Odds Man Out

Anyone who has spent any time in a gambling casino has certainly seen this typical gentleman at the roulette table. In Europe he is likely to be elderly, distinguished looking, and rather shiny at the elbows. He sits quietly at the table with a ledger in his lap and watches the movement of the ball with an alert eye, making notations in his book after every spin. Behind him there may be one or two curious spectators. Finally the conditions are favorable. From the modest stack of chips in front of him he selects several and disposes them on the green felt: "Les jeux sont faits. Rien ne va plus." With a slight quickening of interest he watches the ball as it spins, tumbles, hops, hesitates, and comes to rest. "Le douze. Rouge, pair, et manque." If he has won, he accepts his gains with the negligent air of one to whom the outcome was never in doubt. If he has lost, he bows his head and carefully records the event in his ledger.

He is, of course, a system player.

Perhaps, in the early morning hours, you will come upon this man at the moment when his destiny catches up with him. He may be the only player still at the table. His stack has only three chips in it. Almost regretfully, in the iron grip of his system's requirements, he bets them. Then, after the bored croupier has raked them in, he sits for a while staring at the rows of numbers and symbols in his ledger. He looks older and more threadbare. It is sad.

In Las Vegas, at the crap tables, one sees another sort of system player. In fact, it is likely to be a pair: two young men in sport shirts. Here, all is action, verve, excitement. Their system requires an immediate reaction to what has just happened – it takes two of them to figure out what to do next and to get the bets placed.

"$14 on pass and $6 on come," hollers the boy with the book. The other places the bets. With glistening eyes and fierce whispered cajolery they watch what the dice do; then they consult, argue, scramble to get the next bet down in time. Usually they end up screaming at each other. "You stupid idiot! We were supposed to have an insurance bet on the bar number! Now you've loused the system completely!" A few days later one may see them on the edge of town, thumbing a ride to L.A.

There are literally thousands of systems being played at this very minute in gambling establishments throughout the world. In spite of their diversity, all have one thing in common: none of them work. They fall into six broad categories:

Superstitious systems. In these, bets are placed in obedience to tips received from dreams, numerology, astrology, or "significant" accidents – for instance, seeing three redheads all in one city block. Off to the casino for an evening of bets on red. We need not concern ourselves with these systems at all.

Observational systems. The bettor watches the dice or the wheel until he detects a pattern. Then he says to himself, "Maybe this pattern is merely the result of chance – or maybe something is wrong with the equipment. I will bet on the continuation of the pattern. If it has resulted from chance, my bet is as good as any other. If the equipment is out of whack, I have an advantage."

This is sound thinking. Around the beginning of the century a British engineer, Charles Jaggers, detected a bias in one of the wheels at Monte Carlo and cleaned up about $100,000 before the house caught on and corrected the fault. But those good old days are no more. Now the casinos take daily measurements to make sure everything is shipshape. A few years ago there was a lot of publicity about a couple of college boys who made a similar discovery, and a bundle, at Reno; but the suspicion is large that the whole thing was a publicity stunt by the house to bedazzle potential customers and fill them with spurious dreams. Nowadays, the apparatus does not go bad often enough to outweigh the house odds.

The monetary advantage to players of these systems lies in the amount of time spent in observing and tabulating. There isn't much time left to bet.

Cynical systems. Also sound. Suspecting that the game is crooked, the player bets on the opposite side from the big money, figuring that he will win as it loses. The trouble with this system is that the house will resent the implications of this play (whether the house is honest or crooked), and pretty soon a sinister fellow of great strength will invite the player to get the hell out and never show his face again.

Law-of-averages systems. Here the player, observing a long run in one direction, reasons that the law of averages is going to step in soon and balance things out. He waits for such a run and then bets against its continuing. In the lingo, he "coppers the play."

This is very unsound thinking. The chances on any spin or roll are not affected one whit by what has gone before. That little ball on the roulette wheel doesn't know what it just did, and it doesn't care. It's going to continue the run about half the time, and about half the time it's going to break it off.

