The BBC points out that the so-called "gambler's fallacy" has never worked, and never will. It's a mathematical calculation that many don't understand.
... a reasoning flaw called the “gambler’s fallacy” [is] a worryingly common error that can derail many of our professional decisions, from a goalkeeper’s responses to penalty shootouts in football to stock market investments and even judicial rulings on new asylum cases.
To find out if you fall for the gambler’s fallacy, imagine you are tossing a (fair) coin and you get the following sequence: Heads, Heads, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails, Tails. What’s the chance you will now get a heads?
Many people believe the odds change so that the sequence must somehow even out, increasing the chance of a heads on the subsequent goes. Somehow, it just feels inevitable that a heads will come next. But basic probability theory tells us that the events are statistically independent, meaning the odds are exactly the same on each flip. The chance of a heads is still 50% even if you’ve had 500 or 5,000 tails all in a row.
For the same reason, HTHTTH is just as likely as HHHHHH. Once again, however, many disagree and think that the mixed sequence is somehow more probable than the streak.
As its name suggests, the gambler’s fallacy has been of most interest to researchers studying games of chance. Indeed, it is sometimes known as Monte Carlo Fallacy, after a notorious event at one of Monaco’s roulette tables in 1913, with 26 blacks in a row. Observational studies – using casino security footage – have confirmed that it continues to influence bets today.
Surprisingly, education and intelligence do not protect us against the bias. Indeed, one study by Chinese and American researchers found that people with higher IQs are actually more susceptible to the gambler’s fallacy than people who score less well on standardised tests. It could be that the more intelligent people overthink the patterns and believe that they are smart enough to predict what comes next.
Whatever the reason for these false intuitions, subsequent research has revealed that gambler’s fallacy can have serious consequences far beyond the casino. The bias appears to be present in stock market trading, for instance. Many short-term changes in stock price are essentially random fluctuations, and Matthias Pelster at Paderborn University in Germany has shown that investors will base their decisions on the belief that the prices will soon “even out”. So, like Italy’s lottery players, they trade against a streak. “Investors should, on average, trade equally ‘in line’ with the streak and against it,” he says. “Yet that is not what we can see in the data.”
The gambler’s fallacy is a particular problem in the very professions that specifically require an even, unbiased judgement.
There's more at the link.
It's interesting how often one encounters this in everyday life. A good example are the big interstate lotteries, the Powerball and Mega Millions. I've heard any number of people say something like "Sooner or later my luck's got to change!", or "I've bought so many tickets, the odds have to be shortening in my favor!". Sadly, neither is true. They've both been fooled by the Gambler's Fallacy.
It's not a bad idea to examine our own conduct, and see whether this affects us in any way. If others are being promoted around us at work, and we're convinced that the odds of us being next are better and better . . . no, they're not. If others are being fired or laid off around us, yet we're convinced that our odds of not being fired are better . . . ditto.