Gamblers Who Always Win (Aug, 1950)
Gamblers Who Always Win
The odds are that you can get odds on almost anything today because modern statisticians have really taken the risk out of chance
ONE afternoon a Lincoln, Nebraska, businessman sat in his car in a suburban gas station while his tank was being filled. As he waited, the telephone inside the station rang and presently the attendant came out.
“Are you Mr. L. R. Johansen?” he asked.
“I am,” replied the businessman in some surprise.
“You’re wanted on the phone,” the attendant told him.
As he went inside, Johansen wondered who could have know that he had stopped for gas at this particular time and at this particular station. Then, a moment later, his wonder turned to astonishment. The caller thought that Johansen was answering the phone in his own office!
The caller, it turned out, had dialed the wrong number. And the phone that rang, amazingly, was the phone in the filling station where Johansen happened to be for the brief time it takes to buy a few gallons of gas!
Call it a coincidence if you want toâ€”and you’ll be right. No one has figured out the odds involved but one statistician has said that by comparison perfect bridge hands and human quintuplets would seem like everyday occurrences. Who knows, he may try to compute the actual odds some day when he hasn’t much to do.
But there isn’t likely to be such a day. Statisticians are among the busiest people of our fast-moving modern world and their still youthful profession is rapidly expanding. New statistical jobs develop every year, in almost every imaginable field of human activity.
The life insurance business, of course, is statistical science’s towering triumph. It got that way thanks to the mathematical magic that finds a mysterious orderliness in random jumbles of facts. Its rock-solid foundation is a dry-looking set of tables built around a simple statistical truth: that although it would be the wildest kind of gamble to bet on the life-span of any particular individual, the number of years remaining to the average person can be figured so exactly that every shred of risk is eliminated. So free are life insurance tables from the rule of chance that a single company, the Metropolitan Life, is today the largest private business enterprise on earth.
Look almost anywhere and you’ll find statisticians. Industry, science, government, education and recreation are some of their favorite haunts. They chart the weather and the stars, population trends and the ups and downs of markets, the opinions of the man on the street and generations of fruit flies in the geneticist’s laboratory.
They know how tall you are and have turned the information over to architects, clothing manufacturers and (you might as well know it) coffin-makers. They’ve given your head size to the hatters, measured your feet for shoe and hosiery manufacturers, the length of your fingers for glove makers. If they didn’t measure you personally, they got the facts from someoneâ€” a thousand or ten thousand someonesâ€”like you. You may never have met a statistician face to face but you’re in his book as neatly ticketed, labeled and classified as a biologist’s favorite kind of amoeba.
Turn a statistician loose on a batch of census data or the results of a psychological survey and he can tell you more about your future than a dozen gypsies with a ton of tea leaves. His predictions usually take the form of odds.
Are you single? If so, it’s seven to one you’ll still be single a year from now. But if you are 20 years old, it’s ten to one you’ll marry within five years, that your wife will be younger than you and that you’ll have three children.
If you’re married, it’s three to one that your wife wished she had married the other man. For one thing (according to a study of women’s pulse-beat-increase reactions), the chances are that she is less than half as much thrilled by your kisses now as she was in the days of your courtship. But don’t worry: it’s 113 to one that she’ll still be your wife next year at this time.
Incidentally, if it’s a long marriage you’re after, your chances are best, according to records, in Brooklyn.
As for your career, the chances are 900 to one you won’t have the job you now hold ten years from now, 1500 to one you’ll never become boss, and a million to one you’ll never be a millionaire. But don’t be downcast. There’s also a statistical silver lining.
It’s better than two to one that you’ll be earning more money in the future, 14 to one that you are healthy enough to pass an examination for life insurance, 220 to one that you’ll never go to jail, ten to one that your house won’t suffer damage from fire this year, and 2.5 to one that any telegram you receive will contain good news.
A gambler assisted at the birth of modern statistics. Some 300 years ago, the Chevalier de Mere noticed that the odds were better than even for a six to appear at least once in four successive throws of a die. From this he figured that since two dice can show six times as many combinations as one die, a pair of sixes should, on the average, turn up at least once in two dozen throws. At this point, however, De Mere got lost in figures.
