


 * In fact, every time a case that does not contain the big prize is eliminated, the contestant's odds improve. If only five cases remain, and the big money has not yet been uncovered, then each of the five remaining cases shares an equal, one-in-five chance of holding the big money, and this includes the contestant's choice.  (This issue is addressed in the third and fourth paragraph of the "Mathematical basis" section of the main article.) Vslashg 06:02, 21 December 2005 (UTC)


 * I disagree. That situation seems to me to be a variation of the Monty_Hall_problem. When there are 4 unchosen and the chosen case left, I suspect that the unchosen cases present a 25:104 chance (1:4 given the 25:26 chance of incorrect initial selection), whereas the chosen case is still only 1:26. --76.184.164.189 04:38, 26 March 2007 (UTC)


 * How so? If the game starts with only 4 cases, are your odds of winning the top prize not 1 in 4?  How do these odds change, if the game makes it down to 4 cases, with the top prize still in play?  —Preceding unsigned comment added by 24.83.110.145 (talk) 02:45, 13 December 2007 (UTC)

There is a major inaccuracy in the article; Expected Value Theory does not include "runs of luck" as that is a superstitious concept that has no bearing on future events. Only reason I don't fix it is because I don't know if the US show honestly incorporates such a silly thing, or if the person who put that in the article was mistaken and I don't really know how to go about finding out which is the case.
 * Although the expected value of the case clearly doesn't have anything to do with the run of a player's luck, the algorithm that they use to figure out how much money to offer *does* seem to take the player's lucky or unlucky streaks into account. Players who have runs of good luck and eliminate many small-value cases while preserving large-value cases for several rounds seem to have the offered "deal" amount drop to a lower and lower percentage of the remaining expected value. Players who have catastrophic bad luck and see the expected value of their case drop by a substantial amount in a single round seem to be offered deal amounts that represent a larger fraction of the remaining expected value. I suspect that they are trying to compensate for a player's reluctance to pass up the certainty of getting a large amount of money even when it's below the expected value, as well as their eagerness to "make up for losses" when the offered amount drops. - October 8, 2006

There is a very easy way to calculate the contestant's Expected Value at any point in the game, assuming that is the basis behind the contestant's decisions. If the game were to choose one suitcase and then open it, the average amount won would simply be the arithmetic mean of the contents of all suitcases as the formula would be to multiply each suitcase amount by the probability of choosing that suitcase, then add all the numbers together. The probability of opening any individual amount is (1/n) where n is the number of suitcases left, so you would add (1/n)(payout) for each payout which works out to the average.

If we assume that the contestant never makes a deal for less than the arithmetic mean of the suitcases, then this means that the worst thing that possibly happens is that the contestant opens all suitcases except for the original randomly selected suitcase (I'm assuming the contestant never switches cases because as others have pointed out, that doesn't do anything). This is strategically the same thing as the contestant just picking a suitcase and then opening it at the outset.

Of course the contestant does get to open a few cases and reevaluate, but by the formula above her EV will still be the arithmetic mean of all the remaining suitcases at any point if she never accepts a deal. And if she does accept a deal that is greater than the arithmetic mean of the remaining suitcases, then her EV actually turned out to be higher than that. This is why the contestant's EV can be more than the average (depending on the Banker's strategy) but never less using this dealing strategy, assuming EV is the basis of the contestant's decisions. It gets a bit more complicated if the contestant decides to accept a -EV deal to avoid risk of ruin (for example, electing to settle for $350K if the remaining cases are .01 and $1M); it may be worth it to accept a "bad" deal on one round if accidentally knocking out one of the big prizes will force you to accept a worse deal on a later round.

BTW, I saw an episode yesterday where the remaining cases were $1M, $500K, and two meaningless little amounts and the deal offered was still under 75% of the contestant's EV ($275K vs. the $375K or so she should expect to make by "gambling"). She then eliminated the $500K case and was offered 81% of her EV which she accepted. So I also have a hard time believing the statment about the banker ever offering above the arithmetic mean as a deal. I haven't seen every episode so I can't say for certain that it's never happened, but it seems doubtful to me as well. People are more likely to settle for a -EV deal as the amounts get larger; http://www.cardplayer.com/poker_magazine/archives/?a_id=15067&m_id=65575 (ignore the poker stuff and read the stuff under subheading "Asymmetric Risk Preferences")Xhad

In the NFL special, after the player took the deal, they did a review of what might have been. The last two amounts left were $5 and $1,000,000 and the banker made an offer of $520,000 which is clearly higher than EV, approx 104% EV. So assuming you can believe that they didn't adjust the banker's formula with the money not really on the line, they will sometimes offer a premium over the EV. 216.68.56.218 (talk) 03:04, 31 January 2008 (UTC)

Moved from article
Please source this if you want to put it in the article:
 * The most famous international version is arguably the Australian version hosted by Andrew O'Keefe. It currently screens on the Seven Network.

Argued by who? Soo 12:17, 23 December 2005 (UTC)

Clean-Up
I think that this article needs to be cleaned up. Here's what I propose...

The following layout:
 * (Introduction)
 * Format
 * International Versions (heavily cut back)
 * Mathematical Basis
 * Analyzing decision making under risk
 * External Links

This would be achieved through the following steps...


 * 1) A "Format" section be created. This will explain the general format of the show without going into detail about specific international variations.
 * 2) The "US version" section be scrutinised. The subheading "Odds and Probability" and "Strategy / Winning a million dollars" aren't really US-specific and should probably be removed and incorporated into "Mathematical Basis".
 * 3) Pages be created for the Australian, British and American versions of Deal or No Deal (eg, Deal or No Deal (Australia), etc). Fill these pages with the information currently listed for each respective version on the main Deal or No Deal page (variation from general format, briefcase values, other country-specific information such as History for the Australian version). While the content is note-worthy, it distracts from the main article. In addition each version is repetitive in it's explanation of the basic format (which can be solved through the first step)
 * 4) The listings of International Versions be heavily reduced. With the creation of country-specific pages in step 3, the listing on this page could be reduced to something like...
 * Australia
 * ''Main article: Deal or No Deal (Australia)
 * Deal or No Deal airs in Australia on the Seven Network, and is hosted by Andrew O'Keefe. The program debuted in late 2003 as an hour-long program, airing in prime-time on Sunday nights. In 2004 the show was reduced to a 30 minutes format, airing weekdays at 5:30pm.
 * Ideally the length of the new Australian, UK and US versions would match the existing versions (Dutch, Italian and Indian).

So... how does that sound? DynaBlast 19:53, 2 January 2006 (UTC)

Could we perhaps have a 'general problem/format' section before diving into the Australian format? I was trying to understand the basic concept of the show, particularly of the UK version, and it's very confusing the way it is laid out. Could we have a basic summary on the common points of all versions, only later followed by the differences? 12:00, 9 January 2006 (UTC) (Skittle)


 * Much clearer. Thanks. 57.66.51.165 09:04, 13 January 2006 (UTC)

I still think the article needs some revision. If anything, it should be a brief discussion of the rules of the game and how the game is similar among the various countries in which it airs. All the stuff about strategies, etc. is really inappropriate for this encyclopedia. Specifically, these sections should either be rewritten, cleaned up, or deleted. Beatdown 01:29, 13 October 2006 (UTC)
 * Optimal strategy: when to deal
 * Will someone win the top prize?
 * Modeling the outcome
 * Comparison with the Monty Hall problem
 * Analyzing decision making under risk
 * Antecedents


 * I suggested that we split off sections 3-6, which is most of the questionable content. In a separate article, the material can stand by itself to be improved or deleted outright. So far, no one has bothered to provide me with a any reason not to and if no one does within the next couple days I'll just go ahead and do it. -Anþony 01:27, 14 October 2006 (UTC)

Clean-Up and Deletions for Mathematical Basis
Okay, I removed almost all of the free-floating US/UK/Australian math & odds & strategy paragraphs and consolidated them under Mathematical Basis. I tried to meld important stuff into the math version that had been written from the point of view of decision theory / game theory / utility theory. I deleted duplications and similar analyses. Here are several orphaned paragraphs that I didn't feel qualified to meld in -- if you think that they add to the article please move them with segueways into appropriate places:


 * "In the Australian version, where audience members are given the chance to guess the value of their case to win $1,000, it is common practice to leave one's friends or companions until last. So, in this case, the probability of having the top prize from the start is 1 in 26, the probability of having the top prize left in the final two cases from the start is 1 in 13. Having said this, there is no reason to assume that the top prize is any more likely to be in the friend's case than the player's own. However, just as players can rue an early deal if they hold the top prize, so can they if their friend contains the top prize, because they know that their final offer would have been high regardless."

Since I've never seen the Australian version, this passage wasn't entirely clear to me.


 * "The banker's offers are worked out using a software program which offers a range of values, taking into consideration the probability, the player's value of money, and the current run of luck."

