How to Do the Math Magic Trick That Will Impress Everyone You Know

Math is magic, according to a new YouTube video depicting the Kruskal count.

Brain teasers and magic tricks help bring math to relatable real life even for the mathphobic.

The Kruskal count is a probability for a deck of cards and a certainty for a clockface done in English.

YouTuber Michael Stevens (who hosts the popular Vsauce series) has brought a classic math magic trick back from its '90s heyday. In the video, Stevens walks viewers through a magic trick where they choose a number on a clock face, then trace around the clock by spelling out their numbers.

With your finger beginning at 12, you spell "five" or "eight" or "twelve" (or whatever number you've chosen!) and take one step for each letter, ending up at 4, 5, or 6, respectively. Now, you spell "four," "five," or "six" and keep going around the clock. Stevens says to do this a few times, then he guesses the final number you've landed on.

Cool, right? In the video, Stevens says the math behind the trick is part of an idea called the Kruskal count, named for mathematician Martin Kruskal. He discovered this special case of the absorbing Markov chain, where probabilities line up until people's outcomes end up being the same.

There are a lot of variations on this trick, although calling it a "trick" at all isn't quite right. The most famous application is probably by TV magician David Copperfield, who took a break from making the Statue of Liberty disappear to do different versions of a close-up trick where he predicted the numbers viewers had chosen:

What's going on here? Also, why don't any of the explanations talk about how important the language is to how this trick works? Basically, the secret is how the set of number words "one" through "twelve" in English end up pointing to each other around a clockface until they've all pointed to the same one value.

All the outcomes of the clock trick.

Caroline Delbert

To show how delicate the equilibrium is, here's an example where "six" is replaced by the seven-letter "sixteen":

The outcomes with one seven-letter number value.

Caroline Delbert

In this case, 11 out of 12 people would still end up at the same number value, and the "trick" would still almost always be a success! The same can be said if we do the trick in Spanish:

The clock trick en español.

Caroline Delbert

Here, 10 out of 12 end up on the same number value. For other languages that use letter systems, some will work better than others. For languages that use phonemes, pictographs, or characters, all bets are off.

The Russian Way to Multiply Numbers

Faced with probabilities instead of sure things, this is also when you can start to think about how what's at play is a very simplified form of the same "likely outcomes" math that poker players and casino card counters do. And, in fact, there's a version of the Kruskal count that works on a deck of cards. Stevens goes through it in the video, too.

The idea is that you can shuffle a deck of cards and end up with a deck where you can iterate from any initial card and end up on the same card an astonishing amount—about 85 percent of the time, Stevens says. He shuffles a deck and deals out an example where just 70 percent end up converging, which he says is remarkably low in the pool of overall options.

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There's a similar math magic trick where you walk people through some simple arithmetic before guessing their number. Start with any counting number. Add 23, multiply by 3, subtract 6, and multiply by 3 one more time. Then add the digits together progressively until you have just one digit left. What's that number?

An arithmetical mathemagic trick.

Caroline Delbert

You can see I've used arithmetic to guarantee everyone's number will be 9. In the meantime, show your work while I make a cruise ship disappear.

This Math Magic Trick That Will Impress Everyone You Know

From Men's Health

Math is magic, according to a new YouTube video depicting the Kruskal count.

Brain teasers and magic tricks help bring math to relatable real life even for the mathphobic.

The Kruskal count is a probability for a deck of cards and a certainty for a clockface done in English.

YouTuber Michael Stevens (who hosts the popular Vsauce series) has brought a classic math magic trick back from its '90s heyday. In the video, Stevens walks viewers through a magic trick where they choose a number on a clock face, then trace around the clock by spelling out their numbers.

With your finger beginning at 12, you spell "five" or "eight" or "twelve" (or whatever number you've chosen!) and take one step for each letter, ending up at 4, 5, or 6, respectively. Now, you spell "four," "five," or "six" and keep going around the clock. Stevens says to do this a few times, then he guesses the final number you've landed on.

