In the long run, with millions or billions of flips, a fair coin will produce increasingly even numbers of heads and tails. The numbers will show something very close to a 50\/50 split.\u00a0 But when you\u2019re dealing with only a few handfuls of flips, the law of small numbers applies: seemingly unlikely strings of coin flips are not that improbable after all. In our example, there is a probability of 1\/64 that six flips of a fair coin will result in heads each time (that\u2019s 1 over 2 to the sixth power). Those odds aren\u2019t great; they come out to about a 1.6% chance. The gambler\u2019s fallacy is to look at those meager odds and conclude there is a 98.4% chance the sixth flip will be tails. But here’s the fundamental problem: the probability of the first five flips coming up heads is now 100 percent. They have already happened! The only question is what will happen with the next<\/em> flip, and those odds are, again, 50\/50. Here is another way to look at it: any permutation of six coin flips\u2014all<\/em> heads or all<\/em> tails or three heads and three tails or one tails and five heads, e.g.\u2014has a probability of 1\/64. So it\u2019s just as likely\u2014and just as unlikely\u2014that six flips of a coin will produce six heads, or three tails and three heads\u2014or any of the other 62 possible permutations.<\/p>\n When we zoom in on a string of one or two dozen flips, then, we are likely to find some series of flips that don\u2019t look so random. Such non-random-seeming strings are to be expected from time to time. And this principle holds outside the realm of coin flips; it applies to purportedly amazing coincidences you might experience in your life.<\/p>\n It\u2019s clear how a gambler can suffer from this fallacy: he can lose big money. If you throw all your chips on black in a game of Roulette after the ball has landed on red 10 times in a row because it couldn\u2019t possibly<\/em> wind up there an eleventh time\u2014well, you have a good chance of walking home empty-pocketed. On August 18, 1913, scores of French gamblers left the Monte Carlo casino bereft after falling victim to this mistake: the Roulette ball landed on black 26 times in a row that day; during the run, everybody was betting that the wheel would even itself out and turn to red. But of course the wheel had no memory of its previous spins. Only the irrational bettors thought that previous spins had anything to do with how the next spin would turn out.<\/p>\n A new piece of research shows there are weighty implications of this cognitive bias well beyond the casino floor. In next Friday’s Praxis, I will discuss evidence that judges, loan officers and baseball umpires tend to succumb to the gambler’s fallacy in their decision making\u2014dramatically expanding the damage the fallacy can cause to innocent bystanders.<\/p>\n Stephen Maxie writes:\u00a0 Last August, my wife and I welcomed our third daughter into the world. It\u2019s wonderful to be the parent of three girls. There is one significant drawback, however: having to field the question, over and over again, … Continue reading ![\"Gambler's](\"http:\/\/www.w-t-w.org\/en\/wp-content\/uploads\/2015\/01\/Gamblers-Fallcy-300x198.jpg\")
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