Is this true? I'm not sure how it could be proved one way or the other. I would assume that the banker's offer considers probability and general marginal utility and risk aversion, and then is worked out using marketing execs and focus groups for the purpose of maximizing the excitement-value (i.e. ratings) of the TV show -- I guess this could be loosely interpreted as run-of-luck...

Of course, if we could determine the formula then we can predict the offer. For example, your chance if having the jackpot is 1 in 26. The offer might be your case/26 time a certain amount. The credits state the banker's offer is not his own but submitted by the producers. In any case, getting an agreed-on formula to the article is a challenge. That's unless the banker is a mathematician willing to do it himself. BuickCenturyDriver (Honk, contribs, odometer ) 09:36, 1 April 2007 (UTC)


 * "It has been known for the Banker to offer slightly over the odds (e.g. 53,000) as a form of insurance to avoid a player winning a very high prize."

I doubt Bank offers have much to do with insurance - the show is almost certainly insured independent of "the Banker's" particular offers. If anything, banker's offers are based on what makes the show the coolest, as guessed by whoever projects ratings. Nonetheless it would be neat to include some explicit examples of Deal or No Deal bank offerings that exceeded the arithmetic mean.

--Brokenfixer 02:12, 14 January 2006 (UTC)


 * I believe that the word "insurance" was used here in the sense that it is used in poker, rather than finance. unless 21:51, 23 June 2007 (UTC)

Mathematical discussions that are not Monty Hall-related
Offhand, it seems that the likelihood of having a high-value case relative to the likelihood of having any of the remaining cases (including those of low-value) could be calculated using Bayesian inference. This would then allow the player to always make the statistically best decision whether to accept or refuse the banker's buy-out offer. Any truth/value to this? Or if that that, perhaps Combinatorial auctions? (unsigned comment by 151.197.239.92 01:42, 21 December 2005)


 * The expectation of having a high-value case, and the expected value of your chosen case, can be easily calculated (as the uniform average of all remaining values). So it is easy for the player to make the naive 'statistically best decision' about the banker's offer. However, as noted elsewhere, an offer of certain $500,000 is more valuable than a 50/50 chance at $1million (because of risk aversion as well as the declining marginal utility of money). It might make good economic sense to accept a banker's deal that has lower mathematical value than your briefcase's expected value -- depending upon your particular financial needs. As of Jan 13, the DoND article (math basis section) reflects this analysis, although it doesn't reference Bayesian inference. (... However, references to the Monty Hall problem are confusing and false, except to say that because (among other things) Deal or No Deal briefcases are chosen randomly (without using prior knowledge), Monty Hall does not apply.) --Brokenfixer 22:46, 13 January 2006 (UTC) [edited --Brokenfixer 02:48, 14 January 2006 (UTC)]


 * Brokenfixer, I think the comment by 151.197.239.92 ("Offhand, ...") was not Monty Hall related. It appears to be about the decision as to accept the buyout offer or not. Note the lack of indenting implying it was not a reply, instead it was meant as a new subject. When it first appeared it was at the top of the Talk page and not under any explicit subject heading. Therefore, I think we should move these three comments (151.197.239.92's, your 13th Jan 22:46, this one by me) out of the Monty Hall threads. If you agree, then you can move the three to another heading. I would have just moved them myself, but you had mad made Monty Hall related comments so I wanted to ask you first.


 * Ok, moved these comments. I also took out my mad boldfacing and added a sentence to my earlier comment. In response to the Comment, note that all the math behind the decision to accept the buyout offer is currently analyzed in the first Mathematical Basis section, called When to Deal. You and the original commenter (and anyone else reading this) are encouraged to expand or clarify that section, describing exactly why and how (mathematically) one can best play the DoND game.


 * (At each step, one portfolio is to accept the banker's certain offer. The other portfolio is a blend of obtaining the contents of each of the remaining briefcases - first, each briefcase is dimished by the non-linear utility curve of money (degrading the value of very large briefcases) and then those values are averaged. Second, that modified average is reduced by a risk factor which reflects undesirable uncertainty; the final number is compared to the banker's offer. An extremely accurate model might even iteratively take into account predictions of the banker's future offerings, which typically become more favorable as the game progresses. But imho this is Talk Page material and not material for the DoND Article.) --Brokenfixer 02:48, 14 January 2006 (UTC)


 * I meant to say mad, not made, last night. Sorry about that. That's what I get for commenting so late at night! Aaron McDaid 10:53, 14 January 2006 (UTC)

As Brokenfixer said above, accepting a banker's deal does not only depend on how it compares to the expected value of the suitcase; it also compares to the expected values of future banker's deals! If for instance you have $1, $5, $10, $1,000,000 left, then a somewhat high offer might look good given the chances that the next suitcase you open will be the $1,000,000, decreasing the next banker's offer. This seems extremely key to even a somewhat accurate analysis.

Monty Hall discussions
There are multiple subthreads below regarding the Monty Hall-ness of Deal or No Deal. They originally started off as separate top-level threads, but they are now grouped together here. Hopefully we'll be able to merge or delete these duplicates.

1. Claim that Deal or No Deal (random selection) still has Monty Hall properties, and Responses:
Random selection doesnt I believe destroy the Monty Hall factor. Try imagine 100 boxes and elimate 98 at random. - IF your box survived as one of the final pair ( only 1/99 chance) you must still swap as per MH. If it did not survive - as the £250 k rarely survives - a ' virtual ' new game is started with a new highest prize and the number of boxes left when it was eliminated.- and so forth.

'''Let H be highest sum on the board Let N be the 2nd highest sum on the board

Let x be the number of boxes unopened when the highest number first appeared Let y be the number of boxes unopened'''

) 	 	'H/x + N / ( pairs at y = z )'

H=     250 N= 	100 x=   22 y  = 22 	     	£11,797

H = 	100 N= 	50	      	£10,877 x = 	11 y=      8

H = 	250 N= 	100	         £14,935 x = 	22 y=      8

H = 	250 N= 	100	         £21,364 x = 	22 y=      8 AubreyA 21:14, 29 December 2005 (UTC)


 * Ugh. I'm impressed by the math but Monty Hall doesn't apply here. In your example, there are 100 boxes. Firstly, the chances of your box making it to the final pair with the big prize still up is 1/50, not 1/98. To prove this; pair each box with another box. Pick your favourite box. Eliminate all the boxes except for yours and the one it's paired with. There's a 1/50 chance your pairing contains the big prize. (Within that pair, each box has a 1/2 chance of course).


 * But if you want iron-clad proof, consider this. Say there are 4 boxes, A, B, C, D, randomly worth $1, 2, 3, or 4. You pick A. Then you eliminate D. It had $4. So now, A, B, and C are randomly worth $1, $2, or $3. Do you swap from A? Answer: doesn't matter. Now you elimate C and it was worth $1. A and B are worth $2 or $3, but one doesn't have more of a probability than the other.


 * The main thing here is that the cases eliminated are purely random. In Monty Hall, they know door 2 is worthless, and they reveal this. In this game, you go to eliminate case 2, but it could just as likely as your case be the one with the big prize. --Headcase 08:11, 9 January 2006 (UTC)


 * - You are wrong. The cases eliminated are not "random" because contestant can see what was in them. That is, it doesn't matter do you know what's in the case a priori. It is absolutely doesn't matter who selects the case. The only important thing is that the case which is opened is low-value one. Were you any good at probability at college?

Better than you evidently. Maybe didn't take classes as advanced, but have a better grasp on the concept, unless you're a troll, in which case congratulations, you've made me spend time to disprove you and are good at your task.

Monty Hall never eliminates the right one (right = $100, wrong = $0), so... Chances of picking $100 and then eliminating $0: 1/3 * 1/1 = 1/3 Chances of picking $0 and then eliminating $0: 2/3 * 1/1 = 2/3

Since the eliminated is always the same ($0), it ends there. When $0 is revealed, you have a 1/3 chance of having $100 and a 2/3 chance of having $0.

To compare Deal or No Deal, say there are 3 cases, and only one has $100, the rest nothing... Chances of picking $100 and then eliminating $0: 1/3 * 1/1 = 1/3 Chances of picking $0 and then eliminating $100: 2/3 * 1/2 = 1/3 chances of picking $0 and then eliminating $0: 2/3 * 1/2 = 1/3

So if we remove the unfortunate instance where $100 is removed... Chances of picking $100 and then eliminating $0: 1/2 Chances of picking $0 and then eliminating $100: 1/2

Better swap the suitcase, it's going to make a difference.

