Deal Or No Deal

[X-Act]

Deal Or No Deal is a TV show that is shown in around 50 countries around the world. The details vary slightly from country to country, so I'll stick to the American version:

1) There are 26 boxes, each containing varying amounts of money, from as little as $0.01 to as much as $1,000,000.
2) You choose one of those boxes.
3) You choose 6 boxes to open.
4) A banker will propose a deal for you to 'buy' your box for some money. If you accept the deal, the game is over and you win the money proposed by the banker. If not, you continue.
5) You open 5 boxes, and the banker proposes a new deal as before.
6) You open 4 boxes, and the banker proposes a new deal as before.
7) You open 3 boxes, and the banker proposes a new deal as before.
8) You open 2 boxes, and the banker proposes a new deal as before.
9) You open 1 box, and the banker proposes a new deal as before.
10) Repeat step 9 until there are only 2 boxes left unopened, yours and one other. The banker will propose one final deal, and you can accept or not accept. If you don't accept, you open your own box and you take its contents' worth.

The interesting thing about the game is that the banker's deal depends, in part, on the values of the boxes left unopened. The higher their prize money, the higher will be the banker's deal. This allows for sometimes mind-bending decisions on whether to accept the banker's deal or not.

Here's an example: Suppose there are 5 boxes left, worth: $1, $50, $3000, $5000, $750,000, one of which you're holding yourself. The banker's deal is $150,000. You have the choice of either going home with $150,000, or else open up one of the other boxes you're not holding at random, in which case the banker will offer you another deal. What should you do?

There are two different ways of looking at this problem:

On the one hand, there is only a 20% chance that the contents of your box contains more than $150,000, and hence you should accept the deal.

On the other hand, there is only a 20% chance that you will open the box containing the $750,000 next round, and hence you should not accept the deal, since there is a good probability that the banker's deal will be larger after opening another box.

Such dilemmas make the game very interesting. It seems like there is no 'good play' here, since both choices entail a 20% chance of going wrong. What would YOU do in such a scenario (which, by the way, happens all too commonly in the game)?

 

[Havak]

Wow, the UK version only goes up to £250,000 with only 22 boxes.

To be honest though, with an offer like that I'd take it. In the latter rounds I'd only ever "no deal" if I was at a huge advantage. I don't take too many risks though, to be honest.

 

[Zephyrman]

I'd more than likely "no deal" to the very end.

How often are you going to have the chance to win so much money? Whatever I'd come away with would be more than I'd go there with, so why not push my luck to the maximum.

 

[Havak]

Yeah, but there are other things to take into account. What if you had to take weeks off work just to be there? With the same chance of being chosen to play the game evey time. A woman was once on there for 50 shows before getting picked.

Taking so much time off work, paying to travel there for filming all the time. It can all add up. And is it really worth it if you walk away with 50p to show for it all?

I'd definately want to walk away with more than all that costs, so I'd make sure of it.

 

[Zenigame]

Wow, the UK version only goes up to £250,000 with only 22 boxes.

To be honest though, with an offer like that I'd take it. In the latter rounds I'd only ever "no deal" if I was at a huge advantage. I don't take too many risks though, to be honest.

Not that it makes it equal, but euros and pounds are worth more than US dollars.

 

[Havak]

Yeah, I know. I've been to America and got practically double my money when converting my pounds to dollars. So it's still basically half the money that the American version plays with.

 

[CaptKirby]

Um, I would fucking take the $150,000, because I understand how to invest money, and I would rather have the $150,000 that I can grow and live off of than nothing at all!

 

[Atlas]

Um, I would fucking take the $150,000, because I understand how to invest money, and I would rather have the $150,000 that I can grow and live off of than nothing at all!

ya same here. hell, i probably would have sold out long before. act like im committed to the million in every way then bam! run away with the first deal made.

 

[sbc]

Yeah, I know. I've been to America and got practically double my money when converting my pounds to dollars. So it's still basically half the money that the American version plays with.

But also in Who Wants to be a millionaire, Americans get $1m whereas you could win twice as much, £1m

 

[Tinnacious]

God, I hate this fucking show. So obnoxious, the contestants make me wanna chokabitch.

But for some reason beyond my knowledge, if I ever appear on this show, chances are I'd gun it until the end.

 

[Brawley]

I would take the money, just to be safe. What would you do X-act?

 

[Sunday]

In almost every game I watch someone goes too far and kills all the "green" (high money) cases and is left with squat. The game is all about knowing when to pull out.

 

[X-Act]

Lemme think.

If I say "Deal", the worst that could happen is if I had $750,000 in my box, and the best that could happen is if I had $1 in my box. But, either way, I still went home with $150,000.

If I say "No Deal", the worst that could happen is if I open the box containing the $750,000 next turn, leading to an offer of only around $2000, and a maximum prize of 'only' $5000. The best that could happen is if I open up the box not containing $1, leading to an offer from the bank of around $185,000 to $188,000 (and another dilemma).

