# Why No One Will Ever Win A Million Dollars on “Deal, or No Deal”

No one will ever win a million dollars on the game show, “Deal, or no Deal.”  At least not the standard game, not the ones where they have multiple \$1,000,000 values on the board or something.   I make this statement with certainty because to do so would require a very odd type of person with exceptionally good luck.  The creators of the show were brilliant in that they make it look like people are playing for a million dollars, but in actuality, they’re playing for \$500,000, or maybe even \$50,000.

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The reason a person would need to be very lucky is obvious.  There are 26 briefcases, so the first thing you would need to do to win the million dollars is to choose the million dollar briefcase as your case.  This means that your chances of choosing the right suitcase at the start are 1/26, or about 3.8%.  Not great odds.  This would mean, however, that probably by the time the 26th contestant came along, and almost certainly by the time the 50th of 75th contestants came along, someone would choose the million dollar suitcase.  You would then think that you would see a couple of million dollar winners a year, which you don’t and you won’t.

The reason is the second factor, and that factor makes the odds far lower.  This second factor is human psychology, and human psychology causes most people to choose the certain thing over the chance at something more if the risk/reward ratio is not great enough.  Most people, if given a hundred dollars and told that they could keep the hundred dollars or risk it for a chance at \$110 would hold onto the hundred dollars.  The gain they could get was not worth the risk of losing the sure thing.  Many people, however, would play the lottery and put down \$2 for a chance to win \$300 million dollars, even though their chances of getting killed in a car accident on the way to buy the ticket is much better than their chance of winning.  They do the math instinctively and realize that the gain was enough to justify the risk, mainly because the amount risked is so little and it would not affect their lives very much if they lost it (hey – it’s \$2!  That’s cheap entertainment.), so it makes sense to take the risk for the chance at great rewards.  The penalty for losing is low but the gain from winning is astronomical.

And this psychology works against people playing “Deal, or No Deal.”  If the show were simply a matter of choosing suitcases and then seeing if you could make it to the end and have the million dollar case, there would be a winner or two a year.  The reason they have the “banker” making offers as they go is to make people have to make the choice of trading a sure thing for a chance at the million dollars.  (Note the offer is just the average value of the cases, minus a small amount.  It is not made by the guy in the shadowed booth who supposedly is rooting against the player.  Why would someone make their money available to be given away in the first place?)  This puts people who have the million dollar case, a \$300 case, and a \$10,000 case in the position of giving up a \$300,000 offer and risk ending up with \$300 if they want a chance to actually win the million dollars case.  Not many people would make this choice.  If you combine the chance of choosing the million dollar case with the percentage of people who would give up a sure \$300,000 for a chance of winning a million dollars, you can see why no one will ever win.   The only time that they might have a chance of winning is if they had a large amount whether they won the million dollars case or not.  For example, if the only two suitcases remaining were the million dollar case and the \$500,000 case. In that case, someone might be willing to risk it since they would still win \$500,000 if they didn’t have the million dollar case.  Still, the banker’s offer would be around \$740,000, so most people would take the sure \$740,000 instead of risking a loss of \$240,000 for only a chance to win \$250,000 more.

And what does this have to do with investing?  Well, while plugging the average long-term investment return of 10%-12% into a financial calculator will show you that you can end up with \$5M, \$10M, or more by putting money away regularly into a retirement account and letting it grow in the stock market, few people will ever see these kinds of sums.  The reason is that the biggest gains are made near the end when you are getting near retirement.  For example, compounding at 10% per year, someone would see their nest egg double about every 7 years.  Someone at 50 who planned to work until he was age 70 would, therefore, see the potential for his \$750,000 portfolio to grow to  \$6 M before he retired, with gains of several hundred thousand dollars per year during the last few years.