Hell, I'll even go with an extended version of it: 3 suitcases, $1, $10, $100. Chances of picking $1 then eliminating $10: 1/3 * 1/2 = 1/6 Picking $1, eliminating $10: 1/3 * 1/2 = 1/6 10, 1: 1/6 10, 100: 1/6 100, 1: 1/6 100, 10: 1/6

If we only keep instances where $1 is revealed to be eliminated: Chances of picking $10 then eliminating $1: 1/2 Chances of picking $100 then eliminating $1: 1/2 (no difference)

Copy and paste If we only keep instances where $10 is revealed to be eliminated: Chances of picking $1 then eliminating $10: 1/2 Chances of picking $100 then eliminating $10: 1/2 (no difference)

Copy and paste If we only keep instances where $100 is revealed to be eliminated: Chances of picking $1 then eliminating $100: 1/2 Chances of picking $10 then eliminating $100: 1/2 (no difference)

Hey, let's copy and paste that whole thing and do it with four suitcases: 1, 10, 100, 1000. Chances of picking $1 then eliminating $10: 1/4 * 1/3 = 1/12 Picking $1, eliminating $10: 1/4 * 1/3 = 1/12 1, 1000: 1/12 10, 1: 1/12 10, 100: 1/12 10, 1000: 1/12 100, 1: 1/12 100, 10: 1/12 100, 1000: 1/12 1000, 1: 1/12 1000, 10: 1/12 1000, 100: 1/12

If we only keep instances where $1 is revealed to be eliminated: Chances of picking $10 then eliminating $1: 1/3 Chances of picking $100 then eliminating $1: 1/3 Chances of picking $1000 then eliminating $1: 1/3 (no difference)

If we only keep... no way I'm doing more of this.

In all the Deal or no deal examples, after the elimination the value of the case is still one of the values that remains, completely at random. Of course the value of the case fluctuates, no one denies that (especially the banker). If you picked a case and then eliminated the $10 case, one of the lower valued ones like you say, then now our case as either $1, $100, or $1000. Exactly 1/3 chance of eachof those. So why, may I ask, would I switch? The mean value is more, but switching does nothing (from a probability standpoint. It certainly does something from a "the amount of money that is now in your case" standpoint).

But if the banker offered my even one red cent to change to any other closed case, then if I had no psychological attachment it would be logical to do it. If you majored in stats and passed, please state your college so I can blacklist it. Well, maybe that's unfair to the college. Maybe you just know what the Monty Hall problem is. --Headcase 21:19, 13 January 2006 (UTC)


 * Headcase's examples and math are all correct. AubreyA's probability computations are wrong for Deal or No Deal. If there are 100 boxes and only one contains $1million, and if 98 are opened at random and the $1million doesn't show (which is unlikely but 2% possible...), then your initial choice has a 50/50 chance of being $1million. (This is directly unlike Monty Hall, where Monty looks behind the 99 remaining doors and forcefully demonstrates to you which of those 99 doors contains the $1million (99% of the time).) --Brokenfixer 23:22, 13 January 2006 (UTC)


 * Sidenote: However, IF the Banker knows the contents of all of the briefcases, then the Banker could make an offer that communicated information to you. For example, consider a game with only two briefcases, one containing $100 and one containing $0. You choose Briefcase "A" (random choice). I open Briefcase "B", look inside, frown enigmatically, and offer you a penny to switch (or perhaps I offer you a penny to stay with your original choice). To always be bribed by a penny is a bad strategy in my game -- you'll get a penny and open an empty briefcase. (Assuming that the Banker has incentive to reduce your winnings -- for example they get to keep the contents of the other briefcase.) Meanwhile, in Deal or No Deal, unlike my game, you never get any useful information distinguishing unopened briefcases, so there is never mathematical incentive to swap or stick. --Brokenfixer 23:22, 13 January 2006 (UTC)


 * Brokenfixer is correct in that the essence of the Monty Hall "paradox" (which is paradoxical only to those who do not understand it), is that the host has perfect information about the hidden items and the contestant of course does not. The host then takes an action that conveys information to the contestant. The contestant can then then act on that information to improve his/her chance of winning. However, in this game the host does nothing of the sort! No extra information is being conveyed to the contestant; contestant and host learn the same information at the same time. Therefore the host has no opportunity to give information to the contestant that might change the odds of winning. And therefore the Monty Hall argument is entirely irrelevant to the game Deal or No Deal! Arguments that the banker "might" inadvertently convey a little snippet of information are similarly irrelevant; there is no evidence whatever that it actually happens. See the discussion of banker algorithms... the fact is that nobody really knows how the "banker" is arriving at the amounts that are offered. -- Jane Q. Public 02:25, 21 January 2007 (UTC)

2. Claim that revealing lower-valued cases randomly still yields Monty Hall, and Responses
In the section "Mathematical basis", it is stated that this game is not a version of Monty-hall problem. This is untrue. It doesn't matter who opens the cases (a person who knows what's in them, or who doesn't know). The only thing that matter for Monty-hall is that the cases which are revealed have average value lower than at start of the game.

I will not change the original article because of my bad english. Can someone do that?

(Unsigned comment by 83.131.134.247 15:31, 13 January 2006)


 * Your english is good but unfortunately your math is bad. Consider 100 boxes, 99 empty and one with $1 million. You choose one box. 98 remaining boxes are opened at RANDOM, and all happen to show empty. This is unlikely but possible (2% chance). Your chance of having originally chosen $1 million is 50/50, (lucky you), which is totally different from Monty Hall. Try it with a deck of cards (52 "boxes") with the Ace of Spades as a win card, or run a computer simulation. With Random Selection, the last briefcase is worth more than the initially chosen briefcase 50% of the time, REGARDLESS of the values of all of the revealed briefcases. Contrast this with 100-box Monty Hall, where the last briefcase is 99% likely to contain more than the initially chosen briefcase! --Brokenfixer 23:45, 13 January 2006 (UTC)


 * DoND is not Monty Hall. In Monty Hall, the host is NOT always choosing randomly, sometimes he is choosing deliberately to avoid the car door. In Deal Or No Deal the player IS always choosing randomly up to the choice to swap boxes. It is this difference that is crucial in Monty Hall. This element of non-randomness is what makes the final decision non-random, so to speak. In DoND, everything is random. Aaron McDaid 01:33, 14 January 2006 (UTC)


 * There is no reason for me to completely repeat myself; see my statement in section (1) above. There is also no need for any math. The Monty Hall situation is entirely dependent on the host conveying information to the contestant that the contestant otherwise could not know!! That does not take place here: in this game the host and contestant receive the same information at the same time. There is no opportunity for the host to act in "Monty Hall" - type ways that would alter the odds. -- Jane Q. Public 02:34, 21 January 2007 (UTC)


 * This is not Monty-Hall. Let's say there were 3 cases left (one with $5, one with $1000, one with $75000).


 * Option 1: Contestant has $75,000 case. They can
 * Open the $5 case, $1000 remaining (would lose money by swapping)
 * Open the $1000 case, $5 remaining (would lose money by swapping)
 * Option 2: Contestant has $1000 case. They can
 * Open the $5 case, $75,000 remaining (would gain money by swapping)
 * Open the $75,000 case, $5 remaining (would lose money by swapping)
 * Option 3: Contestant has $5 case. They can
 * Open the $1000 case, $75,000 remaining (would gain money by swapping)
 * Open the $75,000 case, $1000 remaining (would gain money by swapping)
 * Now each of the above options, and each choice resulting in those options, are totally random. You've got as much chance as picking the $75,000 case at the start as you do the $5 case (1/26 chance for each in America). So in the end, 50% of the scenarios (3/6) would see you benefit by swapping at the end. The other 50% and you'd lose. This is proof that Monty-Hall does not apply when case selection is random. DynaBlast 16:05, 13 January 2006 (UTC)


 * In Monty Hall, the player actually has a 66%, not 33%, chance of winning the car if he/she plays the optimum strategy (swapping). In Monty Hall, the player chooses one of three doors, one containing a car, two containing a goat. At this stage the player has a 33% chance of having selected the door with the car. The host now opens a door containing a goat and offers the player the option to change doors, and the player accepts. There are two possibilities:
 * The player had originally chosen the door containing the car (33% likely), and then changes to the door containing the other goat.
 * The player had originally chosen the door containing a goat (66% likely), and then changes to the door containing the car (all three doors can't contain goats).
 * This clearly means the player who swaps has a 66% chance of going home with the car. The player who doesn't swap only has a 33% chance of going home with the car.
 * In the above evaluation of the Monty Hall swapping strategy, I was able to rely on the certainty that the host will definitely open a door containing a goat. To evaluate the swapping strategy for Deal or No Deal, there is no such certainty, so we need a more complicated 'tree' of possibilities, like this: (I'm going to imagine there is $1000, 1c and 2c still in play).
 * Player had originally chosen the $1000 box (33% likely). Now a box is opened. It will contain a worthless amount, and the player will go home with the other worthless amount.
 * Player had originally chosen a 'worthless' door (66% likely). Now a box is opened. It's 50/50 whether it'll be $1000 or not:
 * - The box opened contains $1000. This is (66% x 50%) 33% likely. Player goes home with worthless amount.
 * - The box opened contains the other worthless amount. This is (66% x 50%) 33% likely. Player swaps and goes home with $1000.
 * Therefore, in Deal or No Deal when you are at three boxes, even if you swap you have only a 33% chance of going home with the $1000.
 * --Aaron McDaid 18:40, 15 January 2006 (UTC)

Deal or No Deal is not the same as the Monty Hall game show. In Monty Hall, extra information is given to the contestent which, of course, changes the odds. In Deal or No Deal, no such information is given to the contestent.