Cool, right? In the video, Stevens says the math behind the trick is part of an idea called the Kruskal count, named for mathematician Martin Kruskal. He discovered this special case of the absorbing Markov chain, where probabilities line up u ntil people's outcomes end up being the same.

There are a lot of variations on this trick, although calling it a "trick" at all isn't quite right. The most famous application is probably by TV magician David Copperfield, who took a break from making the Statue of Liberty disappear to do different versions of a close-up trick where he predicted the numbers viewers had chosen:

What's going on here? Also, why don't any of the explanations talk about how important the language is to how this trick works? Basically, the secret is how the set of number words "one" through "twelve" in English end up pointing to each other around a clockface until they've all pointed to the same one value.

View photos

Photo credit: Caroline Delbert

More

To show how delicate the equilibrium is, here's an example where "six" is replaced by the seven-letter "sixteen":

View photos

Photo credit: Caroline Delbert

More

In this case, 11 out of 12 people would still end up at the same number value, and the "trick" would still almost always be a success! The same can be said if we do the trick in Spanish:

View photos

Photo credit: Caroline Delbert

More

Here, 10 out of 12 end up on the same number value. For other languages that use letter systems, some will work better than others. For languages that use phonemes, pictographs, or characters, all bets are off.

Faced with probabilities instead of sure things, this is also when you can start to think about how what's at play is a very simplified form of the same "likely outcomes" math that poker players and casino card counters do. And, in fact, there's a version of the Kruskal count that works on a deck of cards. Stevens goes through it in the video, too.

The idea is that you can shuffle a deck of cards and end up with a deck where you can iterate from any initial card and end up on the same card an astonishing amount—about 85 percent of the time, Stevens says. He shuffles a deck and deals out an example where just 70 percent end up converging, which he says is remarkably low in the pool of overall options.

There's a similar math magic trick where you walk people through some simple arithmetic before guessing their number. Start with any counting number. Add 23, multiply by 3, subtract 6, and multiply by 3 one more time. Then add the digits together progressively until you have just one digit left. What's that number?

View photos

Photo credit: Caroline Delbert

More

You can see I've used arithmetic to guarantee everyone's number will be 9. In the meantime, show your work while I make a cruise ship disappear.

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String Theorist Brian Greene Wants to Help You Understand the Cold, Cruel Universe

If you're feeling all dreamy about the universe, here's a pro tip: don't tell Brian Greene. That guy can chill your cosmic buzz fast. I recently swung by the office of the Columbia University theoretical physicist full of happy, giddy questions and came away pretty much empty. Is there such a thing as a natural moral order? I wondered. Not in this universe, there isn't. What about a purpose to the universe, then–the reason the whole 13.8 billion-year-old shebang with its hundreds of billions of galaxies and trillions of planets happened in the first place? Nope, Greene says, no such purpose, adding, "And that's O.K." Maybe for him it is.

Surely, though, Greene will grant the existence of free will–that first item on the wish list of every freshman-year philosophy student who ever lived. Sorry, not a chance.

"Your particles are just obeying their quantum-mechanical marching orders," Greene says. "You have no ability to intercede in that quantum-m echanical unfolding. None whatsoever."

But here's the thing about Greene, founder of the World Science Festival; host of multiple TV series on PBS; and the author of five books, including the blockbuster The Elegant Universe and the just-released Until the End of Time: he says it all with such ebullience, such ingenuous enthusiasm, that if he told you the whole cold, amoral universe was ending tomorrow you'd roll with it the way he would–as just one more dramatic chapter in an extraordinary tale in which we all have a precious if fleeting role. That's not to say everyone embraces his cosmic view so easily.

"I'll be frank," Greene says. "I have some students come in crying. And they say, 'This is kind of shaking my world up,' and I say to them, 'That's not a bad thing. It's fine to have your world shook. The pieces may fall back in the end to where you were, and they may not.'"

On the day I saw him, the man who has made himself the mast er of some of the most abstruse aspects of physics–superstring theory, spatial topography–was instead being mastered by one of the more basic ones: gravity. He was struggling about on crutches, the result of two ruptured spinal disks, which can give out over time whether or not you're the kind of person who can explain the attraction between the mass of the earth and the mass of your back.

