## Tuesday, February 25, 2020

### No, it doesn't figure

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.

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.

Peter

C. S. P. Schofield said...

While the Gambler's Fallacy is real, one should note that very few things are actually random. If you have flipped a coin fifty times and gotten a heavy preponderance of 'heads', it's highly likely that something about your methodology is influencing the flips. The Stock Market is not a concatenation of statistical randomness, but a collection of opinions of the value of the listed companies...and some of those opinions will be sound. Of course some of those opinions will be total pigswill, too. What they WON'T be is random.

NITZAKHON said...

Every time I play I understand that \$4 a week is a price for a fantasy. Cheap entertainment.

Some years ago, when the Megamillions was something insane like \$500 million, there was a line of people. I don't normally play that one, but for that much coin, OK. People were buying hundreds of dollars of tickets. Me, I bought one, which got some stares. One person said "One"?

"If He wants me to win, I need one. If He doesn't want me to win, it doesn't matter. And if He doesn't care - which I suspect - then I know what the statistics are."

Rob said...

I've talked with people who tell me luck doesn't exist, in my world luck is having the roulette ball land on black while I have money bet on black. If my luck is running it's a lot of fun, it will end but right now it's a lot of fun.
The big lotto games? The only guarantee is if you don't play, you won't win. If you do play your \$2 bet has a chance and that \$2 can be a lot of fun up until the drawing in dreams.

Matthew Dixon Cowles said...

Everything you say in the post above is of course entirely correct. But as Steven Pinker pointed out in his book How the Mind Works, it's not actually terribly surprising that people's minds often think in that way because the real world often works that way. No weather system is infinitely large, so additional days of rain actually do make it more likely that the next day will be sunny. The caboose on a train is more likely to follow the 100th car than the 10th.

It's called the gambler's fallacy because gambling games generally need to be carefully constructed so that past events have no bearing on the likelihood of future ones.

Brass said...

The casinos increased the amount of money they won by installing the "scoreboard" on the roulette table to show what has come up all because of gambler's fallacy.