If Monty Hall opened a door at random without prior knowledge, this would act in a similar way to deal or no deal. That is, if Monty hall opened a door at random and it wasn't the car (or whatever the good prize was), the contestent would be left with a 50/50 chance rather than a 1/3-2/3 split. 50 / 50 because there are 2 doors and one prize. In deal or no deal there may be 6 doors and 1 prize (1/6 chance) or maybe 5 doors with 2 prizes you are willing to take (2/5)

The mathematics of Deal or No deal are simple. 1/26 chance of winning £250k to begin with with odds improving as the game continues without the 250k showing up. Any complications are errors. If you are willing to settle for, say, the top 3 prizes, then your odds begin at 3/26 etc.

3. (Nov 2005) Notice that UK section calls DoND a Monty Hall problem
I have just archived the thread that was here, as it contained little that is not in the other Monty-Hall subthreads. --Aaron McDaid 17:58, 15 January 2006 (UTC)

4. Statistical Test
I ran this problem through a simulator 1,000,000 times using 100 cases. The chance that switching cases will get a higher amount than not switching when only 2 cases are left is above 50%. I fixed the section on Monty Hall to explain that, in accordance with the Monty Hall problem, switching will increase the chance of getting a higher amount, but will not increase the chance of winning the highest amount possible at the beginning of the game. I think that explains why the chance of winning the big prize isn't increased even though the Monty Hall problem would make it appear that you could win the big prize easily. --Kainaw (talk) 19:51, 17 March 2006 (UTC)

I just reran it again with one more addition. The 100 cases were valued $1 to $100. With the slight advantage gained by switching (51.2% chance of getting a better case this time - 50.9% chance last time), the average winning was $50.56. So, all in all, the percentage chance of increasing your money is very small as is the actual cash increase. --Kainaw (talk) 20:24, 17 March 2006 (UTC)

I ran into something rather odd here. I ran the simulator on my Sun server overnight so it could go through 1,000,000 games repeatedly and send the results of each set. I also kept it looping on my Dell PC. The Dell PC came back with 6 completed 1,000,000 game sets - each one giving the player a very slight advantage in switching (avg 50.89%). The Sun ran through 14 1,000,000 game sets. Every one came back with the chance of winning exactly 50.0% if you keep or switch. The Dell has a single Intel chip. The Sun has two AMD chips. Could this be a problem with Intel's math processor? I'm going to run this on other PCs over the weekend and see what I get. --Kainaw (talk) 14:26, 18 March 2006 (UTC)

I ran my simulator over the weekend on all of my servers, my PC, and my laptop. The PC and the Laptop both have Intel Celerons in them. They show a small advantage (slightly less than 1%) in switching at the end of the game. The servers have real Intel and AMD chips in them. They all show that it is clearly a 50.0/50.0 chance of getting more money by switching. I then reversed the check to try and lose money. The celerons claimed you had about a 1% chance of losing money by switching. So, it is my opinion that the Celeron's math processor is terrible. I already knew it was not to be used for statistical analysis, but this is pathetic. I'm going to alter my edits to the article to show that it is clearly a 50/50 shot of getting more money, not a Monty Hall problem. --Kainaw (talk) 13:32, 20 March 2006 (UTC)


 * Long runs of random tests do not converge on the average; if for instance you play the simple coin flip game (+1 on heads, -1 on tails), while your expected value is always zero, the actual values slowly but surely diverge from 0, and in fact the odds of having exactly 0 at any given point are quite small. (The odds of having 0 at *some* point are effectively 1, but at any given point rapidly drops to effectively 0.) Thus, 50.89%, even run several times is not surprising. Remember, if the Monty Hall effect were actually in play, you should be getting values closer to 99%. Your simulation was most likely fine, and effectively proved the Monty Hall effect is not in play. -- Unsigned, date unknown.


 * Kainaw, you must keep a couple of things in mind. First, contrary to what was stated just above, statistics do not prove anything... they merely point us toward what is more likely to be the truth. Those are definitely not the same things. Second, since it is a statistical sampling, it would be fishy if you did get identical results. The fact that one or more came out to exactly 50/50 is very suspicious and raises questions about your methodology. That could reflect more on the quality of the random number generator used by your software than about the nature of the problem itself. -- Jane Q. Public 02:40, 21 January 2007 (UTC)

Other comments
Excellent show. I think this should be brought back on a weekly basis and it's a good show to watch until Survivor returns. -- Eddie

The US explanation...sucks. The Australian version makes much more sense. The US version fails to mention that a person decides more based on what the next bank offer will be rather than what their case contains. 68.7.151.162 04:12, 21 December 2005 (UTC)


 * But that is irrational for at least a couple of reasons. First, it requires that you second-guess the banker, who is not at all consistent. Second, the banker usually makes offers that are too low, based on the expected return ("expected utility" in the jargon). So basing your decision on what you guess the banker will do, rather than the actual statistics, will result in a lower average return. -- Jane Q. Public 02:53, 21 January 2007 (UTC)

"see the banker's offer after the deal"? what does it mean
What does this recent addition to Deal_or_No_Deal mean? I don't understand it as it's written:


 * The main difference is that once a person has made a deal with the banker, we are able to see the banker's offer after the deal with the deal that the contestant has made. This will give a clearer picture to the TV audience on whether the contestant has made a good deal.

--Aaron McDaid 00:32, 19 January 2006 (UTC)
 * It's badly worded, and I'm not sure of the details of the UK version of DOND, but it sounds like the following features of the Australian version: After making a deal, the contestant continues to open briefcases. After opening a number of cases the Bank sometimes shows what it would have offered had the contestant chosen to keep playing. This usually occurs if the contestant knocks out large value after making their deal (the bank revealing the lower offer that would have resulted from this) or if the contestant manages to avoid large values (showing that had they kept playing they may have recieved a larger bank offer). This makes it clear whether or not the contestant has optimised their winnings through correct timing of taking a deal. - DynaBlast 04:17, 19 January 2006 (UTC)
 * Q4 just made an edit that looks good. I'll probably be watching the UK DOND on Saturday, so I can check it out. The UK version always (from very early January 2006 at least) followed through and got the other offers from the Banker after a player dealed. I think this new feature is simply to display the number on screen in case the viewer forgot. i.e. They're not displaying any new information, just helping the viewer to remember. --Aaron McDaid 10:39, 19 January 2006 (UTC)

US page moved, mathematical analysis
I would think that the mathematical analysis that was moved to Deal or No Deal (USA) applies (at least most of it) to any version, and perhaps belongs on this page rather than being on the US page? Elpaw 10:38, 23 January 2006 (UTC)
 * I agree that it can go on this page, but that section is currently very much based on the American version (a million dollars, for example) and can do with a little globalising. Bluejam 15:58, 26 January 2006 (UTC)

add Average vs. Expected Payout?
It'd be nice to have a up-to-date table of the average payout on each version of the show and the expected payout per episode assuming the player turns down every offer. It seems to me that if the Banker makes offers that are below the expected value of the game most of the time, he should expect to pay more over the course of the show. On the other hand, when players do accept a low offer, he makes up for the losses. It'd be interesting to see which factor is stronger.


 * through 41 games played through May 3, 2006, the US version has paid out an average of $131,142 (assuming that a pony is worth $10,000.) The average value of the contestants' cases has been $125,592.

Banker Offers:

Defining Average Payout as the sum of the all the amouts/# of cases, and Expected Payout as what people walk away with (I know, not the best choice of terms);

If the Banker decides to offer the "Average Payout" each time, then the Expected Payout would=Average Payout (on average). If the Banker decides to offer zero each time, noboby would take zero, again, the Expected Payout=Average Payout (again, on average). There has to be some number, between zero and "Average Payout", that the banker could offer, to minimize his loses. I would be based on the constestents utility curve for money. Can some mathmatition take a stab at this?Steve kap 16:59, 10 May 2006 (UTC)
 * Nothing in this game is of consequence. Just play to the end, it's a game of luck not skill. Carewolf 08:50, 17 September 2007 (UTC)

Well, yes it's a game of luck, but there are still good choices and bad choices, even in a stocastic environment. Blackjack is a game of luck, but I still woundn't hit on hard 17!! —Preceding unsigned comment added by Steve kap (talk • contribs) 17:04, 17 September 2007 (UTC)

Do odds change?
I was puzzled over this question: at the beginning the contestant obviously has a 1 in 26 chance of getting the briefcase with the $3M. Suppose the contestant then opens ten cases which are small prizes and worthless, so there are now 16 cases remaining. Are the odds that the contestant has the $3m briefcase now 1 in 26 or 1 in 16? -Abscissa 04:46, 4 March 2006 (UTC)


 * 1 in 16. Because you only had a 16 in 26 chance of reaching this stage in the first place. It would only be 1 in 26 if the chance of the $3M already being knocked out was zero (as in the Monty Hall paradox). --Bonalaw 10:30, 4 March 2006 (UTC)

The authors of the article claim that the contestant should make a deal if the deal exceeds the mean of the remaining cases. This is simply not true. The contestant should maximize expected utility, which in most cases means rejecting even actually fair bets because of risk aversion.

