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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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Parenting

Yet another school district shifts to 4-day week and parents are sounding off

So...when are we getting the matching 4-day work week?

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Students working; an empty classroom.

When talking with other parents I know, it's hard not to sound like a grumpy old man when we get around to discussing school schedules: "Am I the only one who feels like kids have so many days off? I never got that many days off when I was a kid! And I had to go work in the coal mine after, too!" I know what I sound like, but I just can't help it.

In Georgia where I live, we have a shorter summer break than some other parts of the country. But my kids have the entire week of Thanksgiving off, a week in September, two whole weeks at Christmas, a whole week off in February, and a weeklong spring break. They have asynchronous days (during which they complete assignments at home, which usually takes about 30 minutes) about once a month, and they have two or three half-day weeks throughout the year. Quite honestly, it feels like they're never in school for very long before they get another break, which makes it tough to get in a rhythm with work and career goals. Plus, we're constantly arranging day camps and other childcare options for all the time off. After a quick search, I can confirm I'm not losing my mind: American kids have fewer school days than most other major countries.

 school's out, school days, school week, work week, schedules Schools Out Fun GIF by Pen Pals  Giphy  

So, it caught my attention in a major way when I read that Whitney Independent School District in Texas recently decided to enact a four-day week heading into the 2025 school year. That makes it one of dozens of school districts in Texas to make the change and over 900 nationally.

The thought of having the kids home from school EVERY Friday or Monday makes me want to break out in stress hives, but this four-day school week movement isn't designed to give parents a headache. It's meant to lure teachers back to work.

Yes, teachers are leaving the profession in droves and young graduates don't seem eager to replace them. Why? For starters, the pay is bad—but that's just the beginning. Teachers are burnt out, undermined and criticized relentlessly, held hostage by standardized testing, and more. It can be a grueling, demoralizing, and thankless job. The love and passion they have for shaping the youth of tomorrow can only take you so far when you feel like you're constantly getting the short end of the stick.

School districts want to pay their teachers more, in theory, but their hands are often tied. So, they're getting creative to recruit the next generation of teachers into their schools—starting with an extra day off for planning, catch-up, or family time every week.

Teachers in four-day districts often love the new schedule. Kids love it (obviously). It's the parents who, as a whole, aren't super thrilled.

 school, kids, teachers, instruction time, classes, schedule Class in session Photo by National Cancer Institute on Unsplash  

So far, the data shows that the truncated schedule perk is working. In these districts, job applications for teachers are up, retirements are down, and teachers are reporting better mental well-being. That's great news!

But these positive developments may be coming at the price of the working parents in the communities. Most early adopters of the four-day week have been rural communities with a high prevalence of stay-at-home parents. As the idea starts to take hold in other parts of the country, it's getting more pushback. Discussions on Reddit, Facebook, and other social media platforms are overrun with debate on how this is all going to shake up. Some parents, to be fair, like the idea! If they stay-at-home or have a lot of flexibility, they see it as an opportunity for more family time. But many are feeling anxious. Here's what's got those parents worried:

The effect on students' achievement is still unclear.

The execution of the four-day week varies from district to district. Some schools extend the length of each of the four days, making the total instructional time the same. That makes for a really long day, and some teachers say the students are tired and more unruly by the late afternoon. Some districts are just going with less instruction time overall, which has parents concerned that their kids might fall behind.

Four-day school weeks put parents in a childcare bind.

Having two working parents is becoming more common and necessary with the high cost of living. I know, I know—"school isn't daycare!" But it is the safe, reliable, and educational place we send our kids while we we work.

Families with money and resources may be able to enroll their kids in more academics, extracurriculars, sports, or childcare, but a lot of normal families won't be able to afford that cost. Some schools running a four-day week offer a paid childcare option for the day off, but that's an added expense and for families with multiple kids in the school system, it's just not possible.

This will inevitably end with some kids getting way more screentime.

With most parents still working five-day weeks, and the cost of extra activities or childcare too high, a lot of kids are going to end up sitting around on the couch with their iPad on those days off. I'm no expert, and I'm certainly not against screentime, but adding another several hours of it to a child's week seems less than ideal.

Of course there are other options other than paid childcare and iPads. There are play dates, there's getting help from family and friends. All of these options are an enormous amount of work to arrange for parents who are already at capacity.

