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How to Win a Coin Toss: Scientists Reveal the Secret After Flipping 350,757 Coins

The starting position of the coin matters more than you think.

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Many sports use coin tosses to determine who gets to choose the first move or the batting order.

This seems like a fair way to settle disputes. You might think that since a coin has two sides and you flip it randomly, the chances of getting what you want are 50/50 (or one out of two). However, a large-scale study of 350,757 coin tosses shows that this is not true. You can actually improve your odds slightly by paying attention to how you flip the coin.

A team of researchers led by American mathematician Persi Diaconis discovered that when you flip a coin, you create a small wobble in its motion.

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How to Win a Coin Toss

“This wobble, called precession, makes the coin stay longer in the air with the same side facing up as when it was flipped,” the team wrote in a paper that has not been peer-reviewed yet. “As a result, the coin is more likely to land on the same side as it started (this is called ‘same-side bias’).”

Diaconis and his colleagues analyzed a smaller number of ideal coin tosses and found that coins landed on the same side they started about 51 percent of the time. The new team asked 48 people to flip 350,757 coins from 46 different countries and found that on average, the coin showed the same side it started with 50.8 percent of the time.

ALSO READ: What Is Cowgirl in Sex Position and Its Risks?

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The team also found that coin tosses vary a lot depending on the person who flips the coin. Some people had a strong same-side bias, while others had none at all. This means that the outcome of a coin toss depends (a little bit) on the skill of the flipper.

The difference between 50/50 and 50.8/49.2 might not seem significant, but it can add up over time. For example, if you could persuade someone to bet on coin tosses with you for 1,000 times, knowing the starting side of the coin would give you an extra 19 dollars on average.

“To illustrate the impact of the bias, we can use a gambling example,” the team said in their paper. “If you wager a dollar on the result of a coin toss (i.e., you pay 1 dollar to play, and you win either 0 or 2 dollars depending on the result) and repeat this 1,000 times, knowing the starting side of the coin would earn you 19 dollars on average.”

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“This is more than the edge that a casino has over a perfect player in 6 deck blackjack, where the casino would make 5 dollars on a similar bet, but less than the edge that a casino has in single-zero roulette, where the casino would make 27 dollars on average.”

The team also offered a simple way to make coin tosses fairer for people who need to make decisions based on them.

“When coin tosses are used for important choices, the best thing to do is to hide the starting side of the coin.”

The paper is available on the pre-print server arXiv.

This article was updated from an earlier version published in October 2023.


(1) Coin Bias Calculation Using Bayes’ Theorem – Probabilistic World. https://www.probabilisticworld.com/calculating-coin-bias-bayes-theorem/.

(2) Tossing a Biased Coin – Harvard University. http://www.eecs.harvard.edu/%7Emichaelm/coinflipext.pdf.

(3) Coin Toss Bias: Do Coin Tosses Only Have a 50/50 Probability? – The …. https://thehyperhive.com/coin-toss-bias-50-50-probability/.

(4) Coin Toss Is Not As Fair As Thought, Researchers Prove Bias After …. https://www.timesnownews.com/viral/coin-toss-is-not-as-fair-as-thought-researchers-prove-bias-after-350757-flips-article-104392309.

(5) Coin tosses are not 50/50: Researchers find a slight bias – Phys.org. https://phys.org/news/2023-10-coin-tosses-slight-bias.html.

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I'm Michael, a young enthusiast with an insatiable curiosity for the mysteries of science and technology. As a passionate explorer of knowledge, I envisioned a platform that could not only keep us all informed about the latest breakthroughs but also inspire us to marvel at the wonders that surround us.
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