Story continues

When he makes his way from desk to couch, he drops down gratefully. Behind him is a whiteboard with a storm of equations written on it. The numbers and glyphs frame his face in a perfect metaphor for the impossibly complex ideas that play out in his head, then somehow emerge comprehensibly and coherently on the page.

It's a busy time for Greene. His World Science Festival will begin its 13th season in May in New York City and its fifth year in its satellite venue in Brisbane, Australia, in March. The Down Under version attracted a total of 700,000 visitors in its first four years. The New York edition has drawn a cumulative 2 million people and more than 40 million online views of its content.

Greene, 57, is also preparing for a promotional tour for his new book, and keeps up a full schedule of teaching, holding office hours and advising graduate students. During our conversation, he mentioned that he was booked to give an evening talk on superstring theory to a gathering of the university's Society of Physics Students. It's a Friday night, a party night, but for the students and Greene, talking superstrings is a party.

"I've found that the theoretical physicists I've spent the most time with are the ones who are just enthralled by the ideas and the minutiae of an equation working out," he says. "The only difference I have seen relative to my colleagues is I've never found pure research to be enough. I've always felt like the world is so big and rich that I need to engage with it in different ways. And t hat can be the books, it can be the TV shows."

Greene comes by his love of performance rightly. His father was a vaudeville entertainer as well as a composer and voice coach. But Greene's own passion was math and science and then big science–the kind that seduces you with questions that both demand and defy answers, that can cross the line from science to something else entirely. Here, too, a close family member helped.

"My brother is a Hare Krishna devotee," Greene says. "He's 13 years older than I am. When I was little and getting interested in math and physics, he'd say, 'What are you learning?' I'd describe the Big Bang, and he'd pull out the Vedas and read to me from them. It was a very interesting back-and-forth over the decades between the scientific pathway toward a certain kind of truth and the spiritual, religious pathway to a certain kind of truth."

That tension plays out elegantly in Greene's new book, and to make sure no one misses the dialectic, the chapter names make it clear: "Duration and Impermanence," "Origins and Entropy," "Particles and Consciousness." Greene takes one of his most powerful whacks at entropy, attacking the nettlesome business of the second law of thermodynamics–the broad truth that all systems tend to disorder, which is often used to challenge the truth of evolution itself: that profoundly complex order can emerge from the chaos.

"I resolve that tension in Chapter 3," Greene says, a boast that could pass as arrogant except that, well, he does resolve the tension in Chapter 3. "It relies on the force of gravity. Without gravity, everything just spreads out, diffuses, and that's all there would be. But gravity has this wonderful capacity as a universally inward-pulling force which can undertake the following magic trick: it can pull things together, making it more orderly here, at the expense of releasing heat that makes it more disorderly out there. I call it 'the entropic two-step.'"

There's a lot of satisfaction in such neat solutions to head-cracking problems. But there is an equivalent neatness to the ostensibly dispiriting conclusions Greene reaches in his books and in his research: that unhappy business of a cold universe, an insentient universe, of the individual as just a quantum contraption, behaving as a product not of choice but of probabilities and randomness. It's where the free-will thing comes in: the universe is guided by quantum probabilities, and your "choices" are simply a part of that, the way a local breeze is part of the global weather system.

"My feeling is that the reductionist, materialist, physicalist approach to the world is the right one," Greene says. "There isn't anything else; these grand mysteries will evaporate over time." But despite such empirical bravado, Greene says more too–and whether he likes it or not, it's not reductionist, and if it's written in a book like Until the End of Time, it could be written in the Vedas as well.

"Rather than feeling, 'Damn, there's no universal morality,' 'Damn, there's no universal consciousness,'" he says, "how wondrous is it that I am able to have this conscious experience and it's nothing more than stuff? That stuff can produce Beethoven's Ninth Symphony, that stuff can produce the Mona Lisa, that stuff can produce Romeo and Juliet? Holy smokes, that's wondrous." The rational physicist with the deeply spiritual brother surely meant the holy as just a figure of speech–but if so, he picked an apt one.