There is also the article which states that people are "less risk averse" while on the show. This is not necessarily true, and the result is most likely evidence that the researchers failed to correctly decide the utility functions of the contestants. There is certainly utility to be gained by showing the public how brave you are by taking such risks. The same rationale can be used to explain why so many people gamble. Just my two cents. --Dafrk3in

Yes, it IS true! The contestant should ALWAYS make a deal in that situation. The article never says to reject all offers lower than the mean, only to be sure to take all HIGHER than the mean. False dichotomy error!Steve kap 20:25, 1 June 2006 (UTC)

All good comments, to the original question: Yes, odds do change! That sounds surprising, but the way we calculate the odds of something happening IS A FUNCTION OF OUR KNOWLEDGE OF THE SITUATION! Odds ARE relative! A simple example, Say someone puts 5 marbles each in 5 bags, one of the 25 marbles is gold. Say also this person tells me which bag has the gold marble, but doesn't tell you. The odds of ME getting the gold are 1/5. For you, 1/25. Its relative to the knowledge we have. Its not an absolute! Steve kap 20:10, 1 June 2006 (UTC)


 * The fact that odds change based on our knowledge of the situation is what drives the Monty Hall "paradox", and explains exactly why it is not relevant to this game. However, the statement about "odds changing" should be qualified. The statistical odds of where something might be, or which cards are where on the poker table for example, do not change. What actually changes is our chance of knowing where they are, based on the situation. Some people equate the two, which explains the confusion over this issue. They are actually two very different things.


 * In the example above, the odds of the gold marble being drawn at random (being in a specific place) are always 1/25. However, knowing which bag to reach into increases your chance of choosing the gold ball by a factor of 5. The odds of the ball being in a given place have not changed. What has changed is your odds of knowing where that place is. These are two completely different numbers (1/25 vs 1/5) which describe different things. People get confused over this issue (and their math gets fuzzy) when they insist on treating them as though they were the same thing. They are not. -- Jane Q. Public 02:59, 21 January 2007 (UTC)

You seems to be saying that there is an "actual" odds and an "odds of knowing" something. "two very different things" you say. I can assure you that this is not the case. The odds of something happening or something being true is ALWAYS relative, relative to the state of knowlege of the person doing the guessing. So odds DO change. I think the confusion come in not knowing this. In your example, yes, the odds of gold ball being choose DO change if the choose knows which bag its in, and intends to maximise the change of picking it. If, however, the picking is still at random, throwing out the knowelge of what bag its in, yes, the odds are still 1/25 for picking it. Knowledge is usless if its not used. Steve kap 04:20, 24 June 2007 (UTC)

Deal or No deal is dodgy!
Anyone aware of this? : http://forum.digitalspy.co.uk/board/showthread.php?t=349545&page=7&pp=25

Endemol have a problem with their random generator apparently, you can predict whats in the boxes

1	10,000 2	35,000 3	100 4	1p 5	50 6	1 7	750 8	50p 9	20,000 10	250,000 11	500 12	1,000 13	75,000 14	50,000 15	10 16	3,000 17	100,000 18	250 19	5 20	15,000 21	5,000 22	10p

she has 15 000 in her box (Sat 4th march)


 * Already covered in the Deal or No Deal (UK) article. --Bonalaw 11:17, 5 March 2006 (UTC)

Is it possible to win a million?
I happened to watch the Australian contestant who won the top prize. He mentioned during the game that he 'knew' he had the winning case, and rejected every offer based on that guess. The article suggests that the only conditions in which someone would win the top prize would be to have the second-top prize on the board as well. (Surprisingly, often when this happens people will hedge their bets and take the deal, which is usually the exact mean by that point.) The winning contestant didn't have this sort of board, and each case opened only strengthened his conviction that he had selected the winning case from the beginning.

In any case, self-delusion isn't covered in the article, when that was the secret of what appears to be the only top prize winner so far.

UPDATE: There were 2 winners in the United States on Deal or No Deal this season. —Preceding unsigned comment added by J4lambert (talk • contribs) 13:23, 14 January 2009 (UTC)

The 'will someone win the top prize' section
This bit's ridiculously US-centric, but trying to globalise it is tricky. There's many references to dollars, cases, etc - you could just move the entire section to the US page, but it seems a shame for something that despite being so US-centic is very well written. Anyone up for the tough job of globalising? BillyH 11:11, 5 April 2006 (UTC)

Prime Time
I don't want to change it in case I'm wrong, but didn't the Saturday version of the show in the UK go from 5:45pm to 7:10pm rather than the other way round as is currently stated? In any case, having a show move from 7 to 5 because of popularity (as is stated) would be a backwards step. 7 is nearer prime time, so I think I'm right. Ben davison 16:32, 4 May 2006 (UTC)

Philippines Version
The Philippines Version is similar to Deal or No Deal, but it does not seem to be associated with the actual Deal or No Deal Franchise. I have removed it for that purpose. Please, correct me if I'm wrong. Pacdude 20:23, 5 May 2006 (UTC)
 * The Philippines will soon have a local version, one network here is showing teasers for it. Maybe we can restore it when the show has begun airing? Wheeler.059 16:25, 20 May 2006 (UTC)

Too many links?...
Yeah, I looked at the bottom of the page, and there is a TON of links... Seems to me, a few official links and maybe one or two fansites are OK, but 50-so links seems a bit excessive.

Just trying to get opinions before I change anything...

-- N3X15  ( Scream  &middot;  Contribs ) 20:39, 5 May 2006 (UTC)


 * Yeah, go for it, I hate a long list of links. --Robdurbar 17:48, 10 May 2006 (UTC)

Algorithm or formula for banker's offer?
OK, so we're all agreed that most of the banker's offers are below the arithmetic mean of the dollar values remaining in play. In fact, they start far below the mean, and get closer to it as the contestant continues to refuse deals. But has anyone found any more specific pattern, perhaps a formula or algorithm that determines the banker's offers? In the USA version, at least, I don't believe the banker (or a producer conference) decides each offer individually, because I made up an Excel spreadsheet hoping to see a pattern to the offers -- like some predictably increasing percentage of the mean, or a predictable number of standard devs from the mean -- but neither matched. Any thoughts? --Jay (Histrion) (talk • contribs) 14:27, 15 May 2006 (UTC)
 * 1) in post-deal situations, when Howie does his "what would you have picked next?" routine, the hypotheical offers come up quickly; and
 * 2) the official website clearly doesn't have a bunch of producers sitting around watching me play. :)
 * I think the algorithm determining the offer adds or subtracts a random value somewhere, and that's why it doesn't match up. 63.227.185.86 04:22, 19 September 2006 (UTC)


 * I too have wondered about the algorithm for the banker. While the Wikipedia article is quite good at discussing the offer being slightly below the mean, one has to wonder if the wonder if the number is truly random or not. I suppose statistical analysis of all the offers made to date could reveal this. I doubt that NBC would reveal anything, as the banker is always operating in a cloud of secrecy behind that heavily tinted glass. Nodekeeper 02:34, 3 October 2006 (UTC)


 * But there was mention of an actual situation in which a woman opened a case with one of the few remaining large values in it, and the banker's offer after that was considerably above the mean. So either your algorithm must account for such artifacts (which could result from an overshoot in a smoothing algorithm, for example), or you have to admit that it is a human banker. Perhaps it is algorithmic with the option of a human overruling the math. Perhaps the "banker" decisions shown after the deal are purely algorithmic while the real bank offers are not; we have no way to know. -- Jane Q. Public 03:12, 21 January 2007 (UTC)

Its been a long while since calculus, but i would suggest a non-linear equation with variables like

y = banker's offer a = current arithmetic mean a1 = worst case arithmetic mean (after the next round) C = coeeficcient for risk aversion (some constant) D = coeficient for the number of cases remaining (some other constant)

I would expect that the bank is not minimizing cost, but maxmizing revenue (from advertizing). Controlling costs for the show is easy - change the amounts on the board. Since advertising costs are a function of ratings, and ratings are a function of "drama" then what you want to do is maximize the risks being taken by every contestant. From the show's perspective, it is  quite possible that the producers are playing the contestants individually, trying to encourage higher highs and lower lows.


