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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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10 anti-holiday recipes that prove the season can be tasty and healthy

Balance out heavy holiday eating with some lighter—but still delicious—fare.

Albertson's

Lighten your calorie load with some delicious, nutritious food between big holiday meals.

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The holiday season has arrived with its cozy vibe, joyous celebrations and inevitable indulgences. From Thanksgiving feasts to Christmas cookie exchanges to Aunt Eva’s irresistible jelly donuts—not to mention leftover Halloween candy still lingering—fall and winter can feel like a non-stop gorge fest.

Total resistance is fairly futile—let’s be real—so it’s helpful to arm yourself with ways to mitigate the effects of eating-all-the-things around the holidays. Serving smaller amounts of rich, celebratory foods and focusing on slowly savoring the taste is one way. Another is to counteract those holiday calorie-bomb meals with some lighter fare in between.

Contrary to popular belief, eating “light” doesn’t have to be tasteless, boring or unsatisfying. And contrary to common practice, meals don’t have to fill an entire plate—especially when we’re trying to balance out heavy holiday eating.

It is possible to enjoy the bounties of the season while maintaining a healthy balance. Whether you prefer to eat low-carb or plant-based or gluten-free or everything under the sun, we’ve got you covered with these 10 easy, low-calorie meals from across the dietary spectrum.

Each of these recipes has less than 600 calories (most a lot less) per serving and can be made in less than 30 minutes. And Albertsons has made it easy to find O Organics® ingredients you can put right in your shopping cart to make prepping these meals even simpler.

Enjoy!

eggs and green veggies in a skillet, plate of baconNot quite green eggs and ham, but closeAlbertsons

Breakfast Skillet of Greens, Eggs & Ham

273 calories | 20 minutes

Ingredients:

1 (5 oz) pkg baby spinach

2 eggs

1 clove garlic

4 slices prosciutto

1/2 medium yellow onion

1 medium zucchini squash

1/8 cup butter, unsalted

1 pinch crushed red pepper

Find full instructions and shopping list here.

bow of cauliflower ham saladGet your cauliflower power on.Albertsons

Creamy Cauliflower Salad with Ham, Celery & Dill

345 calories | 20 minutes

1/2 medium head cauliflower

1 stick celery

1/4 small bunch fresh dill

8 oz. ham steak, boneless

1/2 shallot

1/4 tspblack pepper

1/4 tsp curry powder

2 tsp Dijon mustard

1/4 tsp garlic powder

3 Tbsp mayonnaise

1/8 tsp paprika

2 tsp red wine vinegar

1/2 tsp salt

Find full instructions and shopping list here.

tofu on skewers on a plate with coleslawPlant-based food fan? This combo looks yums. Albertsons

Grilled Chili Tofu Skewers with Ranch Cabbage, Apple & Cucumber Slaw

568 calories | 20 minutes

1 avocado

1/2 English cucumber

1 (12 oz.) package extra firm tofu

1 Granny Smith apple

3 Tbsp (45 ml) Ranch dressing

1/2 (14 oz bag) shredded cabbage (coleslaw mix)

2 tsp chili powder

1 Tbsp extra virgin olive oil

1/2 tsp garlic powder

1/2 tsp salt

Find full instructions and shopping list here.

frittata in a cast iron skilletSometimes you just gotta frittata.Albertsons

Bell Pepper, Olive & Sun-Dried Tomato Frittata with Parmesan

513 calories | 25 minutes

6 eggs

1/2 cup Kalamata olives, pitted

2 oz Parmesan cheese

1 red bell pepper

1/2 medium red onion

8 sundried tomatoes, oil-packed

1/4 tsp black pepper

1 Tbsp extra virgin olive oil

1/2 tsp Italian seasoning

1/4 tsp salt

Find full instructions and shopping list here.

plate with slices of grilled chicken and a caprese saladCaprese, if you please.Albertsons

Balsamic Grilled Chicken with Classic Caprese Salad

509 calories | 25 minutes

3/4 lb chicken breasts, boneless skinless

1/2 small pkg fresh basil

1/2 (8 oz pkg) fresh mozzarella cheese

1 clove garlic

3 tomatoes

1 Tbsp balsamic vinegar

4 3/4 pinches black pepper

1 1/2 tsp extra virgin olive oil

3/4 tsp salt

Find full instructions and shopping list here.

four stuffed mushrooms on a plateThese mushrooms look positively poppable.Albertsons

Warm Goat Cheese, Parmesan & Sun-Dried Tomato Stuffed Mushrooms

187 calories | 35 minutes

1/2 lb cremini mushrooms

1 clove garlic

1/2 (4 oz) log goat cheese

1/4 cup Parmesan cheese, shredded

2 sundried tomatoes, oil-packed

1 1/4 pinches crushed red pepper

1 tsp extra virgin olive oil

1/4 tsp Italian seasoning

2 pinches salt

Find full instructions and shopping list here.

plate with open English muffin with goat cheese and sliced baby tomatoes on topMove over, avocado toast. English muffin pizzas have arrived.Albertsons

English Muffin Pizzas with Basil Pesto, Goat Cheese & Tomatoes

327 calories | 10 minutes

3 Tbsp (45 ml) basil pesto

2 English muffins

1/2 (4 oz) log goat cheese

1/2 pint grape tomatoes

3/4 pinch black pepper

2 pinches salt

Find full instructions and shopping list here.

pita pocket on a plate filled with veggies, meat and cheeseThis pita pocket packs a colorful punch.Albertsons