How to travel on the cheap: Saving money while seeing the world

Traveling isn't just about the destination. Carry On is our series devoted to how we get away in the digital age, from the choices we make to the experiences we share.

As humans, we tend to hate it when things cost money, especially when those things make us happy.

Travel is one of the things we do to conjure a sense of fun and discovery. It also happens to be insanely expensive. But being on a budget shouldn't exclude you from the joy of visiting new places, so we did our best to figure out some tips and tricks to help you get to and enjoy your dream destination as cheaply as possible. From online tools, to packing tips, to other pieces of general knowledge, here are a few ways you travel while keeping your expenses down.

Plan your trip, consider your costs

Think about what you want to do on your trip. What's important? What's not? Once you have your priorities in front of you, it's easier to decide where you want to spend your money, which also helps you decide where you want to save it. Do you want to spend extra on a nicer/more convenient flight? Or would you rather spend that money on an activity or excursion?

Join a travel rewards program

Rack up those miles! Credit card companies are making the shift to awards based on how much money you spend instead of how many miles you travel. You're gonna use your credit card anyway. You might as well get some well-earned miles on it for that dream vacation of yours.

Find the lowest airfare â€" Use aggregators

Hotel/airfare aggregators like Expedia and Travelocity do the work of finding the best deals for you. All you have to do is type in a few details (where you're going, when you're going, etc.) and the site will comb through various companies' prices to show you your cheapest options for hotel prices, airfare, and/or both. Your best option may not always be the most convenient one, so be prepared to be flexible in your decision-making. The goal is to reduce cost, after all. But just because you're not staying in the world's fanciest hotel or flying first class on the most prestigious airline doesn't mean you can't still visit your dream country. Also consider whether you even have to fly to get to where you want to go. If you're not going far, driving will likely be cheaper.

When you're looking for flights, it might actually help to browse privately by using an incognito window, which could help you avoid price increases tied to users' browsing sessions. 

Another tip: Don't wait around for prices to drop, because they likely won't. If you see a deal you think is good enough, you'll probably want to go ahead and grab it. 

One final thing about aggregators: It's important to be flexible with your options. It's not uncommon for aggregators to offer last-minute pricing and deals on flights and hotels. If you're flexible, you can take advantage of some of those offers.

Consider cheap destinations

We know everybody wants to go to Paris. Or Tokyo. Or Rome. Or all the other places everyone dreams of seeing. But if you're trying to save money, and you just want to scratch that itch to travel, try to find some cheaper destinations that maybe don't get advertised as much but will still give you more bang for your buck. (Ever been to the beautiful beaches of Thailand, for example?)

Timing is everything â€" Traveling off-peak to save money

When it comes to traveling costs, the when is often more important than the where. Think about when most people will be traveling. Spring Break. Winter holidays. Summer vacation. Depending on where you're going, you'll probably find it's cheaper to travel there off-peak. 

If you're someone who's always want to go to New York City, beware the holiday travel season. Better to wait until after the New Year to see the Big Apple.  The crowds will be smaller, too. Looking to get to the Caribbean? September and October are the thick of the hurricane season, and rates will typically be cheaper. Just keep be sure to keep checking the weather during the lead-up to your trip, and consider travel insurance that would cover such a situation.

Consider other housing arrangements

Don't forget there are other ways to visit a city without staying in a hotel. You could stay in a hostel, or crash on somebody's couch. There are sites for that, too. And you've probably heard of sites like Airbnb and VRBO. And to state the obvious, if you have a friend or relative in the place you want to visit, stay with them! You can't pass up free lodging. 

If possible, rent your space while you're gone

It's obviously easier to save money when you have more of it to save. One way to try and offset some vacation costs is to rent out your space while you're away. If you're in a place that allows it, use Airbnb to make some extra dollars while you travel.

Unplug â€" Limit your cell phone data usage

We know it's tempting to stay plugged in when you're in a foreign place, but when you consider what you can save by unplugging, the benefits may outweigh the costs, literally. Your phone is home to a variety of resources to help you navigate an environment you know nothing about, but if you need to use cellular data or WiFi in order to access them, it'll be cheaper to get around the old-fashioned way. 

