The Zurich Axioms By Max Gunther
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Beware the Gambler’s Fallacy
Says the gambler: “I’m hot tonight!” Says the lottery-ticket buyer: “This is my lucky day!” Both are working themselves into a state of expectant euphoria in which they will put money at risk with less than their normal prudence. Both are likely to be sorry.
The Gambler’s Fallacy is a peculiar variety of orderly illusion. In this case the perceived order is not in the chaotic work all around, but inside, in the self. When you say you are ‘hot’, or you get the feeling that today is your lucky day, what you mean is that you are temporarily in a state in which random events will be influenced in your favor.
In a disorderly world, with events whirling wildly around in all directions, you are a calm island of order. Events in your vicinity will stop the horseplay and obediently march to your tune. Roulette wheels and slot machines will click into place for you. Cards will fall your way. Horses will run their hearts out for you. Any lottery ticket you buy will be a winner. Should you decide to play the stock market and select an investment by jabbing a knifepoint into a newspaper while blindfolded, your stock will double by next week. You can’t lose!
Like hell you can’t.
It is surprising how many smart people allow themselves to be fooled by the Gambler’s Fallacy. It shows up wherever money is wagered but in particularly prevalent around gambling casinos (hence its name).
One of the most often-heard bits of useless advice at Las Vegas and Atlantic City is that you should “test” your luck every night before doing any serious betting. Indeed, some otherwise practical textbooks on gambling solemnly suggest this. he idea is that you place a few small bets at first – drop a couple of bucks into a slot machine for instance – to see how your luck is running. If the machine swallows your offering without even saying thanks, you figure the deck of fate is stacked against you that night, so you might as well as go back to your hotel room and watch TV. But if the machine returns your offering with interest, then you are ready for the big-time dice tables or the wheel.
All kinds of people believe in this illusion of order. The high rollers believe in it and so do the nickel-and-dimers. The rich who come to the casinos in furs and Ferraris believe in it, and so do those who will barely be able to afford a bus ticket home if they lose. It might be that all of us believe in it for some part of our lives.
Like many of these illusions, the Gambler’s Fallacy ha a lot of appeal. It seems true. In its cockeyed way, it has a rational sound.
Everybody can recall episodes from his or her own experience that seem to support it. If you play bridge, poker, or Monopoly with any regularity, you are keenly aware that there are some nights when the cards or dice are so good to you that it is embarrassing, and then there are other nights when you wish you’d stayed home with a good book. There are nights when you are hot and nights when you are not.
And the phenomenon is not restricted to the gaming table but extends into all activities of your life. There are days when all your decisions turn out brilliantly right, everybody smiles at you, unexpected checks arrive in the mail, and your rival at the office decides to go off and seek her fortune in Australia. And there are other days when everything you touch turns to dust and ashes.
How natural to see some kind of order-making mechanism behind all this.
The illusion is reinforced by the stories gamblers love to tell: amazing stories of ‘hot’ states and runs of unbeatable luck. You hear those stories around every casino and every newsstand where lottery tickets are sold. Some are only locally famous, but some are international classics.
For example, there is the incredible tale of Charles Wells, who became immortalized in a popular song of the Gay Nineties, “The Man Who Broke the Bank at Monte Carlo”. Wells accomplished this legendary feat not once but on three separate nights in 1891.
“Breaking the bank” was not quite as dramatic as it sounded. It didn’t mean you bankrupted the casino. All it meant was that you exhausted the supply of house playing money allotted to a table. Still, it happened so rarely that it was a front-page news when somebody managed to do it even once. (The casino cooperated happily in the publicity by ceremoniously draping the “broken” table with a black cloth. The news could be counted on to lure in a lot of new suckers and their money on the following night.)
Wells’ game was roulette. The last of his three winning nights was the most astounding of all. On that night he chose to play single numbers. This is roulette’s longest shot. You pick any of the numbers from 1 to 36 and put your money on it. If you win, the payoff is $36 for every $1 you bet. On the old-style Monte Carlo wheel, the odds against you were 37 to 1.
Wells put his money on 5 and let it there to ripen. The number 5 came up five times in a row. The table was busted. Wells walked out of the casino with somewhat more than 100,000 French francs, the spending power of which in those days equaled more than a million of today’s dollars.
