Gambler’s Fallacy Simulator

The gambler’s fallacy simulator tests the feeling everyone has had at a roulette table: five reds in a row, so black must be due. Run a million spins and look only at what came straight after each streak of five. Black lands about 48.6% of the time, exactly the same as on any other spin. Free, and you can run it as often as you like.

Gambler’s fallacy simulator: what it actually checks

It spins a virtual wheel as many times as you choose. Every time the last few results were all the same colour, it notes the very next spin. At the end it tells you how often the streak carried on, how often it broke, and how often zero turned up and beat both.

Try it with five in a row on a single-zero wheel. You’ll see something like this:

• Streak carries on: about 48.6%
• Other colour at last: about 48.6%
• Zero: about 2.7%

Push it to eight or ten in a row and the figures wobble more, simply because long streaks are rarer and there are fewer of them to count. Run more spins and they settle back on 48.6%. Every time.

Why the feeling is so strong

Our brains are tuned to spot patterns and to expect things to even out quickly. Over a million spins, red and black do even out, almost perfectly. But they don’t do it by correcting themselves after a streak. They do it because a million spins is so many that a run of six reds is a speck.

The wheel has no memory. Neither does a slot, a deck that’s been reshuffled, or a coin. Each result is decided fresh.

The best-known example is the Monte Carlo casino in 1913, when black reportedly came up 26 times in a row. The story goes that players lost heavily betting on red as the streak grew, sure it had to end. For any 26 spins you pick, all black is roughly a 1 in 137 million chance. Every one of those spins was still 18 in 37 for red.

Where the fallacy costs people money

• “Due” numbers. Boards showing hot and cold numbers are there to keep you betting. A number that hasn’t come up in 100 spins is no more likely to come up next.
• Slots that “should pay soon”. Each spin is random. A machine that hasn’t paid out a feature in a while isn’t loaded.
• Chasing losses. “I’ve lost five in a row, the next one’s bound to come in” is the same mistake, with your own money behind it.
• Betting systems. The Martingale and its relatives all assume a win is coming soon. See the losing streak calculator for how long “soon” can take.

The opposite mistake

There’s a mirror image called the hot-hand fallacy: red has come up five times, so red is hot, ride it. Just as wrong. The simulator shows the streak carrying on at exactly the normal rate, no more.

If you want to see the house edge doing its work over many spins, the roulette simulator uses play money and the same fair wheel.

Believing a win is “due” often leads to chasing. The chasing losses calculator shows the odds of winning back what you’ve lost.