Working four days is definitely a win for teachers that makes the job more appealing. But it doesn't address the systemic issues that are driving them to quit, retire early, or give up their dreams of teaching all together.

 teachers, stress, education, work, job Season 3 Running GIF by The Simpsons  Giphy  

A Commissioner of Education from Missouri calls truncated schedules a "band-aid solution with diminishing returns." Having an extra planning day won't stop teachers from getting scapegoated by politicians or held to impossible curriculum standards, it won't keep them from having to buy their own supplies or deal with ever-worsening student behavior.

Some teachers and other experts have suggested having a modified five-day school week, where one of the days gets set aside as a teacher planning day while students are still on-site participating in clubs, music, art—you know, all the stuff that's been getting cut in recent years. Something like that could work in some places.

As a dad, I don't mind the idea of my busy kids having an extra day off to unwind, pursue hobbies, see friends, catch up on projects, or spend time as a family. And I'm also very much in favor of anything that takes pressure off of overworked teachers. But until we adopt a four-day work week as the standard, the four-day school week is always going to feel a little out of place.

This article originally appeared in February. It has been updated.

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A woman accepted a new job, then her mom died. Her new boss's response left her in tears.

"She's going to run through a wall for that manager."

Canva Photos & Elijah Linder/LinkedIn

Bereavement leave doesn't get a lot of press, and it's awkward to talk about. But this story will make you smile for sure.

When someone suffers an unexpected loss in their family, there is no simple playbook for how to respond. Grief is immense, powerful, and hard to talk about. It's awkward, and as an outsider you're afraid of saying or doing the wrong thing. You may even want to help but have no idea how other than vague sympathies and platitudes.

It's even stranger when you're the person's boss. There are professional boundaries to consider. Plus, after all, you've got a company to run and a responsibility to the other employees to make sure work gets done and the lights stay on. You're in the uncomfortable and unenviable position of having to make sure the trains keep running, so to speak, while also showing empathy and understanding.

But maybe it doesn't have to be so complicated. One story recently shared by Elijah Linder on LinkedIn shows there might be a better way for companies and managers to handle bereavement.

 death, bereavement, grief, time off, paid leave, work, corporate policy, HR, heartwarming, kindness, good bosses Grief does not fit a 3-5 day schedule.  Photo by The Good Funeral Guide on Unsplash  

Linder runs a company called Bereave, which aims to help organizations set up better bereavement benefits and resources for their employees. So, he talks to a lot of people about what happens at work when the loved one of an employee dies.

One such story was so powerful, he just had to share:

"A woman lost her mom less than a week ago. She also accepted a new sales job during that same time," he begins in a recent post.

Can you imagine? The pain of losing a parent is overwhelming, even traumatic. Doing day to day functions like getting out of bed, eating food, and caring for your own children become almost impossible for many people. Add to that the unimaginable stress that you may lose the job you just worked so hard to get, and on top of everything else, you might be unemployed or at least persona non grata at your new workplace right off the bat.

The good thing for the company to do in this case would be to honor the offer of employment, but delay the start date to give the woman some time to grieve and deal with funeral arrangements. Ultimately, though, you probably couldn't fault either party for just deciding that the timing was unfortunate and going their separate ways. There's really no concrete timetable for how long it takes to properly grieve.

This manager, however, did one better. According to Linder, the boss honored not only the job offer, but the initial start date as well. Then, he gave the woman six weeks of paid leave right off the bat, before she'd ever had a single day of work.

She would keep her job, she would get paid, and it would all be there waiting for her when she was ready to begin. It's an incredible gesture of sympathy and trust for someone he barely knew.

"She's going to run through a wall for that manager. For that company. ... How's that for signaling 'we got you?'" Linder wrote.

Read the whole post here.

The post went viral on LinkedIn, pulling in thousands of Likes and Comments from people who were moved by the story.

Though we don't know much about the woman or the company, what amazed people was the thought process on display. Companies usually think, What's the least expensive and painful we can make this, for the company? This manager decided to make the tragedy less expensive and painful for the employee, even though she hadn't even worked a single day for him yet.

"Companies think because they can't quantify exactly what this person did into literal dollars and cents that it means it's not worth doing. Yet anyone with a human bone in their body knows how impactful something like this is to people and what it does for their motivation and engagement. It's like employment steroids and companies keep sleeping on it," wrote one reader.

"It’s not hard to be kind. I don’t know why these kinds of stories are not the norm," added another.