Systems based on misplaced confidence in the law of averages aren't going to cost the player more than he would lose anyway, but they certainly won't help him.

Lurch systems. These start at the bar. The player, at a certain point, decides he wants to she a li'l action, so he lurches over to the roulette table and puts $10 on his good ole lucky seven (35 to 1). Then, before the spin, he lurches back for another quick transfusion. Lo and behold, seven wins: he has $350 and doesn't even know it. The house courteously sets aside all but $25, the limit on such a bet, and lets the $25 ride, having no instructions to the contrary. Will wonders never cease? Seven comes again! Our man lurches back to the table to find himself $1225 ($350 + $875) richer.

A fairy tale. This system has absolutely nothing to recommend it.

Mathematical systems. Ah, here we broach a subject for which the intelligent, reasoning man can have some respect. Obviously, those other systems have nothing to them. And most of the mathematical systems are for the birds, too: not carefully thought out, not subtle enough – of course they fail. But this system is tried, tested and infallible. Months were spent on dry runs; thousands of trials led to its ultimate refinement. Compilations of random numbers were applied to it and it won every time. A mathematician friend was hauled in to calculate the degree of risk, and it turned out to be utterly negligible. This system is ready to go!

Sorry, man. Your system is not ready to go. No system is ever ready to go.

The True Believer in one particular system will reject this statement as untrue; and toward him we are resigned. We can't dissuade the zealot from his zeal. He is committed on an emotional level to which reason has no access; and, if he ever sees the light, it will come to him on the wings of some stronger and sobering emotion, such as the one that follows on the collapse of his mansion. We are speaking now to those of you who have become intrigued by the notion that perhaps there are mathematical systems that are valid, and that can relieve you of the need to work for a living. We'd like to catch you before you go any further.

The real reason why the notion is false is a perfectly simple mathematical one; and the trouble with it is, almost no one will take it seriously. It sounds too much like all the vague old adages like, "You can't squeeze blood from a turnip," or, "There's many a slip 'twixt the cup and the lip." Nevertheless, the statement regarding the fatuity of systems is a serious statement of mathematical fact, however devoid of practical, real meaning it may sound. It is simply this: all systems have to buck the odds; you cannot add up a series of minus expectations and come out with a profit.

"Nonsense!" cries the True Believer. "Sure, I'm bucking a slight minus expectation. But my system can withstand a fantastically improbable run of bad luck. I can handle the evil day – if it ever comes – with what I have won in the meantime."

He's wrong. Notice how he discounts the "slight" minus expectation – we'll come back later to the question of how slight it is. But first, what is this business of "expectation"?

It is nothing less than the crux of the whole matter.

If you are trying to roll an ace with one die, your chance of doing so is 1/6 (one of the six sides is an ace). Now, suppose someone offers to pay you a dollar for each time you throw the ace, but requires you to pay 15 cents every time you roll. Your expectation per roll is one sixth of one dollar, or 16 2/3 cents, less the 15 cents you must pay. You have a plus expectation of 1 2/3 cents per roll. If you roll 1000 times, your profit will be pretty close to $16.67.

But suppose you are asked to pay 18 cents for the privilege of rolling. Now you have a minus expectation of 1 1/3 cents per roll. After 1000 of them you will be losing about $13.33.

The minus expectation doesn't sound like much – only 1.33% of the money you put up (or bet; for what you have been doing is betting). Surely a good system can handle a risk as slight as that and show you a profit by its skillful technique of varying the size of the bets.

As it happens, this minus expectation of 1.33% is pretty close to the best odds you can find in a gambling casino. The house edge on line bets (bets that the shooter wins) at the crap table is 1.41%. At the Monte Carlo roulette tables (which are four times as easy on you as the tables in this country) it is 1.35% on the even-money bets. Even with this "slight" advantage, the casino manages to realize a 125% return on invested capital every year.