 * In a show like this, they want people to win - but not too often. If every episode, the player walked away with large prizes, ratings would suffer, as the show would get dull. If every episode, the player walked away with little money, the ratings would suffer. Offers by the banker of below the expected value encourage the player to continue. Sometimes, toward the end, the banker will make an offer higher than the expected value to encourage the player to take the deal. I expect that the screening process for the show selects for players who are highly inclined to take risks.--RLent (talk) 22:40, 24 January 2008 (UTC)


 * If I were to be the banker, I'd base bids on a mathematical model of participant behaviour, based on educated guesses in the first program, but progressively more based on statistics of actual behaviour in later programs. Based on such a model, I'd give the bid that minimizes my expected expenses. While the participants have a nonlinear utility function (decreasing marginal utilities), the banker can afford to see things in the perspective of a whole series of programs. The model should include a guess at the participant's utility function, but also the psychology involved in streaks of luck or misfortune. Perhaps something like a neural network, trained by constructed or real past games, could do the trick. The banker might also take into account the psychology of the viewers - how do we best create suspense here? After all, the economy of the TV company is not only decided by the prizes paid to the participants, but also by advertising income and hence number of viewers. Throwing in a bit of plain randomness to keep us speculating on this issue might add to the interest.
 * My point here really is, I don't think anyone is likely to find "the formula" by analyzing the programs. Rather one would need a leak from the TV companies...--Niels Ø (noe) 13:48, 12 January 2007 (UTC)

TRY COMPUTING THE AMOUNTS THAT ARE STILL ON THE BOARD USING THE GEOMETRIC MEAN THEN RAISING THE GEOMETRIC MEAN TO 2 0r 2.5 if you feel CHARITABLE. I THINK THIS WILL WORK IN THE UK VERSION. —Preceding unsigned comment added by 119.92.245.200 (talk) 03:24, 29 January 2009 (UTC)

my dond strategy at high levels
i have a live-action "competitive" deal that i play at home, very similar to the us version, except that it has a "jackpot" that increases every time it is not won by $125,000, and resets to $1,000,000 when it is. it can go up to $9,900,000. everybody who is connected to the internet is eligible to win the jackpot or increase it. all the other high cases increase accordingly. my current record is $2,500,000 in my (switched) case (jackpot $5,000,000). yes, it is bigjon's dond!!

what i do (that is, when the stakes are very high) is calculate the difference between the banker's offer and the potential offer if i open any small case and if i open each specific large case. (if the case is big, but smaller than the offer, i take it separately as one of the small cases.) i multiply by the chance of opening the low cases/high cases to get two totals: the "expected gain" and "expected loss". if the gain is higher than the loss, i continue. if vice versa, i deal. take an example from one of my games. there are $300, $400, $400,000, and $1,875,000 (jackpot) remaining. the offer is $540,000. if i open the $300 or $400, the offer increases to $758,000, for a gain of $218,000. this happens 1/2 of the time, so the current potential gain is $109,000. if i open the $400,000, the offer increases to $625,000, for a gain of $85,000. this happens 1/4 of the time, so the full potential gain is $130,250. if i open the $1,875,000, the offer decreases to $133,000, for a loss of $407,000. this happens 1/4 of the time, so the potential loss is $101,750. the gain is higher than the loss, so i continued. i opened the $400,000 and got the offer of $625,000. now i computed: if i open the $300 or $400, the offer increases to $937,000, for a gain of $312,000. this happens 2/3 of the time, so the potential gain is $208,000. if i open the $1,875,000, the offer decreases to $350, for a loss of $624,650. this happens 1/3 of the time, so the potential loss is $208,220. the odds were VERY SLIGHTLY against me, so i dealed. the next selection would have been $1,875,000, and there was $400 in my case. Andrewb1 18:41, 20 May 2006 (UTC)

Potential Value v. Expected Value
The opening paragraph uses the phrase "... the offer being based on the potential value of the contestant's case." While that's correct, in that the case has a definite value, the offer itself is based on the [b]expected value[/b] of the contestant's case with a little risk aversion thrown in there. Would "expected value," being a little more technical a term, be better than "potential value"? Ryanluck 00:51, 6 June 2006 (UTC)

Monty Hall Problem
There's rather too much about the Monty Hall Problem in this article, considering the similarity is very superficial, and stems purely from an incomplete understanding of the Monty Hall Problem itself. The probabilities are very very simple: you pick two boxes/cases at random, one at the start, one at the end (by eliminating the rest). Is one more likely than the other to contain the larger prize? No. There is no reason to even bring the completely irrelevant Monty Hall Problem into it. --Bonalaw 07:51, 29 June 2006 (UTC)


 * Thank you for pointing this out so directly. I completely agree. Those who have been introducing the "Monty Hall" complication into the issue have done so only because they do not really understand it. I would be tempted to edit out all such comments, if it were not sure to draw heavy fire from those same misinformed individuals. -- Jane Q. Public 06:01, 21 January 2007 (UTC)

Template placement
I know the template on top serves as prominence, but most Wikipedia articles have templates at the bottom or on the right side of the article. Because of this, I moved Deal or No Deal to the bottom. —Whomp t/c  18:55, 15 July 2006 (UTC)

Brazil
Now in Brazil since Aug 6th, 2006, by Sílvio Santos' SBT under "Topa ou não topa" (Accept or not)...
 * Usien6 23:58, 6 August 2006 (UTC)

Trivia
I've deleted the trivia section for now, as the only piece was UK-related, and is mentioned in the UK Deal or No Deal article. Trivia on this page ought to be kept general to at least some of the different international additions. rv if I'm wrong. The post in front was made by Popexvi 14:40, 24 August 2006 (UTC)

...around the world
It doesn't make sense to me that the links to the various national versions of this show are shunted off to a secondary page, while the main article - where one would expect to see these - is almost entirely mathematical theory. Lambertman 15:28, 29 August 2006 (UTC)

DoND - self-defeating?
It certainly seems so:

If a player knocks out a bunch of higher value boxes, they get disappointed, and depending on how many higher boxes are still in the game, they'll either stay (with one or two high value boxes) or keep going (when it's futile and they just want to play out the rest of the game.)

If a player knocks out a bunch of lower value boxes, they get excited, want to continue, fail to accept reasonable bank offers, and have a higher chance of knocking out the higher value boxes (which then disappoint as above). This was shown tonight when the african-american guy (forgot his name) knocked out a TON of low-value cases at the start, then kept going and lost it all.

Based on tonight's episode, it seems as if when you get to a certain point in the game and decide to keep going, you should not stop at all. Rejecting the bank 4 or 5 times, and then getting discouraged after getting rid of a bunch of higher-value cases seems stupid. It is inevitable, if you reject the offer and truly believe there is a lot of money in your case, that you'll hit those higher value cases at some point and simply not care (because you think you have the million or whatever). To start caring seems to show kind of a dumb strategy. It's not like you're going to never hit a higher-value case. Wooty 04:37, 19 September 2006 (UTC)
 * The game itself isn't self-defeating, but players often play in an irrational manner. It's easy to get caught up in the excitement and risk a lot of money on the hopes of getting a little bit more.--RLent 21:50, 28 September 2006 (UTC)

Truly random assignment?
Does anyone know if the values are put into the cases by a truly random process, or if they are placed in the cases by a third party "randomly", i.e., that person's subjective sense that the values are thoroughly mixed? --Jeff 16:56, 26 September 2006 (UTC)


 * In the UK, it is done by drawing balls out of a bag. TomPhil (talk) 13:19, 27 September 2006 (UTC)


 * Ever since the game show hoaxes in the 1950s and 1960s, by law this information is publicly available for all U.S. game shows that give cash or material prizes. You should contact the studio and find out how they do it. -- Jane Q. Public 06:03, 21 January 2007 (UTC)

Original Research
This article is trying to be a research paper rather than an encyclopedia article. The "Actual simulation results and conclusions" contains more detail and analysis about the simulation than the original website source. It also spends way too much time discussing game strategy instead of the show itself. A lot of the stuff is really good, really interesting information, but it needs a new home. -Anþony 06:35, 3 October 2006 (UTC)

Indeed, the research referenced by Anþony is not appropriate for this article. It is written in the first person for a start. But take a closer look at the model used: the banker's offers matched the expected value of the player's box! Hence it is not surprising that, in the artificial model, the player fares no better or worse than his expected winnings at the start of the game, after a thousand simulations. In the real game, the banker offers LESS than the expected value of the player's box.

