Is flipping a coin really 50/50?

By James Dacey |   Nov 24, 2018 

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It is commonly accepted that a cointoss is a 50/50 probability and that there is an equal chance of the coin landing on heads or tails.

However mathematician and professional magician Persi Diaconis says the flip of a coin might not be as fair as you think.. He has studied the basic images of randomness and discovered that it all depends how the coin is flipped.

“Flipping a coins not about probability but about physics,” says Diaconis. It’s about the coin, and how it is tossed. Most times when a coin is facing heads up, it will land heads-up. After intensive training Diaconis is able to flip a coin and make it land on heads every time.

It is the same for spinning a coin. The design of the majority of coins means that the “heads” face often weighs more, so it will fall on heads, leaving the tails side up. Whatsmore, a common trick is to shave a coin to further increase the bias.

Diaconis said people often call him ‘nuts’ but they tend to agree that dropping a coin on the floor is fairer than catching it the hand. As a coin lands on the ground it rotates on its sides and you get more edge-bias.”

All about Physics

“If you flip a coin quite vigorously, it’s as close to being a fair event, however, we usually don’t flip a coin vigorously… If you think about it, it’s not random at all. In fact, there are people who have been able to flip a coin and keep control over it.”

Flipping, spinning and tilting coins

Polish Math Professors, Tomasz Gliszczynski and Waclaw Zawadowski, set their statistics students the challenge to flip the Belgian Euro coin. Heads showed 140 times, while tails showed 110 times.

The coins were spun on a table rather than flipping them in the air. A test by the London-based Times newspaper showed similar results with the German Euro coin for both spinning and tossing. The eagle came out on top 60 out of 100 times when tossing a coin, and 54 times when spinning.

There are 3 common coin experiments in the introductory statistics course: flips, tips and spins.

  1. The “flip experiment” – Toss a coin in the air so it flips over several times and catch it or let it fall on a soft surface
  2. The “tip experiment” – Put a coin on its edge and tip the table until all the coins have fallen over.
  3. The “spin experiment” – Spin a coin on a flat surface.

A flip experiment should not result in significantly more heads or tails than could be accounted for by chance.

Both spin and tilt experiment should result in significantly more tails than heads

Get more detailed statistics experiments results on coin tossing

Cointossing in sports

Are cointosses in sports really fair?

Diaconis explained that due to the larger size of the special coins used in sports coin tosses the bias effect could be even greater. He says that if the coin starts heads-up then it will probably land heads-up. There’s no trick, it’s just simple mathematics.

“Probability isn’t a fact about the world,” Diaconis said in the Against All Odds interview. “Probability is a fact about an observer’s knowledge.”


Dartmouth University

Ryan Clark,

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