What is the Gambler’s Fallacy – How to Avoid the Gambler’s Fallacy

Lady Luck isn’t a sentimental woman. The quicker bettors reconcile this fact, the better. Five coin tosses landing on heads doesn’t mean the sixth will land on heads too.

Every number on a fair die carries even odds. Floyd Mayweather’s perfect 50-0 professional record doesn’t mean he’ll automatically win if he boxes again. If a bettor wants a bankroll to resemble Money Mayweather instead of a fairweather bettor, it’s time to get over the gambler’s fallacy.

What Is the Gambler’s Fallacy?

Gambler’s fallacy rears its ugly, misdirected head in two situations. Gambler’s fallacy manifests itself through the belief that if a certain independent event occurred more frequently than expected in the past, then it’s less likely to occur again in the future. Alternatively, the gambler’s fallacy makes its mark through the belief that if a certain independent event occurred less frequently than expected in the past, then it’s more likely to occur again in the future.

These beliefs both represent an underlying expectation of systematic reversal in random sequences of independent events. This is a false belief since when events are independent of each other, their future occurrences are unaffected by their past occurrences.

For example, say a sports bettor got bored with basketball and took his or her shot at the craps table. The bettor rolls a pair of dice, which both land on 6. The mathematical odds of this happening in a fair roll are 1/36 since the odds of each die landing on a 6 are 1/6.

The odds of this happening will never change, as math is a definite, completely objective subject. Numbers don’t lie, but eyes can.  The gambler’s fallacy could cause someone to assume that the odds of both dice landing on 6 again on the next roll are much lower than 1/36. The assumption is objectively false.

Gambler’s Fallacy and Sports

Gambler’s fallacy makes itself at home on stock trading and casino floors. The equally streaky nature of sports lends itself to the gambler’s fallacy as well. For example, it’s easy to believe undefeated records correlate with invincibility.  When the 12-point underdog New York Giants shattered the New England Patriots’ dreams of becoming the first NFL team ever to go 19-0, Nevada sportsbooks lost a record $2.6 million on Super Bowl bets.

Many scoffed at the idea that the Giants’ stout pass-rushing trio of Michael Strahan, Justin Tuck, and Osi Umenyiora could pressure enough to slow the vicious Tom Brady/Randy Moss aerial assault. Blind believers in the gambler’s fallacy learned that every matchup necessitates individualized attention.

Why is Gambler’s Fallacy a Thing?

The short answer is that humans evolved from knuckle-dragging mongoloids, so everyone is prone to lapses in judgment, such as bias confirmation. The more scientific answer is the gambler’s fallacy is a cognitive bias, meaning that it’s a systematic pattern of deviation from rationality (thinking clearly and logically), which occurs due to the way people’s cognitive system works.

Experts usually attribute gambler’s fallacy to the expectation that even short sequences of outcomes will be highly representative of the process that generated them, and to the view of chance as a fair and self-correcting process. In a nutshell, people often assume that streaks of outcomes will even out in the short term.

In the case of a fair coin toss, for example, the gambler’s fallacy can cause people to assume if a coin just landed on heads twice in a row, then it will now land on tails to even out the streak and maintain an equal ratio of heads to tails. Even in times of presuming there will be a regression to the mean, let numbers be the judge. Math doesn’t lie (the same may not hold true for mathematicians).

How to Avoid

Knowledge is the power that pushes out the gambler’s fallacy. Strong theory supplemented by unbias data spearheads successful betting, not emotions. Analyze a matchup or other bet as a whole instead of the individual parts constructing it. 

Mathematically speaking, arbitrage is a great way to guarantee returns without being blindsided by an unbelievable outcome. An arbitrage bet, or arb, is when a bettor makes two bets on the same event on two different sportsbooks to guarantee a risk-free profit. Arbitrage occurs because sportsbooks set lines independent of each other. As such, for short windows of a time, there are opportunities to seize varying odds and come out on top as a bettor either way.

For example, maybe DraftKings offers  New York Yankees +120 odds, while chief rival sportsbook FanDuel places -105 odds on the Red Sox. The bettor decides to wager $300 on the Yankees +120 odds on DraftKings. Using the OddsJam arbitrage calculator, figures that placing $338 on the Boston Red Sox’s  -105 odds on Fanduel yields a risk-free return of $21.95, regardless of if the Green Monster swallows the Yankees, or the Yankees make everyone green with envy again.

English writer and famed card game theorist Edmond Hoyle summarized the tricky situation in his 1914 edition of “Hoyles’ Games” book series.

Any person who offers to give odds on account of the maturity of the chances is betting against himself. If a coin has been tossed five times heads, and a man offers to bet 2 to 1 that it will not come heads again, he is just as foolish as if he offered to bet 2 to 1 against the first toss of all. It is by knowing the folly of such bets, and taking them up at once, that some men get rich, whether the odds are in business or in gaming. It is the acceptance of unfair odds that makes the keeping of a gambling house so profitable. If a person offers you odds that are not fair, it is your own fault if you accept them. The science of betting is to offer odds that look well but that give the bettor a little the best of it in the long run.”

Edmond Hoyle