Why we fall for fallacy.

Playing in his first professional tournament, Tiger Woods stepped to the tee of the 14th hole during the Milwaukee Open; 6-iron in hand. Woods was many shots behind the tournament leader at this stage. And yet a large gallery had assembled to glimpse the heralded twenty-year-old prodigy. Tiger swung, his shot landing six feet from the pin. It bounced once and rolled straight into the hole. The crowd cheered for several minutes. It was a fitting start to an outstanding career. And yet, it was not the most auspicious start in the history of the game. Comrade General Kim Jong-Il, playing the very first round in his life, was reported to have scored five holes-in-one at Pyongyang Golf Club in 1994. By the end of the round, his scorecard made flawless reading. There are only two possible conclusions here: either Tiger is not such a big deal; or somebody is lying. It is not hard for any of us, except perhaps North Koreans, to figure out which is the case. Tiger has recorded three holes-in-one in his 24-year career (a span in which he has won more than eighty tournaments). Based on a large body of golf statistics, the odds of a professional golfer making a hole-in-one on any given par-3 hole is about 1 in 2,500. Tiger has played about 5,000 par-3s in his pro career so two holes-in-ones would be expected; his career total of three is not extraordinary. The odds of an amateur golfer making a hole-in-one on a given hole is about 1 in 12,500; the odds of shooting two holes-in-one in the same round is about 1 in 26 million; and of sinking four holes-in-one is about 1 in 24 quadrillion (that’s 24 followed by 15 zeros). What makes Jong-Il’s five holes-in-one even more amazing is the fact that, like most 18-hole golf courses, Pyongyang has only four short, par-3 holes. All other holes are at least 340 yards long. To get that fifth "1" in his round, the diminutive dictator must have been, in the immortal words of Bill Murray in Caddyshack, “a big hitter.” We do not need any sophisticated understanding of probability, statistics, or the game of golf to doubt the veracity of the Dear Leader’s scorecard. Nor, for that matter, do we have difficulty determining the improbability of the claim that young Jong-Il wrote 1,500 books and six operas during his three years at Kim Il Sung University. Puncturing fables about Kim Jong-Il is easy. But in other parts of life, it pays to have some grasp of probabilities. Particularly when our hard-earned money, or client's hard-earned money, is on the line. There is something in our primate brain wiring that wants to believe fallacy. About 25 million people visit Las Vegas each year to try their luck at various games of chance. Roulette, keno, craps, slot machines. The house advantage in these games ranges from about 1 per cent (craps) to 30 per cent (keno). That’s how the casinos can afford pyramids, gondola rides, cheap buffets, and Cher. She has a $60m contract with Caesars. Yet, we wager our cash knowing full well that the odds are against our winning. This could be because even in these games of pure chance with dice, wheels, or electronics, many players believe — or at least behave — as if they can do something to improve their odds. By playing their "lucky" number, or betting on a "hot" shooter, or wagering on a colour or number that is "due". People want to believe. People sometimes need to believe. It is more comfortable for the psyche to have an explanation for random events. Say, for instance, in a game of roulette, a black number has come up five times in a row. Should we keep betting on black, because black is "hot"? Or should one bet on red, figuring that a red number is "due"? Does the bet change if black has come up ten times in a row? Or fifteen times in a row? These questions are not hypothetical. On August 18, 1913, at the Casino de Monte Carlo, a remarkable run of black numbers unfolded at the roulette table. On European wheels, a red or black number is expected to come up almost half the time. By the time black had come up fifteen times in a row, gamblers started placing larger and larger bets on red, convinced that the streak was due to end. And yet black hit again, and again. Players doubled and tripled their stakes, figuring that the chances were less than one in a million of a run of twenty consecutive black numbers. But the wheel kept hitting black until the streak ended at twenty-six. The Casino was the winner of course. The incident in Monte Carlo is the textbook case for what has been dubbed the "Monte Carlo Fallacy" (or "Gambler’s Fallacy") — the belief that when some event happens more or less frequently than expected over some period, then the opposite outcome will happen more frequently in the future. For random events such as rolls of dice or the spin of roulette wheels, this belief is false because each result is independent of the previous rolls or spins. Our very powerful brains have trouble grasping this simple reality. And the problem is when this spills over from games, into real-life decisions. Such as parents with children that are of one sex who opt to have another with the hope, if not the expectation, that the next child will be of the opposite sex. But, like the flip of a coin, the sex of a baby is pretty close to a random event ("close" because there is a slight skew in the natural birth ratio of boys to girls of about 51:49). The Monte Carlo Fallacy is an example of what psychologists call cognitive bias — errors in thinking that skew the way we see the world. When investing, these biases distort our sense of control over random outcomes and cause us to overestimate our chances of success. A large body of research has revealed that our cognitive biases and our responses to them are part of our normal brain wiring. Psychological studies on both laboratory subjects and in real field situations (casinos) have documented the Monte Carlo/Gambler’s Fallacy concerning runs of numbers. They have also found that near misses of jackpots (non-wins that fall close to winning combinations) increase our motivation to play. One explanation for our fallacious thinking is that our brains are adapted to working every day to perceive patterns and to connect events. We rely on those perceived connections both to explain sequences of events and to predict the future. We can easily be tricked then to believe that some sequence is a meaningful pattern, when in fact a string of randomly determined independent events is just that — random. It is a matter of our biology, then, that humans have such a complex relationship with random chance. On the one hand, we enjoy games of chance, even though we lose often. Of course, when we lose, we accept it as just a matter of "bad luck". But on the other hand, when we win — and many people do win every day — that often gets an altogether different interpretation. Good fortune is often chalked up not to the mathematics of chance, nor even to mistaken confidence in gambling "strategies", but rather to other forces. For some it is a just reward for good character or deeds, a prayer answered, and for some, it's even skill and strategy. Take California truck driver Timothy McDaniel. On Saturday, March 22, 2014, McDaniel lost his wife to a heart attack. The next day, he bought three "Lucky for Life" lottery tickets. When he scratched them off, he discovered he had won $650,000. McDaniel said, "I think she just kind of sent me this money so I could continue taking care of the (grand) kids." McDaniel’s heartbreaking story reflects how in the larger game of life and death our relationship with chance is even more conflicted. Many people prefer to banish chance altogether, to believe that, as McDaniel told reporters, "everything happens for a reason." But not everyone. Fall not, for fallacy. Accept chance, randomness and probability for what they really are.