The trouble is that there would also be a risk of seeing a big decline during that period that, if it happened during the last few years before retirement, could leave the individual without enough money to make it through retirement.  This drives people (for very good reasons) to become conservative with their money – shifting into bonds and cash – during the periods when they could see the biggest gains by being wholly in equities.  The only way to overcome this (justified) fear is to save enough for retirement early in life to have enough of your money for security in secure investments when nearing retirement while still having enough money in equities to still perhaps “hit the jackpot.”  For example, an individual who had \$2 M in retirement savings by age 50 could move \$500,000 into large, dividend-paying stocks (income stocks) and bonds while still leaving \$1.5M in growth stocks, moving a portion of the growth stock portfolio into income stocks and bonds as she neared retirement age until she had \$1 M or so in income stocks and bonds at retirement.  She would therefore still have the potential to see her portfolio grow to \$12 M or more but still have enough for critical expenses during retirement even if half of the equity portfolio were lost due to a market event.

OK, so I’m sure that some of you have gone to Google by now and found out that someone actually did win the \$1 million on “Deal, or No Deal.”  And I’m not talking about the shows where they put three million dollar prizes on the board, effectively taking away the psychological factor.  There actually were two people who won the million dollars when there were more \$1 M spots added, and you can (and should ) see the video here.  She was helped a little by having the \$200,000 prize remaining, meaning that by giving up the almost \$500,000 sure thing she was only risking \$300,000 for a possible gain of \$500,000.  I doubt she would have gone for it if she would have only won \$300 if she were wrong.  She also had a better chance of getting to the spot she was in since there were five \$1 M on the board.

So why not make it easier psychologically to keep a good amount in growth stocks as you near retirement and maybe win the million dollars.  Make your own choice at retirement between having plenty of money for living expenses should things work out and an incredible fortune if they do instead of between having just enough and having nothing.  Put yourself in the position to take the risks.  Start when you are in your 20’s to build your fortune so that you’ll have five or ten million dollar suitcases instead of just one.

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Disclaimer: This blog is not meant to give financial planning advice, it gives information on a specific investment strategy and picking stocks. It is not a solicitation to buy or sell stocks or any security. Financial planning advice should be sought from a certified financial planner, which the author is not. All investments involve risk and the reader as urged to consider risks carefully and seek the advice of experts if needed before investing.

1. Mark says:

Her odds of winning the million if she switched the case would still be 50% not 96%. Deal or No Deal is not the Monty Hall problem on steroids. The Monty Hall Problem doesn’t apply here because the cases are removed randomly, and not by forced elimination.

• You may well be right – I’ve been wrestling with this one.

• Mark says:

Here’s an explanation

There are three possibilities:

(a) You choose the million dollar box (1/26)
(b) You don’t choose the million dollar box but are left with your box and the million dollar box (1/26)
(c) You don’t choose the million dollar box and you reveal the million dollar box at some point in the game – you are left with your box and another box neither of which contains the million dollars (24/26)

Possibility (c) usually occurs (24/26 of the time) but this game was one of those rare occasions in which (c) did not occur and can be eliminated as a possibility. The remaining possibilities (a) and (b) each are equally likely

• Let’s see. The first time she choose, she had a 1/26 chance of choosing the \$1 M and a 25/26 chance of not doing so. If she did not choose the \$1M box, the first case she eliminates, she has a 24/25 chance of not eliminating the \$1M box, then a 23/24, then a 22/23, all the way to the 1/2 chance when she is down to two boxes and her chosen box. Multiplying these probabilities together, that means she has a 24!/25! chance of not choosing the \$1M box during elimination, or 1/25. Conversely, she therefore has a 24/25 chance of choosing the \$1M box during the elimination.

So the chances that she chose the \$1M box the first time were 1/26. If she didn’t choose the \$1M box at the start, the chance was 1/25 that she then wouldn’t choose it during elimination. Therefore, it would be more likely that she didn’t choose the \$1 M during elimination than it would be that she choose the right box to start with. 1/25 versus 1/26.

But the chance of not choosing the \$1M box to start and then not choosing it during elimination would be 25/26 * 1/25 = 1/26, so that would be exactly the same as the chance of choosing the \$1 M box to start.

All right – I agree, in order for this to be Monty Hall on steroids, Howie would need to know where the case was and be eliminating those that were not the case.

• Jacob says:

The chances actually would be 96% or whatever that she’d win the million by switching given that the million and another case were left. The chances of her NOT picking the million at the beginning were 25/26, and if she eliminated all but the million and another case, roughly 25/26 of the times, switching would give her the million. The Monty Hall problem still applies if the million is still in play when 24 cases are remaining.