I think, knowing me, I'd take the 100% safe option of taking $150,000 than to risk the chance of taking either $188,000 (80% chance) or $2000 (20% chance).

 

[Sunday]

Are these the amounts of money played with in the American version? Crikey Australia get's jibbed, out max is only $200 000...

 

[obi]

I would take the deal. I'd be set for my education and then some with 150,000 dollars or 750,000, and I would not really get so much mileage out of lesser amounts. On average, I'll win ~151K if I say "No deal", which isn't enough of an increased monetary gain to justify the increased risk.

 

[cookie]

If you look from a statistical point of view, I've noticed that the money offered is always less than the mean amount you could win out of the remaining boxes, adding up the totals remaining and dividing by the number of boxes. My understanding is that it is always preferable to continue to the end, and it's the fact that most people who play the game do not realise this and prefer not to take such big risks. The banker knows this and offers less than the mean payout, so he 'wins' in the long run by paiyng less than what's in the final box because people are generally too scared of going away with nothing.

 

[Sunday]

I have to agree with cookie on how unfair the banker is >:(

I've seen games where the player has knocked out an amount (slightly) smaller than what he was last offered and then the next bank offer goes down...

I guess you could put it down to the player having one less decent case to fall back on so they would be feeling insecure and more likely to take the deal, but stasticly it doesn't add up.

 

[Aeroblacktyl]

With these kind of things, the less you know the better, in my opinion at least. Therefore, I know that I have an offer of 150k, the less I know of probabilities and all that stuff, the logical thing would be is for me to take that 150k. 20% doesn't mean anything for me when that 150k is sitting in front of me.

 

[Sub-Human]

With these kind of things, the less you know the better, in my opinion at least. Therefore, I know that I have an offer of 150k, the less I know of probabilities and all that stuff, the logical thing would be is for me to take that 150k. 20% doesn't mean anything for me when that 150k is sitting in front of me.

I agree if I see someone offering me 150k im not just gonna be like oh, fuck that im going to take the money that i was offered and not be selfish.

 

[Somebody]

I wonder what kind of deal you would get should the only two remaining boxes be $0.10 and $1,000,000 (Considering that he apparently doesn't offer you the mean amount)

 

[Amelia]

I wonder what kind of deal you would get should the only two remaining boxes be $0.10 and $1,000,000 (Considering that he apparently doesn't offer you the mean amount)

No matter what the amount is, i would take it. The chances of getting 10 cents only is too risky for me.

But for the first one, i would open 1 or 2 boxes more, because the chances of not opening the grand prize is 4/5 and 3/4 respectively. That is high enough in my opinion to try and gamble.

 

[Bulblax]

generally the banker offers more the fewer boxes are left. if there's a lot left he will offer much less than the mean value of remaining boxes but if it's just 1 million and 10 cents it would be around 600,000 probably

 

[Pneuma]

I would take the deal as well.
Even though the odds of me making more are assured, I'd rather not take odds. 150,000 real dollars is worth more than 200,000 theoretical dollars any day. Besides, after a certain quorum, more money is just money - that is to say everything is paid off and I'm completely content.

The difference from $2000 to $150,000 is, to my mind, like the difference between $150,000 and $200,000 or $750,000 or "a bajillion."

 

[X-Act]

If you look from a statistical point of view, I've noticed that the money offered is always less than the mean amount you could win out of the remaining boxes, adding up the totals remaining and dividing by the number of boxes.

This is true, except for the last round, usually.

My understanding is that it is always preferable to continue to the end, and it's the fact that most people who play the game do not realise this and prefer not to take such big risks. The banker knows this and offers less than the mean payout, so he 'wins' in the long run by paiyng less than what's in the final box because people are generally too scared of going away with nothing.

This is absolutely wrong, though.

The idea of the game is to exit with the highest amount of money possible. Most of the boxes don't contain a large amount of money. If you always continue till the end, you'll end up with that amount of money, and you're almost guaranteed that the banker had offered you a larger amount at some point. The trick of the game is to ask yourself "is the banker likely to offer me a better deal than this, or a lower one in the next deal?" If he's likely to offer you a better one, then you say "No Deal", but if it's likely that he'll offer you a worse one, then you say "Deal". This decision is not always clear-cut, though, as my example shows.

You might tell me "but what if you have $1,000,000 in your box? Then you'll end up with less than that using that strategy." True, but you still exit the game with a good amount of money, not some $100 crap. The amount of money might not be $1 million, but it might be, say, $100,000. In the long run, you stand to lose if you always say "No Deal", since half the boxes contain less than $1000, and hence, you'll only end up picking less than $1000 half the time if you stick to your box.

On a not-so-related note, I found an online version of the game here.

 

[Pneuma]

In the long run, you stand to lose if you always say "No Deal"

This is of course noting the hilarious gaps between $250,000, $500,000, and $1mil as compared to $1, $5, and $10.
Hell, at any time you're offered something over the average of the money at the start of the game (I don't know this off-hand) you've technically won.