So perhaps the house advantage is not so slight as it appears. Things begin to get interesting when you calculate your chance of winning against, say, the 1.41% house edge at craps. That minus expectation begins to multiply. If you bet 100 times at one dollar (and any system player is going to find himself making at least that many bets – unless he goes broke first), your chance of winning even one lousy buck from your 100 bets is only about two in five. Your chance of winning $10 is one in seven, and your chance of winning $20 is one in fifty. Even if you make 1000 one-dollar bets, your chance of winning $20 is only about one in seven.

Of course, these statistics do not take that fantastic system into account. But, as we are about to show, the system makes no difference whatsoever. A minus expectation is a minus expectation; no system is going to turn it into a plus expectation.

What most mathematical systems do is this: instead of letting you take your relatively small losses as you incur them, they save them up and serve them to you in one devastating, wallet-flattening wallop. In the meantime you have the illusion of winning. The final crusher comes when, in the course of increasing the size of your bets as you lose, you run into the house limit. When that happens you invariably find that you have lost more than you had won before it happened.

Let's take a look at a very bad, but apparently imperishable, system: the Martingale. Every year a million more enthusiasts discover for themselves this quick but painful death and think that they have hit on something great. In the Martingale you double your bet every time you lose. When the series is broken off by a win, you win the amount of your initial bet. Like this:

Bet Total Lost

1st $1 loses $ 1

2nd 2 loses 3

3rd 4 loses 7

4th 8 loses 15

5th 16 wins, and you have won $1 for the series. Easy money! But let's go on, assuming that the fifth bet loses too.

5th 16 loses 31

6th 32 loses 63

7th 64 loses 127

8th 128 loses 255

9th 256 loses 511

10th 512 – but wait! The house limit is $500. You would like to be able to bet $512 for the chance of winning $1 – on the face of it a pretty ridiculous situation to be in – but you can't. You will have to content yourself with having lost $511.

And a run of nine straight losses is by (continued on page 115) Odds man out (continued from page 62) no means an unusual thing. In every 1000 spins of the roulette wheel, for example, there will be, on the average, one series of nine straight red or black.

In short, this is a very poor system indeed. It clobbers you with a major loss very soon after you start playing it. But that is not the real reason why it is poor. It is poor for the same reason that every system is poor: it is based on the delusion that there is some way of turning a minus expectation into a win. It can't be done.

The sophisticated systems-man sneers at the Martingale. He has a "good" system – one that increases the size of the bets very gradually in a losing streak. And it is true that the "good" systems postpone the inevitable day of reckoning. But they can never eliminate it. One of the best postponers is the Labouchere. It is played on the even chances in roulette or on the line bets at craps. In the usual form of this system you write down the numbers 1,2,3, and throughout the play you bet the sum of the first and last numbers in the series. Thus your first bet is 1 + 3 = 4. When you win, you cross out the numbers in question. When you lose, you write down the amount of your loss and again bet the sum of the ends. (If you don't understand this, be patient: it's spelled out below.) By the time the series closes out, you have won back everything you have lost plus the 1 + 2 + 3 =6 units that you have crossed out but did not lose, because they were on the paper to begin with.

A simple example. W = a win, L = a loss. You have the following series of wins and losses: L L W L L W W L W.

You write down 1 2 3. Bet 1 + 3 = 4

Loss: write down 4

1 2 3 4. Bet 1 + 4 = 5

Loss again: write down 5

1 2 3 4 5. Bet 1 + 5 = 6

Win: cross out 1 and 5

1 2 3 4 5. Bet 2 + 4 = 6

Loss: write down 6

1 2 3 4 5 6. Bet 2 + 6 = 8

Loss: write down 8

1 2 3 4 5 6 8. Bet 2 + 8 = 10

Win: cross out 2 and 8

1 2 3 4 5 6 8. Bet 3 + 6 = 9

Win: cross out 3 and 6

1 2 3 4 5 6 8. Bet 4

Loss: write down 4

1 2 3 4 5 6 8 4. Bet 4 + 4 = 8

Win: cross out 4 and 4

1 2 3 4 5 6 8 4. The series is closed out. You have lost 4 + 5 + 6 + 8 + 4 = 27. You have won 6 + 10 + 9 + 8 = 33. You are ahead by the 1 + 2 + 3 = 6 that you wrote down to begin with.

