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Science

Scientists find that coin tosses aren't 50/50. Here's how you can get an advantage

The age-old method isn't as fair and practical as we originally thought.

coin toss, math, probability, science, science news, Persi Diaconis
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Coin tosses aren't 50/50 like we've been led to believe

Settling things by coin toss has been around for centuries. The ancient Romans called it “‘Heads or Ships.” Britains of the Middle Ages knew it as “Cross or Pile.” Throughout history, this game of chance was believed to be a fair, unbiased way to settle a dispute, choose which team goes first in a sports game and make decisions.

And the thought behind this makes sense. After all, there are only two sides to a coin, making the odds for each outcome an even 50/50. It doesn’t get more even than that.

However, a team of scientists, led by former magician and American mathematician Persi Diaconis, have discovered that this age-old method isn’t as evenly split as we believed. And there's even a way to slightly cheat the odds to your advantage.


Diaconis made a name for himself by studying (and debunking) randomness, one of his more famous feats being determining how many times a deck of cards must be shuffled in order to truly mix up the deck. Even as a teenager, he exposed how casino scammers would shave their dice to improve their chances against customers.


When it comes to coin games, Diaconis has long argued that while it’s “pretty close to fair,” it’s definitely not 50/50. Especially when a little wobble is introduced into the toss, which increases the chance that the coin will land on the same side it started.


A group of scientists set out to test Diaconis' findings and their study, currently in preprint, revealed that coins did indeed land on the same side they were tossed from around 51 percent of the time.

“According to the [Diaconis] model, precession causes the coin to spend more time in the air with the initial side facing up,” they wrote. “Consequently, the coin has a higher chance of landing on the same side as it started (i.e., ‘same-side bias’).”

The study recorded 350,757 coin flips, carried out by 48 people using 46 different currencies. In the end, there turned out to be a 50.8 percent chance of the coin showing up the same side it was tossed from.

They also found that some tossers showed a strong same-side bias while others had none at all, indicating that coin tosses may come down to the tosser, ever so slightly.

While this might not seem like a huge margin, the advantage becomes clear when you put into a betting scenario. "If you bet a dollar on the outcome of a coin toss (i.e., paying 1 dollar to enter, and winning either 0 or 2 dollars depending on the outcome) and repeat the bet 1,000 times, knowing the starting position of the coin toss would earn you 19 dollars on average,” the team explained.

"This is more than the casino advantage for 6 deck blackjack against an optimal-strategy player, where the casino would make 5 dollars on a comparable bet, but less than the casino advantage for single-zero roulette, where the casino would make 27 dollars on average."

via GIPHY

You could also use physics to your advantage, not just probability. Diaconis also proved that the head side of a coin is a tiny bit heavier than its tails counterpart, causing it to land on tails more often. Especially when it comes to Lincoln Memorial pennies.

So next time you are fighting with a loved one over whose turn it is to do the dishes, you can still settle it with a coin toss. Just conceal the starting position first. Or take a peak a use this hard earned knowledge. No judgement.

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Do you ever feel like you could be doing more when it comes to making a positive impact on your community? The messaging around giving back is louder than ever this time of year, and for good reason; It is the season of giving, after all.

If you’ve ever wondered who is responsible for bringing many of the giving-back initiatives to life, it’s probably not who you’d expect. The masterminds behind these types of campaigns are project managers.

Using their talents and skills, often proven by earning certifications from the Project Management Institute (PMI), project managers are driving real change and increasing the success rate on projects that truly improve our world.

To celebrate the work that project managers are doing behind the scenes to make a difference, we spoke with two people doing more than their part to make an impact.

In his current role as a Project Management Professional (PMP)-certified project manager and environmental engineer for the U.S. Environmental Protection Agency (EPA), Joshua Williard oversees the cleanup of some of America’s most contaminated and hazardous waste sites.

Courtesy of Joshua Williard

“Recently, I was part of a four-person diving team sent to collect contaminated sediment samples from the bottom of a river in Southeastern Virginia. We wanted to ensure a containment wall was successfully blocking the release of waste into an adjacent river,” Williard says.

Through his work, Josh drives restoration efforts to completion so contaminated land can again be used beneficially, and so future generations will not be at risk of exposure to harmful chemicals.

“I’ve been inspired by the natural world from a young age and always loved being outside. As I gained an understanding about Earth's trajectory, I realized that I wanted to be part of trying to save it and keep it for future generations.

“I learned the importance of using different management styles to address various project challenges. I saw the value in building meaningful relationships with key community members. I came to see that effective project management can make a real difference in getting things done and having on-the-ground impact,” Williard says.

In addition, Monica Chan’s career in project management has enabled her to work at the forefront of conservation efforts with the World Wildlife Fund (WWF-US). She most recently has been managing a climate change project, working with a diverse team including scientists, policy experts, data analysts, biologists, communicators, and more. The goal is to leverage grants to protect and restore mangroves, forests, and ecosystems, and drive demand in seaweed farming – all to harness nature's power to address the climate crisis.

Courtesy of Monica Chan

“As the project management lead for WWF-US, I am collaborating across the organization to build a project management framework that adapts to our diverse projects. Given that WWF's overarching objectives center on conserving nature and addressing imminent threats to the diversity of life on Earth, the stakes are exceptionally high in how we approach projects,” says Chan.

“Throughout my journey, I've discovered a deep passion for project management's ability to unite people for shared goals, contributing meaningfully to environmental conservation,” she says.

With skills learned from on-the-job experience and resources from PMI, project managers are the central point of connection for social impact campaigns, driving them forward and solving problems along the way. They are integral to bringing these projects to life, and they find support from their peers in PMI’s community.

PMI has a global network of more than 300 chapters and serves as a community for project managers – at every stage of their career. Members can share knowledge, celebrate impact, and learn together through resources, events, and other programs such as PMI’s Hours for Impact program, which encourages PMI members to volunteer their time to projects directly supporting the United Nations 17 Sustainable Development Goals.

“By tapping into PMI's extensive network and resources, I've expanded my project management knowledge and skills, gaining insights from seasoned professionals in diverse industries, including environmental management. Exposure to different perspectives has kept me informed about industry trends, best practices, and allowed me to tailor my approach to the unique challenges of the non-profit sector,” Chan says.

“Obtaining my PMP certification has been a game-changer, propelling not only my career growth, but also reshaping my approach to daily projects, both personally and professionally,” Chan says. Research from PMI shows that a career in project management means being part of an industry on the rise, as the global economy will need 25 million new project professionals by 2030 and the median salary for project practitioners in the U.S. is $120K.

PMI’s mission is to help professionals build project management skills through online courses, networking, and other learning opportunities, help them prove their proficiency in project management through certifications, and champion the work that project professionals, like Joshua and Monica, do around the world.

For those interested in pursuing a career in project management to help make a difference, PMI’s Certified Associate in Project Management (CAPM) certification could be the starting point to help get your foot in the door.

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