Warm Pita Pocket with Turkey, Cheddar, Roasted Red Peppers & Parsley

313 calories | 20 minutes

1/4 (8 oz) block cheddar cheese

1/2 bunch Italian (flat-leaf) parsley

4 oz oven roasted turkey breast, sliced

1/2 (12 oz) jar roasted red bell peppers

1 whole grain pita

3/4 pinch black pepper

1/2 tsp Dijon mustard

2 tsp mayonnaise

Find full instructions and shopping list here.

plate with toast smeared with avocado and topped with prosciuttoDid we say, "Move over, avocado toast?" What we meant was "Throw some prosciutto on it!" Albertsons

Avocado Toast with Crispy Prosciutto

283 calories | 10 minutes

1 avocado

2 slices prosciutto

2 slices whole grain bread

1 5/8 tsp black pepper

1/2 tsp extra virgin olive oil

1/8 tsp garlic powder

1/8 tsp onion powder

Find full instructions and shopping list here.

bowl of chili with cheese and green onions on topVegetarian chili with a fall twistAlbertsons

Black Bean & Pumpkin Chili with Cheddar

444 calories | 30 minutes

2 (15 oz can) black beans

1/2 (8 oz ) block cheddar cheese

2 (14.5 oz) cans diced tomatoes

2 cloves garlic

2 green bell peppers

1 small bunch green onions (scallions)

1 (15 oz) can pure pumpkin purée

1 medium yellow onion

1/2 tsp black pepper

5 7/8 tsp chili powder

1/2 tsp cinnamon

2 tsp cumin, ground

1 tsp salt

1 Tbsp virgin coconut oil

Find full instructions and shopping list here.

For more delicious and nutritious recipes, visit albertsons.com/recipes.

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A Christmas PSA: Please be mindful about what gifts Santa brings your kids

A mom is asking people to consider the bigger picture when deciding what Santa will deliver to your house.

Mary Katherine Backstrom/Facebook, Photo by Samuel Holt on Unsplash

Mary Katherine Backstrom makes a strong argument for keeping Santa gifts simple.

Every family has its own traditions and ways of doing things around the holidays, from cooking specific foods to engaging in specific cultural rituals to how the myth of Santa gets handled. In general, it's wise to live and let live when it comes to such things, but one mom is making a strong case for rethinking what gifts Santa brings kids for Christmas in the larger context of community.

Mary Katherine Backstrom has been posting a public service announcement of sorts every year for the past decade, asking people to be mindful about other families' economic realities and how a family's Santa gifts can impact other people's children. Her message makes perfect sense, but it's something people who have never struggled financially might never consider.

"My annual PSA from a child who grew up poor," Backstrom captioned her video plea. She began by sharing that her parents separated when she was little, and she lived with her mom, who didn't always have the means to give her kids a lot for Christmas.

"Every Christmas, I would split my time between my mom and my dad," she said, explaining that her dad's side of the family had a lot of money. She would see her cousins getting thousands of dollars in gifts from Santa, while her gifts from Santa at home were far more modest. So she would go from being happy with what she'd received to questioning why Santa didn't think she'd been good enough to receive the expensive gifts he brought her cousins.

"There is seriously nothing wrong with what you can give your child for Christmas. It doesn't matter. That's not the point," she said. "But when we tell children that Santa Claus brings all of our gifts, what happens is kids like me and other children who don't have as many things will see other children getting all of these expensive toys and they'll wonder what they did wrong."

As Backstrom points out, children are naturally going to compare; that's developmentally appropriate. Kids are also very aware of what's fair and what's not, so when Santa lavishes some children with expensive presents and gives other kids a lot less, the kids whose parents don't have as much end up questioning their goodness through no fault of their own.

Watch Backstrom share her story (starting at the 2:00 minute mark):

Many people in the comments expressed gratitude for the message, saying that they, too, were the kid who thought Santa didn't like them.

"I was that child too," shared one commenter. "I hated when school started back after Christmas and the teacher would go around the room and ask everyone to tell what they got for Christmas. It was painful and humiliating. I thought I was the only one who hated how Christmas was such a stressful time."

"I remember very clearly my friend that lived next door getting everything on her letter to santa and I didnt understand why santa hated me! I agree 100%!!" offered another.

"100% CORRECT! I was also that child and yes, I wondered if I wasn't a good enough girl to deserve the same things Santa was bringing the other children," wrote another.

Other people shared that they had simply never thought of this aspect of Christmas giving and they were thankful for the widened perspective.

"Thank you for opening my eyes. I wish I had thought about this when I was Santa!!" wrote one commenter.

"I never thought of it like this. It really has opened my eyes and heart... You are so insightful and wise. Thank you," shared another.

"I love your honesty. I never thought about this when my son believed in Santa. I wish I had," wrote another.

Unfortunately, not everyone received the kind and gentle plea with grace and understanding. Some doubled down on their "right" to have Santa bring whatever gifts they darn well please. Backstrom posted a blunt follow-up video pointing out that she was speaking from her own lived experience, not sharing some hypothetical what-if with no basis in reality.

"This PSA is telling you that you are hurting children when you associate Santa Claus with expensive gifts," she said. "I'm not gonna be delicate about this anymore, because I've been doing this PSA for 10 years now and I still get people arguing with me about it. There is nothing to argue here. We are talking about children's feelings."

Backstrom pointed to the number of people in the comments who shared that they were hurt by expensive Santa gifts as a child to illustrate that this is, actually, a real issue. And the solution is simple: Keep Santa simple and let the expensive gifts come from parents or other family members. It's really not a lot to ask to preserve a little holiday magic for kids who don't have much instead of making them question why Santa doesn't think they're good enough. Santa is a tradition millions of people share—let's keep that collective reality in mind and keep the fun in it for everyone.

You can follow Mary Katherine Backstrom for more on Facebook.

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