Luck

what it is, what it's not—and how to separate fact from fable

It is to be supposed that you are an intelligent, educated, sensible man. As such, you are not likely to forearm yourself for a game of chance or skill with a magic lodestone, a good-luck amulet, lucky-lucky powder, fast luck drops (to be surreptitiously added to your drink when things are going bad), a four-leaf clover, or the foot of a rabbit – all of which, in case you haven't been keeping up with the ads in the pulps, can be bought for good U.S. currency (no checks, please). You know the difference between the fun of hollering at the dice and actually believing that you can influence how they fall. You apply body English to that bowling ball without really expecting it to change its course. You don't put any stock in these devices; in fact, you are pretty sophisticated and realistic about the whole question of luck and how it can be influenced.

But let's look a bit further. Have you ever, in a poker game, changed your seat or the deck in order to improve your hands? Have you ever bet on a horse because of its name? Have you ever, in roulette, bet on red because black had shown six times running? Have you ever called for a fresh pair of dice in a crap game? Have you ever felt a faint qualm when you broke a pocket mirror? Have you ever, God forbid, like a fellow we know, walked around a leaning ladder instead of under it with the apologetic remark, "I'm not superstitious, of course, but it's so little trouble"? If any of the answers was Yes, it is quite probable that you, too, harbor certain ancient and deeply ingrained misconceptions about luck.

You are, let us say, in a game of draw poker. You are a good poker player; yet things are going against you. You haven't won a pot in three hours. Your pat straight is beaten by the jerk who draws two cards to fill a flush (one chance in twenty-four); your three-of-a-kind doesn't improve on the draw and is beaten by the two-pairs hand that draws one to make a full house (one chance in twelve); your four-flushes, which ought to hit about twice every eleven draws, haven't come home a single time.

You are having a run of bad luck.

The question is, what do you do about it? It is the question that makes the subject of luck so fascinating to the student of human behavior. There are several things you can do:

1. Keep on playing the best you know how, convinced that the past fall of the cards can have no influence on the future.

2. Keep on playing because it's time for the cards to change.

3. Quit playing because you realize that your bad luck has affected your judgment and play for the worse.

4. Quit playing because the cards are against you tonight.

5. Quit playing because you suspect that the game is crooked.

6. Call for a new deck, take three turns around your chair, change seats, play a hand standing up, or otherwise seek to outfox or ingratiate yourself with the Goddess of Chance.

The odd numbers above designate rational responses to the problem. Were they yours? The even numbers, sad to say, introduce the typical motivation and behavior of the man whose luck has been bad. Were they yours? Let us hope not. But since they are so typical, and so fraught with error, let's take a closer look at them.

It's time for the cards to change. How reasonable this sounds! The law of averages has been grossly infringed by that bad run – it has to get back on an even keel with a corresponding good run, or else it can't average out, the way it has to. This stands to reason.

In roulette (and other games of pure chance) this theory has a name. It is called the Maturity of the Chances. If black has won six, seven, eight times in a row, the chance that red will come next time is much better than even, since the law of averages implies that the chances for red have now "matured," and must start coming in. Similarly in poker: if you have lost a lot of hands that you should have won, the time has come for you to start hitting.

The main trouble with this theory is that it is wrong. The little ball on the roulette wheel has no memory of what it has just done. It has about an even chance of falling to either red or black on the next roll, and it has just as much chance to continue the run on black as to break it off. It feels no compulsion to get in there and save the reputation of the law of averages.

This law of averages is the popular name given to a theorem propounded by the Swiss mathematician Bernoulli. In simplified form the theorem states that, if there is a certain probability that an event will take place (say, a fifty-fifty chance that a flipped coin will come down heads), then, if the trials are repeated indefinitely, the event (heads) will occur the expected number of times. Note where it says in the small print: repeated indefinitely. The law of averages deals with vast numbers of trials; it is not going to help you out in the next half hour. There is no time of which it can be said that it's time for the cards to change. Forget about the law of averages: it is never going to do you any good.

The cards are against you tonight. This point of view, the very opposite of the one just dealt with, also seems to offer a sound basis for decision-making. After all, what are you to think if, again and again, when you have every expectation of winning, the cards give the pot to somebody else? They're against you and that's all there is to it. Every time you give them another chance to do the decent or probable thing they yank the rug out from under you. The only sensible thing you can do is get out of the game before you get hurt any worse. It stands to reason.