Split Sections
I'm advocating that sections 3-6 be split into new article Deal or No Deal Game Strategy or something similar. The focus of this article should be the discussion of the television show and its various incarnations, not the overwrought analysis of optimum strategy that is here now. Is there a strong consensus either way or should we put it to a vote? -Anþony 03:14, 11 October 2006 (UTC)
 * After tagging the article and posting notice here in the talk page over two weeks ago and hearing no dissent, I have split the sections as I suggested. Topics dealing with mathematical analysis and optimum game strategy should now go to Deal or No Deal Game Strategy. -Anþony 07:40, 21 October 2006 (UTC)

Transliterations/Transcriptions?
In the list of national versions, I have just changed the titles for Hong Kong's version, '一擲千金', and Tunisia's version, 'دليلك ملك', back to 'Deal or No Deal'. The reason for this is that for Bulgaria's version, for example, the name in the list is 'Sdelka ili ne', and not 'Сделка или не'; i.e. it has been transliterated/transcripted. If anyone can transliterate the names above, and add them back into the list, I'd be grateful! Thanks, - Lewis R « &#1090; · c » 11:50, 26 October 2006 (UTC)

External Links 2
Please do not add links to flash games or fan sites. These sites are not symmetrically related to the show per WP:EL. That is, they have a connection to the show, but the show has no connection to them. Repeated re-additions without explanation or justification will be considered WP:SPAM and dealt with appropriately. –  Anþony  talk  11:44, 27 December 2006 (UTC)


 * lots of people have been doing this actually, the same 2 sites now added (and reverted) from 3 different IPs. Strange. Thedreamdied 12:40, 29 December 2006 (UTC)


 * I count several different IPs which all trace back to the Philippine Long Distance Telephone Company:
 * IP Info (logged by Thedreamdied 23:23, 29 December 2006 (UTC), will spam3.)
 * IP Info
 * IP Info
 * IP Info
 * IP Info
 * IP Info
 * IP Info
 * IP Info
 * IP Info
 * IP Info
 * I think it's safe to assume it's one person. Quite strangely, it seems this anon was edit warring with another anon over including a different flash game. The annoying problem is his IP changes so much, he might not even be seeing the spam warnings to his talk page. I'm gonna sprinkle some 's around, then report to WP:ANI if he doesn't stop. –   Anþony  talk  13:31, 29 December 2006 (UTC)


 * I should also point out that one of the sites he's trying to add, DealOrNoDeal.com, is a legitimate link sponsored by Endemol for the UK version. Since that was the only real link in the previous "other websites" section, I moved it up to the official websites section. –  Anþony  talk  13:43, 29 December 2006 (UTC)

Addition of a "criticism" section?
First, let me say that everyone is entitled to their opinion, and I'm certainly not trying to get my own personal *unsupported* opinion into this article. HOWEVER, after being subjected to this godawful show dozens of times over the past few months (my coworker loves it), I really do feel that we need to have a little more than thinly veiled praise for its "deceptively simple format." A cursory glance reveals that game shows can have "criticism" sections (Fear Factor), and there are certainly other (citable) people that agree with me (http://www.metacritic.com/tv/shows/dealornodeal), so... are there any objections?

For the record, the problem I (and many others) have with this show is that it's just so freaking BRAINLESS. There's no silliness or craziness or diversion like Let's Make a Deal, and because (ostensibly) NO ONE knows what's inside the case, there's absolutely no skill involved, no statistical tricks like the Monty Hall problem. It's rather sad that people have spent pages debating this absurdly simple fact--the Monty Hall problem hinges ENTIRELY on the fact that someone DOES, in fact, know what the hidden values/objects are. In Deal or No Deal, no one does, and lacking the zaniness of Let's Make a Deal, the gameplay is thus reduced to a simple mathematic exercise.

The article implies that the bank offer is not always a set percentage lower than the expected value (I don't care enough to check this fact on my own.) I suppose this increases the complexity of the game a bit by introducing some randomness, but it's still blisteringly uninteresting. There's no real skill *at all*, nor does anything unexpected ever occur (contestant behavior aside.) There are only four basic (rational) ways a contestant could play it:

1. Accept *any* offer that comes fairly close to the expected value (you'd base your definition of "fairly close" on previous observation of the show.) Though playing through until the very end is (statistically) a more profitable wager, this is the most profitable  *safe* alternative. This strategy is based on the simple, statistical reality of the situation.

2. Play it through to the end, no matter what. Mathematically, this is actually the best strategy (though given the real-world differences between the quantities of cash involved, this might not be optimal. See #3 for details.)

3. Pick a value you will not accept less than (e.g. $75,000, and never accept a lower offer until it becomes IMPOSSIBLE to win that value (all cases equal to or greater than the value have been eliminated), at which point you either accept immediately, pick a new "magic number", or resolve to play it through until the end. This strategy is based on the fact that not everyone really cares about risk/reward ratio--and for good reason. $10,000 might not change someone's life very much at all, but $200,000 very well could.  Thus, it can make sense to hold out for the larger prize instead of cashing out.  Similarly, it makes sense to cash out for an offer equal to or greater than your own personal "magic number", because even though the risk of continued play is mathematically in your favor, it doesn't make sense to needlessly jeopardize what is (to *you*) a life-changing amount of cash.

You may or may not elect to take into account the difference between the bank's offer and your expected value while executing this strategy (e.g., you might decide that you won't accept any value less than X AND the value can't be more than N% less than your expected value.)

4. Cheat.

So... yeah. Basically, there's NEVER a question as to whether the bank offer will go up or down (it's often presented as some sort of mystery.) If you had a calculator, you could probably predict with "amazing" accuracy what the bank offer will be, every time (the actual accuracy depends on when and how far they randomize the expected value/actual offer ratio.)  And every time an offer is made, a contestant has two simple things to consider:  the expected value/actual offer ratio (no one ever does this, because they apparently don't allow the mathematically-inclined to go on the show) and whether the current offer is in the range they consider to be "worthwhile" or "life-changing."

If I was exposed to it only occasionally, I might find it MILDLY interesting as long as the contestants and host behaved with a modicum of sense... but they don't. The simple, black and white statistical reality of the situation is completely obscured by laughable melodrama: OMG, I PICKED A HIGH VALUE?!?!? WHAT WERE THE *CHANCES* OF THAT HAPPENING?????! (Well, GENIUS, let's see: There were 7 boxes left--counting the first one-- and there were two very high values left, so the odds were EXACTLY two in seven, approximately 28.6% or, very roughly speaking, a bit less than one in three. I learned how to do that in the fifth grade, I think.)  OMG THE OFFER WENT DOWN?!?!?!!! OMFG THE OFFER WENT UP?!?!?!!! OMFG THE OFFER WENT BACK UP AGAIN!!!!!! It's just this neverending siege of ignorance, superstition and melodrama...

There's a bit of human interest generated by the contestants themselves, but after watching more than an episode or two it's completely overshadowed and obliterated by the over-the-top pretense of the whole thing. It's_simple_math. Assuming Howie and the banker turn down your offers of sexual favors, you never have more than three options: Do you want to shoot for a given "target range" of prize money, settle for the (statistically) best offer you're given (this might require a pocket calculator or at least decent mental math), or, since the bank is going to screw you anyway, just go all the way? Just these three options, and despite what Howie claims there is NO way to develop any more strategy, no way to "outthink the banker" or any such BS... it's like watching someone play rock, paper scissors competitively, but *without* the "complex", "compelling" strategy. At least there's a bit of psychological edge involved in rock, paper scissors. The banker has no such exploitable qualities; his actions are perfectly predictable (with the exception of the aforementioned, apparently-randomized factor in his "offer" equation.) I think that the enormous popularity of the program just goes to show how utterly pathetic the USA's (and indeed, the world's) math skills are.

So yeah, in nutshell I REALLY think the show deserves a "criticism" section (and I'm not alone in my beliefs), but if I wrote it myself it'd probably wind up turning into a rant... -Lode Runner 03:56, 7 January 2007 (UTC)

-

I concur, I cant stand this show, allot of people cannot stand this show, criticism is a worthy section for this article because the article makes out as if this show is widely liked, when in fact many many people dislike it. Criticism could cover the total lack of skill or knowledge required, or the fact in Britain it needs to goddamn assault my brain every single day of the week.

Also it could be asked whether this actually constitutes a gameshow since to play is achieved, it is pure gamble, and that overall it seems to have lowered light entertainment television to its level.