The average length of paid bereavement leave in the US is about three to five days for the death of an immediate family member. That is stunningly low—but it's the norm almost everywhere. Sadly, this is one benefit that's not much better in many European or other developed countries.

In another post, Linder shares a "brief" list of all the things someone has to take care of in the event of a sudden death of a close family member, including arranging funeral services, burial specifics, obtaining a death certificate, writing an obituary, and more. And that's to say nothing of the actual grieving process, which has barely begun in just five days.

And then, he writes, you're expected to go back to work a few days later like nothing happened.




Linder's story prompted others to share inspiring moments when places of work became something more, and how good people step in when corporate policies fall short.

"I'd just hired & relocated a guy & his family. I think he was there not much more than a month after the family relocated. One day jogging, he had a heart attack...and passed away. The HR Manager picked up the phone and called Payroll and told them to keep the paychecks coming, to his wife until he told them otherwise," Don Harkness commented. "And knowing she had just moved, she'd left friends and family behind. He gave her a choice. She could stay in her new home. or if she wanted to return to her previous venue, the company would pay to relocate her back. I think she opted to return. It made a deep impression on everyone."

Linder even shared another one of his own: "We recently heard about a manager who had a teammate that lost a child... The teammate took 30 days away from work. When he came back, the manager told him to delete all of his emails. Told him not to worry about catching up. Told him to start fresh and that he'd support him in doing so. How's that for signaling 'we got you...'"

One man shared a tear-jerker of a story on a Reddit thread about bereavement: "I lost my wife of 20 years when I was 44. It was cancer, 21 days for diagnosis to death. ... My company said the same...3 days [of bereavement]. I had been with the company for 20+ years. My boss said, 'Take the time you need. You will continue to get paid. If anyone says anything to you, tell them to contact me.' I will always be grateful that my boss stood by me."

Bereavement doesn't get the PR that vacation time and parental leave get, so the policies at large may not change any time soon. It's the leave you hope you never have to use, but let's be clear, it's no vacation. Having at least a few paid days off is the bare minimum a human being needs to function after a loss. But we can do better than a few days, even if we have to do it in some unorthodox ways. That's what people looking out for other people is all about. It's great to see and hear examples of it happening out there in the real world.

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Psychologist explains why everyone feels so exhausted these days and it makes a lot of sense

"A gentle reminder about why you are utterly exhausted…"

Photo by Jamie Street on Unsplash

It seems like most people are feeling wiped out these days. There's a reason for that.

We're more than four years past the onset of the COVID-19 pandemic, and it's been a weird ride, to say the least. These years have been hard, frustrating, confusing and tragic, and yet we keep on keeping on. Except the keeping on part isn't quite as simple as it sounds.

We've sort of collectively decided to move on, come what may. This year has been an experiment in normalcy, but one without a testable hypothesis or clear design. And it's taken a toll. So many people are feeling tired, exhausted, worn thin ("like butter scraped over too much bread," as Bilbo Baggins put it) these days.

But why?

Psychologist and speaker Naomi Holdt beautifully explained what's behind the overarching exhaustion people are feeling as we close out 2022, and it makes perfect sense. Holdt is a psychologist, author, and speaker with over two decades of experience, and specializes in the emotional well-being of children and young adults. She is also the author of "How to Raise Resilient Kids and Teens."

In a post on Facebook, she wrote:

"A gentle reminder about why you are utterly exhausted…

No one I know began this year on a full tank. Given the vicious onslaught of the previous two years (let’s just call it what it was) most of us dragged ourselves across the finish line of 2021… frazzled, spent, running on aged adrenaline fumes…

We crawled into 2022 still carrying shock, trauma, grief, heaviness, disbelief… The memories of a surreal existence…

And then it began… The fastest hurricane year we could ever have imagined. Whether we have consciously processed it or not, this has been a year of more pressure, more stress, and a race to 'catch up' in all departments… Every. Single. One. Work, school, sports, relationships, life…

Though not intentionally aware, perhaps hopeful that the busier we are, the more readily we will forget… the more easily we will undo the emotional tangle… the more permanently we will wipe away the scarring wounds…

We can’t.