This fallacy is essentially the same as the one above. It assumes that the cards know what they are doing. Above, they knew they were acting wrong and would soon reform; in this case they are determined to keep on being naughty. Therefore, on the next hand you do not have your usual expectation of success: you have less.

This sort of thinking derives directly from the "belief" in luck, about which we shall have more to say. The point to make now is that the mathematical probabilities in a series of independent events (such as poker hands, spins of the roulette wheel, draws at blackjack, throws of the dice) cannot possibly be affected by what has happened before. If things have gone for you or against you in the past, it is perfectly correct to say that you have had good luck or bad luck. But – and listen carefully, because this truth is worth its weight in your gold – to act as if you will be lucky or unlucky is sheer superstition. In fact, the word "superstition" is the operative word here. And now, at last, we are about to get into the realm where it is sovereign.

Call for a new deck, circumambulate the chair, etc. Here we approach one of the crossroads in man's perilous hike toward his present precarious eminence. His main instrument of survival has been his rational brain. Ever since he got up on two feet and began to think, his struggle has been to see the physical universe in the right perspective; and his chief problem has been that of every animal, his tendency to regard himself as the most important thing in the world. Gradually he has begun to overcome this tendency. In the last few hundred years he has succeeded pretty well in formulating – and putting to his use – the rules by which the physical world operates. He has evolved the scientific view of things, according to which matter obeys laws that are proof against manipulation to give any man an advantage or disadvantage.

The intelligent modern man does not question this. On going out to his car in the morning, he does not say to himself, "I don't think it will start this morning – I spilled the salt at breakfast and neglected to throw a pinch over my shoulder." If the car should not start, he does not walk around it three times to make it behave better; he looks for the cause under the hood, or calls a taxi. And yet, observe his behavior when he becomes involved in a game of which chance is an element. An ancient memory, an atavistic impulse, takes over. His clear intelligence becomes willing to accept the notion that a mysterious force called luck has attached itself to him, or to the inanimate objects with which he plays. He does not believe in haunted houses, but he may very well believe that he or his adversary is haunted by a spirit called good luck or bad luck. And – what is more extraordinary – this spirit or force can be controlled and influenced by the proper application of techniques.

But this is manifestly impossible. Luck is that which happens by chance. The element of the unforeseen, the haphazard, and the uncontrollable is an essential part of the meaning of the word. By its very definition, luck is something that cannot habitually attach itself to a particular person.

What conclusions can we draw from this analysis so far? Several – even though we shall confine ourselves to games that involve betting.

1. There is no such thing as a lucky or unlucky gambler. Chance may favor him for a day, or a week, or even (most improbable) a year. But if he wins over the long run he is not lucky. He is skillful.

2. In games of pure chance, there is no such thing as a valid hunch. However strongly you may feel that a certain event will occur, you are kidding yourself.

3. There is no such thing as being "hot." There is only the fact of having been hot – at one or another time, or so far. What has happened in the past offers no likelihood that it will continue.

4. There is nothing you can do to change your luck. If you are deeply debauched by superstition, the fact of your observing some ritual may so far restore your confidence as to make you play better. In this case you have improved your skill, not your luck.

Luck, in short, has an utterly negligible influence on success. In games, as in life, the elements that make a difference are probability and skill. They are closely related. Because of the general misuse of the word luck, and the misconceptions regarding it, we want to examine these two elements in some detail.

Probability informs all our lives. The wildest improbabilities happen to us every moment of every day. The very fact that you are you, and not any one of a million other possible persons, depended on the highly improbable union of a particular sperm with a particular ovum. Now, in that poker game we mentioned above, you are dealt a hand consisting of Q?, 10?, 9?, 3?, 2?. There was just one chance in 2,598,960 that you should get those five cards. How utterly improbable that you should have done so!

Quite true. But you are perfectly justified in asking, "So what? Who needs a hand like that?" Probabilities, or improbabilities, though our lives are full of them, are of absolutely no interest unless some significance is attached to them. If you have anted two dollars for the privilege of getting this stinker, you are not a bit awed by how unlikely it was that you should have got it. Probability would begin to take on some meaning if four of the cards had been hearts and you had to calculate whether it was worth your while to draw to the four-flush.

We can gain our best insight into the relation between probability and luck if we look at it in connection with the games of pure chance (e.g., craps, roulette, chuck-a-luck, slot machines). These games are usually played in a gambling establishment, which prescribes the pay offs for all bets. Built into these prescriptions is the house percentage, or cut. It should not come as a surprise to you that gambling places, since they are not nonprofit organizations, stay in business by rewarding your wins at less than the true odds.