 * But remember, on Wikipedia, your opinion doesn't matter. In order to fill the criticism section you'll have to find criticism in outside publications. Val42 18:22, 26 January 2007 (UTC)
 * Finding criticm is not hard. The questions is if it's appropiate. This show is a blindingly stupid waste of time, but is that fact really relevant for the article? Carewolf 08:42, 17 September 2007 (UTC)

RELEASE DATE
Why isnt anything listed for it as well as seasons, episodes, and other similiarities.74.195.3.199 02:16, 1 February 2007 (UTC) kappa

Map
I'm sorry, but I find the map tediously unnecessary. How is it really helpful to anyone reading this article to see a map? --Brandon Dilbeck 02:51, 17 April 2007 (UTC)

Protection
I have protected this page until consensus can be found with respect to the Monty Hall section. The persistent edit-warring is harmful, and comments are increasingly incivil. Andrwsc 02:57, 27 June 2007 (UTC)
 * Gosh, I just noticed I was compared to Hitler. Anyway, I don't think there's any controversy around the Monty Hall stuff, is there? Surely nobody apart from whoever keeps adding it in agrees it should be there? In any case, I'm going to keep deleting it if it keeps getting added in.--PaulTaylor 12:04, 27 June 2007 (UTC)
 * He keeps adding information that this game is like the Monty Hall Problem, but it isn't. I removed his comments once or twice.  &mdash; Val42 03:08, 28 June 2007 (UTC)

cite needed
A citation is requested for "However it is not uncommon for the bank's offer to exceed the player's expected value very late in the game". A few days ago, they got down to the final two boxes, and the amounts were $750,000 and $1,000,000. The expected value is $875,000 and the banker offered $880,000. (This was the highest offer to date. The player wound up with $750,000 - the largest payout to date.)  Bubba73 (talk), 00:49, 18 October 2007 (UTC)

Explanation of the game?
The article doesn't seem to have any explanation of how the game is actually played. It starts talking about "the cases" and "the banker" without any context; the second and third paragraphs are unintelligible without prior knowledge of the show. Kapow (talk) 23:00, 5 April 2008 (UTC)


 * It looks like the opening description of the game got chopped in a revert somewhere. I've brought it back and tidied it up to be more unspecific to any particular version of the show.  Psuwhammy (talk) 03:30, 4 May 2008 (UTC)

Everything in USD
Why is this? Seems a little offensive to other nations IMO, why is USA so great? I highly doubt that the winners of the grand prize travelled to the US after winning, so why do we want to know the prize amount in USD? Furthermore, there needs to be some sort of explanation in the various country's winners section. it has 3 values, the last one being "back then". what on earth is that supposed to mean? and why? And what are the two values before it? —Preceding unsigned comment added by 121.210.64.214 (talk) 06:32, 4 November 2008 (UTC)

Merge proposal
Deal or no deal christmas star is a article about Christmas specials (UK) which needs some rewriting and merging here, as it is insufficiently notable to stand on its own. Over to you. -- Rodhull andemu  21:32, 24 December 2008 (UTC)
 * Two comments: number 1, that stub, if it's to be merged anywhere, should be merged into the article about the UK version instead of the generic page. Number 2, it's written so poorly that I'm not sure it's worth saving. Psuwhammy (talk) 01:06, 4 January 2009 (UTC)
 * Since nobody's defended it, and per your point 2 (incomprehensible), I've deleted it as WP:CSD#G1. Should anyone think it worth saving, I will gladly restore it to userspace. -- Rodhull andemu  23:45, 18 January 2009 (UTC)

Usage of pronoun 'they'
I'm sorry, but a grammarian would vomit if he saw this page. 'They' has never been, is never, and shall never be singular. There are plenty more practical and grammatically tidy ways of expressing oneself without resorting to such grammatical tomfoolery. Whoever changed the article to support the 'they' usage did so without regard for the English at hand. 149.254.58.80 (talk) 00:01, 26 December 2008 (UTC) User:Oliverbeatson
 * And a feminist would vomit if they saw your use of the word 'he' to describe people of both genders. You're probably not as right as you think you are. - Mark 02:15, 26 December 2008 (UTC)
 * I'm glad that feminists are finding such productive ways of promoting their cause. The point is that 'they' creates vortices of grammatical mayhem. I am not suggesting that continuing to use 'he' as a gender-inclusive pronoun (as historically has been the case) is ideal. I'm saying that 'they' is grammatically incorrect. I am requesting that different ways writing be pursued, for example writing about the 'players' where 'they' is appropriate, or else to rephrase the sentence in a way that does not require the gender to be defined. 149.254.51.253 (talk) 21:31, 26 December 2008 (UTC)
 * 'They' can never be singular?? Really?? If you don't know whether someone is male or female then how else would you refer to THEM!! In the UK, the banker is allegedly singular but never actually appears on screen nor is ever heard, so for all we know they might not even exist.  I am a grammarian.  I'm not vomitting at this sentence, but I burp at the thought of using he for pronouns of unknown gender.  I'm male incidentally so this has nothing to do with sexual politics, just clarity and accuracy.
 * I'm from Quebec and I've also been surprised when I saw it for the first time (while I was translating Facebook in Quebec French). Sincerely, Jimmy Lavoietalk

Dates in the section "Top prize winners on international versions" = Episode air dates?
I was wondering if the dates displayed on the table in that section of the article are the dates of the airing of the episodes featuring the contestants who won the top prize. Kevzspeare (talk) 01:19, 13 January 2009 (UTC)

ruined numerous lives??
Someone added this text " The Deal or No Deal Series has ruined numerous lives; the term hitting case refers to the uncontrollable desire to stay up all night playing the online version of the game while wagering small amounts of money. Although some people have built up small fortunes online, the case of Jason Middleton gained international prominence after he lost his life savings when playing 146 consecutive hours of an online version of the game on the PKR website."

it's kind of interesting, if true, but I've moved it here since at the moment it's just hearsay. if anyone fancies researching it, referencing it and putting it in the right section, they can. raining girl (talk) 12:50, 18 January 2009 (UTC)

A very good source
For explaining the format. Hope it helps. -- can  dle &bull; wicke  23:57, 18 May 2009 (UTC)

Section repeat
There are two 'international versions' sections in the article. They need to be merged into one. Sk8er Boi (talk) 14:15, 14 August 2009 (UTC)

SANTHI
Dear sir, I Am SANTHI From ERODE. I Am DEAL OR NO DEAL GAMES, Please call me My Phone No:95787-48606  —Preceding unsigned comment added by 122.178.133.67 (talk) 05:03, 16 March 2010 (UTC)

Image
Does the image really relate to the series? Which contestants? American? English? The image might be of interest to people who watch the show (which ever country) but the picture doesn't really relate to how the show is played, or who hosts the show, or much really. 92.7.182.133 (talk) 08:14, 24 September 2010 (UTC)

Biggest wins
Some of the prizes are converted to two USD amounts. If the other is to be current (as I understand), then there should be some formula that could get current exchange rates. I looked the code and didn't see anything like that there. If only someone will update it often enough... 85.217.20.154 (talk) 06:13, 13 January 2011 (UTC)

Banker? What Banker?
This discussion page makes a number of references to a "banker" but the article does not mention one. An encyclopaedia article should not assume any previous knowledge of the format of the programme. It should be described in detail.109.154.74.121 (talk) 15:41, 19 September 2011 (UTC)

Mean vs. Median
I believe that the contestant is better off taking the deal if the amount is greater than the median, which is what is to be expected if they were to hold on until they were finished.

The median vs mean issue is really not significant here since simulations showed no net win win several different threshhold values both above and below the mean.

In the long run, in pure probabitity terms, it is better to only take a deal greater than the mean of the remaining boxes (which I don't think ever happens). However, in terms of decision theory, and in reailty, it is the mean utility of the money that is important (basically, how much the money means to someone). Due to the law of diminishing returns (winning twice as much money is better, but not twice as good), this means that the offer of mean utility is always less than the offer of mean money, though how much less varies from person to person, which is why the banker's offer is invariably less than the mean (he could potentially get them to accept a lower offer). —Preceding unsigned comment added by 82.6.96.22 (talk) 18:53, 9 February 2011 (UTC)

Broken sentence
In Gameplay section there's a sentence that should really be two sentences:

''The value of each of The contestant claims (or is assigned) a case to begin the game. ''--Melarish (talk) 16:19, 30 November 2011 (UTC)

Photo
The photo of the Deal or No Deal models adds nothing useful to this article. I have now removed it twice from the article only to be reverted on both occasions by the uploader. It is a freely licensed image, but seems to have no actual link to the gameshow format other than that it is features a group of models described as "Deal or No Deal models". There is no other real reference. Photographs of studio sets, or a screenshot of an episodes from any of the variations would actually mean something. The photo does not, so I will be removing it again. I would welcome comment from the wider community on whether it should really stay or not. Cloudbound (talk) 21:49, 18 April 2013 (UTC)

KOREA
There is now a version in korea called YES OR NO will you have the nerve

I noticed that the section "Deal or No Deal around the world" is constantly vandalized, replacing the actual prizes with ridiculous and/or fake amounts of money (for example: 200.000.000 Canadian dollars instead of 500.000 for the French Canadian version, or 500.000 yuan instead of just 100.000 for the Chinese version). I suggest that this article should be semiprotected, in order to avoid vandalism caused by unregistered users. Thank you for listening. TeleJuancho (talk) 04:32, 2 December 2013 (UTC)

External links modified
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Merge
It has been proposed that Trilyon Avı be merged into Deal or No Deal. I do not think that there is enough content in the Trilyon Avı article to support it having its own article.--5 albert square (talk) 19:00, 8 January 2017 (UTC)

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Monty Hall Problem
There is a hyperlink equating the Month Hall Problem to the hypothetical situation in which the bank knows what is in the contestant’s case. I believe this comparison is incorrect, as in the Monty Hall Problem, the host opens doors, whereas in this game, the contestant always chooses cases to open, regardless of the bank’s knowledge of their case’s contents. Will be removing this clause after confirmation. — Preceding unsigned comment added by 47.184.40.46 (talk) 04:55, 10 January 2019 (UTC)