He then took his problems to Blaise Pascal, the noted French scientist, philosopher and mathematician. Amused at first, Pascal presently found himself casting dice and intently studying the results. He even contacted another famous mathematician, Pierre de Fermat, and soon the two men, top-drawer intellects of the day, were wrapped up in matters that quickly went far beyond the Chevalier’s gaming-table worries.
What eventually grew out of these pioneering dice-throws was the mathematical underpinning of modern statistical method. We call it the Law of Probability.
Briefly, this law defines an event’s probability as the number of favorable cases divided by the total number of cases. Thus, the probability of throwing heads with a coin is one divided by two, there being one heads side out of a total of two sides. Other ways of saying this, of course, are that the odds are one-half, or even, or fifty-fifty.
Cards and dice still pose fascinating problems. Many statisticians, in fact, start their training by learning to play poker and shoot craps. Calculating the odds in card games often provides busy scientists with needed mental relaxation. Professor George Gamow, distinguished George Washington University physicist, for example, recently worked out the chances of drawing a flush in poker. Watch closely now:
You get your first cardâ€”a spade, let’s say. That leaves 12 spades in the remaining 51 cards. Applying the probability law, your chances for a spade as your second card are 12/51. For your third card the ratio becomes 11/50, for your fourth, 10/49, and for your last, 9/48. To find the total probability, you now multiply these figures. The result is a real beauty, as fractions go: 13,068/5,997,600. Boiled down, this means that your chances of drawing a flush, after the first card, are about 1 in 500!
Probability mathematics is always at work in games of chance. Card-wise poker players, calculating the odds, remember that there are 2,598,960 possible combinations of five-card hands. Bridge players are faced by no fewer than 635,013,559,600 thirteen-card combinations. So if a royal flush is a great rarity, a perfect hand at bridge (containing all thirteen of a suit) is rarer still: one in 153 billion!
But the fact that statisticians sometimes find it convenient to study cards and dice doesn’t mean that gamblers are statisticians. Far from it. Many gamblers, in fact, avoid looking at the cold truth that statistics reveal about their profession. Their trust is in the thou-sand-and-one superstitions that characteristically clutter up the various rackets.
A prime favorite with gamesters everywhere is the so-called “maturity of chance” notion. Every gambler in the midst of a losing streak believes that his luck is getting ready to change. Some mysterious force in the cards, coin, or dice is maturing, he thinks, and a favorable run must inevitably occur, sooner or later.
Tails, for instance, has turned up six times in a row. The gambler’s idea is that the coin is gradually “getting hot” for an eventual display of heads.
The truth, of course, is that, on the seventh toss of the coin, the odds for an appearance of heads are exactly what they were on the first tossâ€”namely, one-half, or fifty-fifty. For all anyone can predict, tails could turn up on the seventh, eighth, ninth, tenth, and on up to the twentieth toss. And beyond that, too!
It’s true that in the course of a very large number of throws (several hundred or a thousand) , the number of heads and tails will tend to be equal. But for any particular toss, the odds are no different from the odds for any other toss.
What about gambling systems? “Scientific” gamblers work out elaborate arrangements whereby bets are spread out here, or grouped there, or so ingeniously distributed that the element of chance all but disappears. They set great store by such systems.
No matter how complicated or scientific a betting system may be, it invariably turns out to be superstition for the simple reason that, somewhere or other, it runs counter to the mathematics of chance.
“Every system,” says statistician H. D. Grossman, “carries the small chance of a great loss, and the smaller the chance, the greater the loss. No mathematical jugglery can cancel one iota of the total risk. You can only rearrange the hazards, concentrate them or distribute them. But you cannot change their sum.”
Recently two University of Chicago students worked out a roulette system and invested $300 in an extensive tryout in some of Nevada’s gambling palaces. Their method workedâ€”for a while. Their $300 became $8,000. Then the “system” soured and they lost most of it. However, they came back the next year and started winning great sums all over again. Rumor has it that they finally quit $26,000 ahead but experienced Reno hands doubt it.
All human beings are statisticians, to some extent, in that we all use our past experience in an effort to predict the future. However, the trained statistician has fine-edged mathematical toolsâ€”thoroughly tested formulas and techniquesâ€”which help raise his forecasts to a high pitch of probability. He’s the only gambler in the world who always wins! â€¢