At the crap table, let us say, you wish to bet that the shooter will roll a seven on his first roll. There are six ways he can do this: 6-1, 5-2, 4-3, 3-4, 2-5, 1-6. There are thirty-six possible rolls of two dice. Thus he has one chance in six of rolling the number you want. The probability that he will do so is one/six; or, stated differently, the chance that he will fail is five to one.

If you bet one dollar on this proposition, the correct odds demand that you should get five dollars for winning. Over the long run you will lose one dollar five times for every time that you win five dollars, and you will break even. But the house doesn't offer five to one on this bet; it offers four to one. This means that you will lose five dollars for every four dollars that you take in. You will lose one dollar for every six bets that you make. That is, the house percentage is 16.67.

Betting under these circumstances is called bucking the odds. You have no (continued on page 70) Luck (continued from page 68) other choice in a gambling house: you are always bucking the odds, and in the long run you are going to lose. It is your privilege to call your losing bad luck if you wish, but it is precisely what probability tells you to expect. It is, from another point of view, the price you pay for the entertainment you get from gambling. But if your purpose in gambling in such places is to win, you are exhibiting a lack of skill in not taking the probabilities into account.

In the games of skill (e.g., poker, bridge, backgammon) a knowledge of probabilities is absolutely essential, as it is in the vaster game of life. But here skill and chance(luck) are intermingled, and it is not always easy to separate the two.

Let's take an instance from a game of golf. Sixth hole, 165 yards over a water hazard. Player A addresses his ball with an imprecation and a five iron. He shanks it: the ball loops off to the right, hits a tree, ricochets into the pond but lands on the one projecting rock, bounces up onto the green, and trickles into the cup. A hole in one!

"You lucky bastard!" Player B exclaims.

"What do you mean, 'lucky'?" rejoins Player A. "This is a game of skill, isn't it? I was trying to get my ball into that hole with as few strokes as possible, wasn't I? Well, that's what I did. Where do you get that 'luck' stuff?"

They can argue about this forever. The consensus will be that Player A was indeed an extremely luck bastard. (There will be another school that argues how unlucky he was, since he must now stand drinks for everyone in the clubhouse. But this introduces an extraneous consideration.) He was, to be sure, engaged in a game of skill. However, he evinced a lack of skill when he shanked his ball. From that moment chance took over and did a thoroughgoing job of conferring luck.

Another example. Mortal A is a Mexican peasant, born in a mud-floored hut in the mountains, condemned by his circumstances to illiteracy and lifelong poverty. Mortal B, American tourist, drives up to the village in his T-bird on a sightseeing tour. He was born in a big house in Scarsdale; his parents gave him every advantage, put him through college, placed him in the family brokerage business. Now he earns $50,000 a year.

"These primitive people have a happiness and a simple joy of life that we have lost," he says to his well-groomed female companion.

¡"Cabrón suertudo!" says the Mexican, enviously. "Lucky devil!"

Again, the concept of luck is being correctly applied. Mortal B is unquestionably luckier, at least in material things, than Mortal A. His advantages are due primarily to the accident of birth, not to superior skill. Similarly, the pretty girl is, in one respect, luckier than the plain, the athlete than the weakling, the talented than the imbecile. Life deals out such inequalities, and luck may be the only word for them.

Case three. Stockbroker X, with extensive holdings in many securities, sells every last one of them in the week ending October 28, 1929. On October 29 the Crash finds him comfortably counting his money while his colleagues on Wall Street shout "You lucky bastard!" as they plummet past his window. They cannot pause to argue the matter, but Mr. X is not lucky, in the correct use of the word. Here, as in the hole-in-one case, there is a mixture of luck and skill, but the preponderance is on the other side. Mr. X was lucky not to have waited a week longer, but it was skill that dictated his significant act of getting out at about that time, while his friends were blithely riding the gravy train to its destination.

• • •

Probability and skill being the factors that mainly count in one's gaming and one's day-to-day encounters with life, what is the explanation for the widespread and often vehement belief in the existence and pervasive power of luck? What are the psychological sources of this rational disorder? – and that is as good a name for it as any.

They are manifold and complex, but perhaps we can suggest a few avenues of approach.

Its most immediate emotional source lies in the stress that attends the exposure to any situation in which chance plays a large part. In such a situation the human being feels himself vulnerable to powers that, because he has no command over them, are the more mysterious and dangerous. He loses his detachment. His rational control, shaky at best, yields to the primitive voice that tells him he can regain the upper hand.

