Is a number ever due? The gambler's fallacy

"Seven hasn't come up in months. It's due."

"This machine's hot tonight."

"Red's come up five times in a row, so it's got to be black next."

They all sound like common sense. They're all the same mistake, and it has a name: the gambler's fallacy. It costs people money every single day.

Lotto balls have no memory

A lotto ball doesn't know when it was last drawn. A Keno machine doesn't keep a list of numbers it owes you. A poker machine picks each result at random, with no record of whether it's paid out lately.

So every draw and every spin starts fresh, with exactly the same chances as the one before.

That's hard to swallow, because in everyday life things often do even out. After weeks of sunshine, rain probably is on the way. Our brains hunt for patterns and expect runs to fix themselves. In a game of chance, they don't.

We tested it on real draws

We went through the full history of Australian lotto draws. Before each draw, we picked out the numbers that had come up most lately (the "hot" ones) and the numbers that had gone longest without showing up (the "due" ones). Then we counted how often they came up next.

Neither lot did any better than chance. See the results for every game.

Keno tells the same story. The numbers drawn most in one month come up about as often as any other number the next month. See Keno's hot numbers put to the test.

Streaks are normal

Random results are streakier than you'd think. Toss a coin 100 times and you'll very likely get five heads in a row somewhere in there.

Look back over any lottery's results and you'll find numbers that went quiet for months, and others that kept popping up. That's just what random looks like. Spotting a pattern tells you nothing about the next draw.

"I'm on a roll"

This is the flip side of "it's due". A few wins in a row feel like skill, or luck that's going to last. So people bet bigger right as the run ends, which runs always do.

On a poker machine or in a lottery, your next result has nothing to do with your last one.

What it costs you

If you think a machine is about to pay, you stay on it longer and put more in. If you think you're on a hot streak, you bet bigger.

And if you think your lotto numbers are due, it gets very hard to stop. Even after you've decided to quit, the fear of missing the one draw they finally come up keeps you buying tickets.

A better rule

For any game of chance, assume the next result has nothing to do with anything that came before. Because it doesn't.

The only thing you can predict is the long-run average, and that always favours the house. Before your next lotto ticket, see what it's really worth.