2. mike says:

Some already did back in 2008.

• Yeah, I actually have a link to the video in the post. But you notice that it wasn’t a standard game. There was more than one \$1M case. It was still extremely unlikely and it probably won’t happen again, given human emotions.

3. Note I’m amazed at how popular this post is, and yet it has an average rating of “poor” – 2 stars – by the five people who rated it. Apparently people like to read things they don’t think are very good.

• Now 12 have rated and it’s still “poor!”

4. Peace says:

two people won in 2008. The real reason no won will win is because the show was canceled

• Actually I have a link to the first winner in the post. You’ll notice that the board has five \$1 million spots on it, so it was not a standard game. Her chances of winning were a lot better than normal. Still, she had eliminated everything but one of the \$1M spots and the \$200,000 spot, so she was taking a big chance. The offer was more than \$500,000, so if she had lost, she would have given up more than \$300,000, so she had some guts. If it had been the choice between \$500,000 and \$300, I think she would have taken the offer. The second winner was also not on a standard game.

• peace says:

You talked about no one being able to win in 2014. Which is for one reason only. The show was already cancelled. So your premise was invalid from the start

• I think you’re missing the point.The way the the game was designed was ingenious because it would be extremely unlikely that anyone would ever actually win the million dollars. Even winning \$500,000 was very unlikely. That is because it combined a very low chance of selecting the right case with the psychological factor of people not wanting to give up a valuable sure thing for the possibility of a somewhat better thing because they calculate how much they will lose if they don’t get the better thing. It would take both a person who was really lucky and who was willing to risk losing a lot of money for the chance to increase their winnings modestly. How many people, given a sure \$300,000, would decide to go for the million when the alternative was \$200?

This same psychology comes into play in investing for retirement and helps explain why most people get nowhere near the 10-15% return from stocks over their whole investing career and don’t retire with \$8 M even though the you can punch the numbers into an interest rate calculator when they’re 20 and get \$8 M. The reason is that once they have \$500,000 or so, they start to do things to preserve that money like shift into bonds and cash, and perhaps pull out of the markets when they get worried and miss big rallies. Because you make most of your money in the last few years, for example, \$500,000 will double three times between age 50 and age 70 at about a 10% return, turning into \$4 M, they miss out on the big returns. My point is that to combat this, which is a reasonable fear since you don’t want to have everything riding on the stock market when you’re close to retirement, is to save and invest more when you’re young so that you can put enough money aside for retirement to be safe and still have a lot invested.

• And you need the combination of someone like that combined with the luck to actually have the million dollar case for someone to win. Thanks for sharing the video – I hadn’t seen that one before.

5. Regina says:

I need to win some money

6. Why? You could win a million dollars today, and it would be gone before next year if you didn’t manage it properly. Instead, learn to make yourself valuable as an employee or become a business owner supplying things people need; use the income you earn to build assets, learn to manage your spending so that your income always exceeds your outflows, and gain financial independence for yourself. That is how you gain lasting wealth. It doesn’t come from a game show.

• “Valuable employee” “Lasting wealth”

Hahahahahahahahahha

Wow…. You don’t build wealth working for someone else. Wealth is not 100k a year. Wealth is owning assets. Companies that make millions in revenue are assets of the wealthy.

The lottery is a fun way for the rest of us to dream. You can absolutely win a lottery/game show and turn it into long term wealth. To say “you have to be smart” and simply winning a game show isn’t enough is like saying you have to breath. No s***. Not ground breaking.

• No, you can become wealthy working for someone else if you manage your cash flow correctly and invest as you go. You can easily retire with wealth on the order of \$10M to \$20M if you do this your whole life with a \$100,000 income. Give a lot of this to your kids and start them with a \$5M investment account when they are born and they can be as rich as Buffet and Gates within their lifetimes. Read a few other posts in my blog or buy my books and I’ll show you how.

• Standard game or not, two people did win the \$1mill. (Everyone knows taxes make it less than 1 mill.

So you wrote this despite two people doing it?

Research.

• I think you’re missing the point….

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