This motivation shows up vividly in warfare, when men will commit the most irrational acts to gain the illusion that they have reduced chance to their service. The story is told of the British seaman at Trafalgar who, when a cannon-ball passed through the side of his ship, at once put his head through the hole, explaining that this was the safest spot on the vessel because of the unlikelihood that two shots should land in exactly the same place. In World War I, soldiers leapt into new shell holes for the same reason. (Shell B, of course, does not know where shell A landed, and may land there just as well as anywhere else; but, just for kicks, ask yourself whether you wouldn't feel safer in a nice new hole instead of a beat-up old one. And then ask yourself why.)

A second source of the belief in luck is not so much emotional as it is a flaw in the reasoning process itself. Even persons highly trained in scientific thinking are prone to this error when chance enters their lives. It is the error of forgetting that there is only one set of natural laws, that things work in only one way. If the laws can be set aside in response to special pleas, or if they habitually favor one person over another, then the whole reasoning of science is wrong from top to bottom and our image of an orderly world is nonsense.

Another factor that contributes to the belief in luck is something we will call the subconscious selection of evidence. It works like so: Suppose you have a bias towards believing some particular thing – that Friday the thirteenth, for example, is an unlucky day. Any misfortune, big or little, that befalls you on a Friday the thirteenth will impress itself indelibly on your memory and will serve to "prove" that your theory is correct. Quite subconsciously you will forget whatever good things have happened to you on that day; and you will certainly not go to the trouble of compiling accurate statistics for the amount of good or bad fortune you have had on other days of the month, which would show that Friday the thirteenth is a day just like any other. You want to believe in its maleficence and, by a careful process of selection, you will gather the "evidence" to "prove" it.

Having made this point, we will now admit that Friday the thirteenth may indeed be an unlucky day for you. For there is another process at work in this matter of luck: the self-fulfilling expectation. If you are really convinced that a certain day means bad luck, you are subconsciously predisposed to create that bad luck for yourself on that day. You are more accident prone; you are more likely to commit errors in judgment. Without conscious volition you will make the day unlucky. Similarly, if you believe that good luck comes in streaks, you will, on the day that gets off to a good start, create more so-called good luck for yourself. Your mental tone will be better; you will attack life, or a game, with more confidence that you will succeed.

The same process is at work, of course, whenever you are under heavy psychological pressure. If you are up against a man in a business deal who has a reputation for being fantastically lucky in the way things turn out for him, subconsciously you expect him to get the better of you, and you are at precisely the sort of disadvantage that can result in your (concluded on page 74) Luck(continued from page 70) enhancing his reputation at your expense.

The belief in bad luck often derives from what might be called pressure failure. If we are engaged in a game at stakes much higher than we can afford, and need desperately to win, our skill is going to be affected adversely by our anxiety. We shall be particularly sensitive to the loss that we shall probably suffer, and will blame it bitterly on bad luck of the worst sort. Our emotional involvement will conceal from us the extent to which our misfortune resulted from a failure of skill because of pressure.

Finally, the belief in luck can have its source in defensive rationalization. Good luck, in a great many cases, is simply the good things that happen to a person we don't like. We are unwilling to admit that he earned his good fortune through skill. It is painful to say, "He certainly showed how capable he is when he pulled that one off." How much more gratifying it is to attribute his success to the blind operation of chance! In the same way, our own lack of success is much more digestible if we blame it on bad luck rather than on some fault in ourselves. In either case we are rationalizing what happened as a means of defending our self-esteem.

As a general rule it will be found, on objective examination, that the person with a reputation for being lucky is the person who has at his command the skills that enable him to make the most of the situations that come his way. It is this fact that Napoleon had in mind when he wrote, "Chance remains always a mystery to mediocre spirits and becomes a reality to superior men." The mediocre spirit, the poor unlucky fellow, the schlub, the guy for whom everything goes wrong, is very likely to be the self-defeater, the injustice-collector, the man who subconsciously wishes to do himself harm because he hates himself. Such a man, of course, is particularly prone to discover the source of his misfortune in the malevolent machinations of chance.

Aside from the gross inequalities of opportunity that are an inevitable part of life, a man makes his own luck. His attitude toward it will be a very personal thing. If he has been successful, whether in games or in the larger arena of life, he will be less likely to saymuch about luck, and will probably have very little belief in it. Skill, alertness, insight, intelligence – these are the qualities to which he will attribute his well-being. If he has been unsuccessful, luck will in all likelihood loom large in his picture of himself. Bad luck, of course.