And attempts to re-create some semblance of 'normal' on steroids while disregarding that for almost two years our sympathetic nervous systems were on full alert, has left our collective mental health in tatters. Our children and teens are not exempt. The natural byproduct of fighting a hurricane is complete and utter exhaustion…

So before you begin questioning the absolutely depleted and wrung-dry state you are in- Pause. Breathe. Remind yourself of who you are and what you have endured. And then remind yourself of what you have overcome.

Despite it all, you’re still going. (Even on the days you stumble and find yourself face down in a pile of dirt).


 tired, exhausted, wicker chair, psychology, tired woman,  A tired woman relaxing in a chair.via Canva/Photos

Understanding brings compassion… Most of the world’s citizens are in need of a little extra TLC at the moment. Most are donning invisible 'Handle with care' posters around their necks and 'Fragile' tattoos on their bodies…

Instead of racing to the finish line of this year, tread gently.

Go slowly. Amidst the chaos, find small pockets of silence. Find compassion. Allow the healing. And most of all… Be kind. There’s no human being on earth who couldn’t use just a little bit more of the healing salve of kindness."

Putting it like that, of course, we're exhausted. We're like a person who thinks they're feeling better at the end of an illness, so they dive fully back into life, only to crash midday because their body didn't actually have as much energy as their brain thought it did. We tried to fling ourselves into life, desperate to feel normal and make up for lost time, without taking the time to fully acknowledge the impact of the past two years or to fully recover and heal from it.


 tired, exhausted, wicker chair, psychology, tired woman,  A tired woman laying on the couch.via Canva/Photos

Of course, life can't just stop, but we do need to allow some time for our bodies, minds, and spirits to heal from what they've been through. The uncertainty, the precariousness of "normal," the after-effects of everything that upended life as we knew it are real. The grief and trauma of those who have experienced the worst of the pandemic are real. The overwhelm of our brains and hearts as we try to process it all is real.

So let's be gentle with one another and ourselves as we roll our harried selves into another new year. We could all use that little extra measure of grace as we strive to figure out what a true and healthy "normal" feels like.

You can follow Naomi Holdt on Facebook.

This article originally appeared three years ago.

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Amazing stylist goes viral for work with client in a wheelchair who was hit by a drunk driver

“She found herself again!”

Credit: TikTok (@stylingbykenzie)

Bri receives a fashion makeover.

Discovering yourself through clothing can be a wonderful experience: trying different colors based on your color theory match (whether you're a “true winter” or “soft summer”), experimenting with new styles, and trying on personas that transform you. But what happens when your body changes drastically, and you no longer know how to dress it?

For 31-year-old Bri, this became her reality.

Eleven years ago, a drunk driver hit her head-on. The accident left her paralyzed from the waist down. Suddenly thrust into an entirely foreign world, Bri struggled to feel confident in her new body. Fashion, once a source of enjoyment, became merely a chore—a way to hide herself and simply “blend in.”

In a fantastic viral TikTok by stylish Kenzie Welch (@stylingwithkenzie), Bri receives a full fashion makeover. Not only does Welch find incredible outfits and individual pieces for Bri to wear, she works with her one-on-one to teach her the building blocks of dressing for a seated lifestyle—giving her the tools to freely express herself and love the result.

“Bri has always looked to standing influencers and Pinterest photos for outfit inspiration,” writes Welch in her post, “but she never felt like her style could translate to a seated lifestyle… So, I gave her a style makeover!”

 

The breakdown

 

Here are the different aspects of Bri’s style makeover by Kenzie Welch.

On showing legs:

“Bri was afraid to show her legs,” writes Welch. “But I wanted to encourage her that they look beautiful, and we could find a fashion forward way to wear the style she loves! She also struggled with layering, but I showed her that cropped jackets and fun color helped balance the style and her proportions!”

In the photo, Bri is shown with a big, bright smile, rocking high-waisted jean shorts and super cute knee-high boots. This is paired with a smart gray blazer and delicate pink blouse, plus glasses, for a chic, ready-for-work look.

 wheelchair, seated, lifestyle, makeover, fashion Finding the right fit for seated individuals can be challenging.Credit: TikTok (@stylingbykenzie)

Welch continues, “Mini skorts were perfect to add to her wardrobe! This outfit is so simple, but the shows add something fun and comfy!”

