# Why No One Will Every Win A Million Dollars on “Deal, Or No Deal”

Posted on the 21 November 2014 by Smallivy

No one will ever win a million dollars on the game show, “Deal, or no Deal.”  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.

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 \$150 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 \$5 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, partly because the amount risked is so little and it would not affect their lives very much if they lost it, 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.

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 reason) 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 was one person who legitimately won the million dollars 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 did something that was a very poor choice and she was very lucky that it worked out for her.  At the end of the show, if you get down to two suitcases, Howie Mandel offers to allow you to switch cases with the one remaining.  Believe it or not, if she had switched cases her chance of winning would have improved dramatically.  In fact, her chance of winning the million dollars would have gone from 1/26, or 3.8%, to 25/26, or 96%.

The reason is that “Deal, or No Deal” is the Monty Hall Problem on steroids.  In the Monty Hall problem, you are on “Let’s Make a Deal” and choose one of three doors.  One door contains a new car and the other two doors contain a goat.  Monty Hall then shows you one of the doors that has a goat behind it, then offers you the choice of staying with your door or swapping to the other, unopened door.  Because your chances of choosing the right door originally is 1/3, and because Monty Hall, who knows where the car is, eliminates one of the wrong doors, your chance of winning if you switch is 2/3, versus 1/3 if you stay with your original door.

With “Deal, or No Deal,” if you can somehow manage to get down to having only one suitcase and your suitcase left, one of which contains the million dollars, your chances are 25/26 of winning if you switch suitcases.  Your chance if you don’t switch remain 1/26.  This is because your chances of choosing the wrong suitcase at the start, and therefore the chances of the right one being the other suitcase if you know that the other 24 suitcases don’t contain the million dollars, is 25/26.

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 of 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.