Then there was Caroline (“La Belle”) Otero, perhaps the most famous and some say the most beautiful of the celebrated courtesans who flourished around Monte Carlo in its days of glory. She was brought to the fabled gambling resort at age eighteen by a man who was evidently both an inept gambler and a scoundrel. He lost his wad at the tables and abandoned her. She was down to her last two louis-20-franc pieces, each worth perhaps $100 in today’s currency. On a desperate impulse, she went to a roulette table and bet those two louis on red.
The color wager – red or black – is one of roulette’s even money or coin-toss bets. If you win, you double your money. Caroline Otero was too frightened to watch the outcome, so she walked away from the table, simply leaving her money to fatten or vanish as the case might be.
Red came up twenty-eight times in a row. The bank was broken, and the abandoned girl, suddenly rich, was transformed instantly into Monte Carlo’s acknowledged queen.
Stories like that are good fun. They and others like them were cited in the nineteenth century and are still cited today in support of the Gambler’s Fallacy. “You see there are times when people get hot!” a believer will say. “These stories prove it – all you have to do is wait till you’re hot, then play like mad!”
They prove nothing of the kind. All they prove, in fact, is that winning streaks happen.
Toss a coin enough times, and sooner or later you are going to have a long run of heads. But there is nothing orderly about this run. You cannot know in advance when it will start. And when it has started, you cannot know how long it will continue.
And so it is with roulette, the horses, the art market, or any other game in which you put money at risk. If you play long enough, you will enjoy winning streaks – perhaps some memorable ones, with which you will undoubtedly bore your friends for the rest of your life. But there is no orderly way in which you can cash in on these streaks. You can’t see them coming and you can’t predict their duration. They are merely one more part of the chaos.
If you are betting on red at a roulette wheel and red comes up three times in a row, that is nice. But what does it tell you about the future? Are you in on the beginning of a run or twenty-eight? Are you hot? Should you increase the size of your bet?
Many would. Which is one reason why many walk out of the casinos with nothing but holes in their pockets.
As we learned in our studies of the Second Axiom, countless speculators and gamblers have been bankrupted by failing to quit while they were ahead. The Gambler’s Fallacy tends to encourage that failure, for it engenders the feeling that one is temporarily invincible.
That is a dangerous feeling to have. Nobody is invincible, not even for half a second.
Caroline Otero and Charles Wells were lucky. They had to stop playing because the house ran out of money – and in any case, some of their own money was removed from the play after each coup because of house limits on the sizes of permissible bets. They were saved by these circumstances. If the facts had been otherwise and they had continued to play, sooner or later both would have lost, and we would not know their names today.
They were not invincible. Both seemed to have the feeling that they were. Perhaps their good judgment was addled by those remarkable winning streaks. It might be hard, indeed, to remain perfectly rational after an experience like that. At any rate, Caroline and Otero and Charles Wells, in their subsequent lives, acted as though they were afflicted with two unusually grandiose cases of the Gambler’s Fallacy.
Both took a lot of long-shot chances, as though airily assuming they would stay hot forever.
They didn’t Caroline Otero died broke in a seedy Paris apartment. Charles Wells died broke in jail.
Speculative Strategy
Now let’s see specifically how the Fifth Axiom advises you to handle your money.
The Axiom warns you not to see order where order does not exist. This doesn’t mean you should despair of ever finding advantageous bet or a promising investment. On the contrary you should study the speculative medium in which you are interested – the poker table, the art world, whatever it is – and when you see something that looks good, take your best shot.
But don’t be hypnotized by an illusion of order. Your studying may have improved the odds in your favor, but you still cannot ignore the overwhelmingly large role of chance in the venture. It is unlikely that your studying has created a sure thing for you, or even a nearly sure thing. You are still dealing with chaos. As long as you remain keenly alert to that fact, you can keep yourself from getting hurt.
Your internal monologue should go like this: “Okay, I’ve done my homework as well as I know how. I think this bet can pay off for me. But since I cannot see or control all the random events that will affect what happens to my money, I know that the chance of my being wrong is large. Therefore I will stay light on my feet, ready to jump this way or that when whatever is going to happen happens.”
And that is the lesson of the Fifth Axiom. You are getting to be a smarter speculator all the time.