The next look is fully Americana, ideal for a 4th of July picnic or a sunny day at the park: the featured jean mini skort is reminiscent of GAP or Ralph Lauren at its prime, and is put together with a fabulous red and white-striped t-shirt, a pearl necklace, tan moccasins, and sunglasses.

 wheelchair, seated, lifestyle, makeover, fashion This look is totally Americana. Credit: TikTok (@stylingbykenzie)

On showing off personality:

“When she enters a room, I want her to feel like people notice HER first, and not her wheelchair,” Welch adds. “Fashion is a place to express personality, and this outfit is easy, but still says something about who she is!”

 wheelchair, seated, lifestyle, makeover, fashion Stylist Kenzie Welch wants to make fashion accessible to all. Credit: TikTok (@stylingbykenzie)

This quote is paired with a posh, sophisticated look: candy cane pinstripe pants are paired with a cherry red manicure as well as a chocolate brown blouse, chunky layered necklaces, a cream-colored purse, and a knit sweater draped around Bri’s shoulders for an extra boost of elegance.

On inspiration:

Next on Bri is a curtained, light blue look, perfect for summer. A matching set, with a peek-a-boo cut-out at the waist, which accentuates the matching red mani-pedi beautifully. A dazzling bejeweled clutch and sparkling cuff bracelet complete the outfit.

“This was an outfit she had on her Pinterest board,” writes Welch. “I wanted to show her that she could wear the stuff she sees on standing girls, and it would look just as good, if not better!”

The final look is refinement, personified.

 wheelchair, seated, lifestyle, makeover, fashion Pinterest inspiration, translated to seated fashion. Credit: TikTok (@stylingbykenzie)

“A reminder that fashion is a place for EVERYONE to explore,” reads Welch’s caption. “Clothes are more than just what we put on our bodies. They shape and influence the way we see ourselves and how we show up in the world.”

In the next photo, Bri is sporting a 90s'-style cocktail dress: dark blue with Robin's blue polka dots, paired with a dark red leather purse and the classiest matte makeup style. Oh, and most important? A giant grin.

 wheelchair, seated, lifestyle, makeover, fashion The best accessory? A giant grin! Credit: TikTok (@stylingbykenzie)

 


 

Fashion struggles for women and girls in wheelchairs

 

Women and girls who use wheelchairs face unique and often overlooked challenges with fashion, making Bri's makeover by Kenzie Welch not just stylish, but revolutionary. These challenges extend beyond appearance to affect comfort, accessibility, and self-expression.

Poor fit and limited options:

 
  • Standard clothing rarely fits well when seated, as most garments are designed for standing bodies. Pants can be particularly uncomfortable around the waistband and stomach due to the body's changed shape while seated. Many wheelchair users report having to buy larger sizes just to button their jeans, resulting in poor fit elsewhere.
  • Length problems are common—pants, skirts, and dresses may be inappropriately long or short when seated. This can cause garments to ride up or drag on wheels, creating embarrassing wardrobe malfunctions or dangerous hazards.

 wheelchair, seated, lifestyle, makeover, fashion Women and girls who are in wheelchair face certain stylistic challenges. Credit: TikTok (@stylingbykenzie)

 

Comfort and health concerns:

 
  • Pressure sores can develop on seated bodies from seams, tight fits, or rough materials. Clothing that bunches or has poorly placed seams worsens this risk.
  • For wheelchair users, fabric choice is crucial—stiff or non-stretchy materials can restrict movement and cause discomfort. Most wheelchair users gravitate toward elastic waistbands, stretchy fabrics, and seamless construction for both comfort and ease of dressing.
 

Accessibility and independence:

 
  • Fasteners like buttons, zippers, and small closures can be challenging for seated individuals, particularly those with limited hand dexterity, making independent dressing difficult.
  • Mainstream fashion lacks adaptive features such as magnetic closures, side zippers, or extended zipper pulls that would make self-dressing more dignified and manageable for women and girls who use wheelchairs.
 

Representation and self-esteem:

 
  • Fashion marketing and design often ignore wheelchair users, resulting in feelings of exclusion and diminished self-esteem. The dominant cultural beauty standard remains largely able-bodied, making it difficult for women and girls in wheelchairs to feel visible and appreciated.
  • Shopping in-person presents additional obstacles. Inaccessible stores and fitting rooms, combined with the need to try numerous items to find something suitable, transform shopping into an exhausting ordeal.
 

Against this backdrop, Kenzie Welch's work with Bri represents a true fashion revolution—unlocking not just her personal style, but opening a world of comfort, functionality, and inclusiveness.

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