Flipping a coin is… not like flipping a coin

Flipping a coin is supposed to be the closest thing to a 50/50 chance we have. Indeed, we use coin flips at the start of sports games to decide which team gets the ball, etc. But has anyone ever tested whether flipping a coin really gives a 50% chance of tails and 50% chance of heads?

Frantisek Bartos and a huge team of volunteers have done so and collected the evidence from a total of 350,757 coin flips - and in the process won an IgNobel Prize last night. The best thing is to read about how they managed to get to this huge number without using a machine:

First, they asked five bachelor students to collect at least 15,000 coin flips each as part of their bachelor thesis project. Clearly history’s most intellectually demanding and exciting bachelor project ever. I can already imagine the job interview for the newly minted bachelors: “So tell me what you did for your thesis…”

Then they recruited 35 volunteers for ‘coin flipping marathons’ that lasted up to 12 hours each, which contributed another 203,440. Talking about finding people with too much time on their hands.

Finally, they issued a call for collaboration on Twitter and recruited another seven people contributing 72,281 coin flips. Which confirms every prejudice I have about people on Twitter.

In order to remove any bias from the results, the study organisers encouraged the (coin) tossers to use different coins of different sizes and various currencies as well as exchange coins between them.

So what did they find?

It turns out that the flip of a coin is unfair. On average, the coin landed on the same side with a probability of 50.8% and a 95% confidence interval of 50.6% to 50.9%. But this wasn’t the coins’ fault. They were exactly equally likely to land on heads and tails, just like one expects.

What causes the deviation from the ideal 50% probability are two things. First, coins are tossed in air, not in a vacuum and the physics of the air turbulence around a rotating coin are such that it becomes slightly more likely that it will land the same side up as it started. Second, people don’t flip a coin like a machine does with an equally distributed force. Because of a slight misalignment of the flipping finger, the tossers create a slight bias towards the coin landing on the same side as it started. As people get more practice, this bias declines and the results get closer to the ideal 50% heads and 50% tails.

Now you know what to do the next time you participate in a football match and the ref asks you to pick a side of a coin…

…and before you complain about researchers getting paid to flip coins, the paper states that the researchers did not get any funding and performed the research in their spare time.