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Coin flips don't truly have a 50/50 chance of being heads or tails

Researchers who flipped coins 350,757 times have confirmed that the chance of landing the coin the same way up as it started is around 51 per cent

By Matthew Sparkes

17 October 2023

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Image Source Trading Ltd/Shutterstock

If you flip a coin, the odds of getting heads or tails are an equal 50 per cent chance – right? While this is what statistics textbooks will tell you, there is increasing evidence that it isn’t quite true in the real world.

In 2007, researchers theorised that when a coin is flipped, the flipper’s thumb imparts a slight wobble to it, causing it to spend more time with one side facing upwards while in the air and making it more likely to land showing that side. They predicted that a coin should land showing the same side that was facing up when flipped approximately 51 per cent of the time.

Now, František Bartoš at the University of Amsterdam in the Netherlands and a team of 49 others have conducted the most robust test of this theory yet carried out. He recruited dozens of friends and colleagues for a marathon coin-flipping session.

“When you and your friends sit in a room, play some music, chat, it’s like a nice activity,” he says. “Some people watch movies together and some people flip coins for 12 hours. It’s actually much more pleasant than you would expect.”

The team tossed coins of 46 different currencies and denominations 350,757 times and recorded both the pre-flipping and post-flipping state. The findings backed up the original research: coins are likely to land on the same side they started on 50.8 per cent of the time.

Crucially, though, the team found large variations in flippers. One person landed coins on the same side they started on 60.1 per cent of the time, while one at the other end of the spectrum landed their coins in this way just 48.7 per cent of the time. The researchers say that different people may impart more off-axis rotation when they flip a coin, causing it to wobble and creating a higher same-side bias.

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Márton Balázs at the University of Bristol, UK, who wasn’t involved in the research, says that coin flips in probability terms are an abstract idea, but that actually flipping a coin “is a complicated physical, psychological process”.

“An ideal coin is an abstraction. There is no such thing as an ideal coin,” he says. “It’s a complicated process. So there is a skew. It seems to be relatively small skew, like a few per cent, but it’s still there.”

Balázs says that anyone looking for a truly random result should avoid coins, but that even turning to a computer won’t be truly random, as they are notoriously unable to generate random results without repeating patterns. Anyone looking for true randomness would have to rely on sampling chaotic systems such as the weather or the motion of blobs in lava lamps, he says.

Bartoš says that although the findings show coin flips have a bias, they can still be used for everyday decisions – as long as both parties don’t see the starting state of the coin before the flip.


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