Since you cross off two numbers when you win and add only one when you lose, the series will close out whenever your wins are as many as two more than half your losses. You chaps with no taste for figures will just have to take our word for it that this is the way the system works. (In a more important sense, as we shall see, the system doesn't "work" at all.) Those of you who dig the higher mathematics might, if it would amuse you, work out what happens with the following (quite likely) run of wins (W) and losses(L):

L L W L L W L L L W L L W L W L L W L L W L L W L W L W L W

Here you have lost 19 times and won only 11, but you have come out a winner. Your largest bet was $127 – nowhere near the house limit of $500 (in Las Vegas). In fact, it seems almost impossible, with this system, that you should hit the house limit before you succeeded in closing the series off.

Well, as it happens, we did not simply invent the above series of wins and losses. A friend of ours had it while we were watching him apply this sure-fire method on the Strip. He had been using it with success for a week, and girls were clinging all over him. But we have edited a wee bit: that last bet was $53 + $53 = $106, and he didn't win – he lost. So erase that final W, above. His sheet now looked like this: 53 53 106. The series had to go on; and it went on L W L W L L L L. Nothing much out of the ordinary in such a run. But his last bet (lost) was $424, and he was now called upon to bet $530. House limit, $500. End of the line.

His choice was to stop betting or to go on at random: the system was dead. Needless to say, he had been blowing his "profits" as they came in. He was $1160 in the hole. He bet $500 and won. He bet another $500 and lost. The girls deserted him like the well-known seafaring rodents. At this point he lost his nerve also and took the bus back to St.Louis.

The moral is that even the "good" and "safe" systems are no guarantee against the runs of bad luck that come up almost every day – or anyway, every week – when you use a system to tackle the odds in a gambling casino.

Of course, there are other mathematical systems – hundreds of them – that do not run the risk of encountering the house limit. They are of many sorts. Some are based on quitting for the day after you have won or lost a certain amount. These systems will leave you, in the long run, exactly where the expectation dictates – in the red. But at least they let you go broke gradually, instead of with one horrible clobber. Other systems, often enormously complicated, involve the placement of "insurance" bets, to mitigate the misfortune of losing the main bet. It goes without saying that the insurance is illusory. Still others involve observing and playing the runs, or the "march of the table." We have dealt with these already under "law-of-aver-ages" systems.

Many systems for winning at the race track make a great show of introducing skill as a factor in the choice of bets: skill either in appraising the horse's chance of winning or in seizing the opportunities offered by the odds on the pari-mutuel board. The minus expectation is 15% at a pari-mutuel track. If you make a hundred $2 bets, you have one chance in 20 of winning $2, and one chance in 125 of winning $10. If skill is enough to overcome that tremendous disadvantage, how is it that trainers, stable employees and jockeys, who have the best sort of inside information – to say nothing of the publishers of tip sheets – stay on the job year after year and do not retire early in life?

There are other interesting questions that one might ask. For instance, why do gambling houses love systems players? Why do they go to the expense of publishing monthly statistics on the numbers that come up on the No. 1 roulette wheel? Could it be because systems players are among their most reliable and productive customers? Or are they, perhaps, eager to lose money?

How about the sellers of gambling systems? There are scores of them. The usual come-on is that a famous gambler, dying in opulence, consented to reveal the secret of his success on his deathbed; and you can buy this secret for only $25. Why is it for sale; that is, why doesn't the vendor keep it and use it himself?

The systems fanatic will have answers to these questions. The answers will be edifying to the person who is asking himself the really significant question: what is it, in the innermost heart and cravings of men, that leads them to pursue, at often ruinous cost, the chimera of the valid gambling system?

The main incentive, without any doubt, is the immemorial longing for the easy solution, the magical gimmick that solves all the problems. In their pursuit of this ideal, men are seized by a passion that blinds them to all else. The belief in systems falls right in line with the quest for the alkahest, the philosophers' stone, the Fountain of Youth, El Dorado, and all the other phantasmal short cuts to bliss. The fact that it shares with its predecessors the deplorable quality of being a fallacy, though it may be "known" to the systems buffs somewhere deep down, never gets through to them strongly enough to influence their behavior. They are rather like a man who intends to fly down from a great height with the aid of the very special kite he has invented. There he is, perched on the very top of the Statue of Liberty, ready to go. "Why not?" he asks.

"There is only one good reason," he is told. "You take that jump and you kill yourself."

"Yeah, I know," he says. "But give me another reason." He simply does not want to believe that his kite won't work.

Reinforcing this predisposition to believe the impossible is the fact that, unfortunately, the case against systems cannot be presented in simple, unmistakable, overwhelmingly convincing terms. The argument that a tiny minus expectation is inevitably going to do the gambler in does not carry conviction for a man whose whole emotional momentum is sweeping him in the opposite direction. Furthermore, the argument, being mathematical, is couched in what for many people is a foreign language. So far as they understand it, they strive to pick holes in it.

"You claim no system will win in the long run," they will say. "OK, I'll go along with that. But who cares about the long run? I'm interested in the here and now. This system of mine has been paying off at about $3 per hour of play. I'll be old and dead before that long run of yours catches up with me."

The reply to this rebuttal is that, if a system "wins" as much as $3 an hour, the "long run" will not be long at all. It will, in all probability, be quite short – a week or two. If it were a supremely conservative system, paying off at maybe a dime an hour, it might go on for many years, even until the player was old and gray. But if he values his time at only a dime an hour he belongs in the state hospital, not the casino.

The belief in systems is also strengthened by the vast mythology that has grown up around them. You cannot talk to a systems man for five minutes without hearing his tales of what his particular system has accomplished for some other person, or of the exploits of this or that fabled practitioner who cleaned up at such and such a time and place. You are sure to be told about Charles Wells, the Englishman who in three days won close to $200,000 and is celebrated in song as "the man who broke the bank at Monte Carlo." Your informant will probably suppress the facts that he: (1) didn't break the bank at all, but merely cleaned out the chips at one table a few times; (2) came back for more and lost almost all he had won; (3) wasn't playing a system.

Finally, almost all believers in systems have tested their systems at home before using them in actual play. Their tests have been convincing, to them: and they have also been ridiculously superficial. Their sample of tosses of the dice, hands at poker or blackjack, or spins of their home roulette wheel has been much too small to justify any generalizations whatsoever. This is one reason why systems that look so good in black and white look absolutely terrible in green and silver. Another reason is that dry-run systems lack all the tension and pace of actual play. At the table, with the action moving along at a fast clip, the player often loses track of his calculations, gets behind, gets flustered, makes the wrong bet, and becomes hopelessly entangled. Actually, it doesn't make any difference: he would have lost anyway. But it gives him a wonderful excuse for continuing to believe in his system even though he has lost.

Very likely the faith in systems is something that almost every would-be gambler must go through, just as every would-be adult must go through the embarrassing postures of adolescence. Most gamblers will emerge from the experience whole. Some will bog down in it, just as some grown-ups will remain little boys until they die. It rests with the individual. Before you go all out on your tried-and-true infallible foolproof system, reflect on whether you might not be wiser to skip this stage altogether and go on to the next, which is – unless you gamble for kicks and fun, and can afford to lose: refrain from all forms of gambling in which skill is not the determining factor.