Before you go, make sure you can read and understand a map of the place you're headed to. Resist the urge to tweet about what you're doing, as cool as it may be. You'll have plenty of time to post about it after you get back home. Same goes for Insta. Take plenty of photos! But wait to post them. If you don't have unlimited data or WiFi, it's not worth it. We're not saying "don't take your phone." It's good to have it in case you need to call someone or if you're in some sort of emergency. Only using it for the basics, however, may just save you enough money to take that well-earned vacay.

Choose your tourist traps carefully 

If you're going to Paris, you see the Eiffel Tower. If you're going to Rome, you see the Colosseum. If you're going to New York, you see the Statue of Liberty. Maybe! Every destination has its tourist traps, which aren't necessarily "traps" but still garner the most attention and, sometimes, cost the most money. So be stingy about the things you want to pay money to see while you're away. Maybe limit yourself to one or two big tours, excursions, or major sightseeing opportunities. Part of the magic of traveling is immersing yourself in a foreign culture and learning about how people live their everyday lives in places you've never been to. Of course it's cool to check off a few big-ticket items from your bucket list, but simply going out and experiencing the simple pleasures of a foreign country is a great way to save money without sacrificing cultural enrichment. 

Pack lightly

You've probably heard it before, but it really does help. The less stuff you bring, the less space you need to keep it. That could mean a smaller suitcase, or a smaller hotel room â€" both of which save you some money. Also, (for flyers) if you can manage to fit everything you need into one carry-on bag, that means you don't have to spend the money to check your luggage. That also means the fewer bags you have, the less you have to spend on space to keep them. Simple math.

A few quick packing tips:

Pack bulky items like jackets and shoes first.

Roll your clothes instead of folding them.

Fold socks and put them in the shoes you packed. Don't wanna waste that space.

There plenty of other ways to pack a suitcase efficiently, which you can find here.

Limit your stay

Speaking of simple math, one way to keep costs down is by traveling for short periods of time. The longer you stay somewhere, the more you have to spend on, well, pretty much everything. Lodging. Food. Taxis, buses, or any way to get around that isn't by foot. Instead of taking that two-week vacation, think about scheduling that trip for a long weekend. If you work and get paid by the hour, that also limits the amount of money you miss out on by taking extended time off, which, by nature, means you're gaining money you wouldn't have otherwise because you're working more. Consider just how much time you need to do all the things you really want to do. Take only as much time as you need, and you'll find yourself holding onto a lot more cash than you would have if you booked that extended stay.

Pittsburgh Penguins Captain Sidney Crosby Amazed By Magician Justin Flom’s Hockey Trick

PITTSBURGH (KDKA)– Night in and out, Sidney Crosby is usually the man amazing thousands of fans with his great play.

The shoe is on the different foot when it comes to a recent magic trick from magician Justin Flom.

The NHL tweeted a video of the interaction with the duo Friday, as Crosby is amazed by the trick that involved a little bit of math.

"No way! 😱 @justinflom dazzles Sidney Crosby with another unbelievable magic trick."

Crosby was asked to enter his birth date, a random U.S. ZIP code and eight random numbers into a calculator for Flom. Crosby multiplied his birth date with the ZIP code, then subtracted that number with the number created by the random eight digits.

The equation equaled 1,742,359. It was a completely random number at first glance, but Crosby was asked to sign a picture of himself raising the cup in 2017 with his teammates, and the equation number was all of the jersey numbers visible in the picture! (17 Bryan Rust, 4 Justin Schultz, 23 Scott Wilson and 59 Jake Guentzel)

The physics behind iconic NBA slam dunks

For those more vertically challenged just hoping to add an inch or two to their jumps, Stein recommends first figuring out whether you’re more comfortable jumping with one leg or two. “Train towards your strengths,” he says, while working with a comprehensive regimen. Along those lines, Onate also suggests working out some less-considered muscles, like those in your toes. Towel scrunches, marble pickups, and barefoot drills could make all the difference between staying grounded or flying through the air, like Mike.

Scenes from ‘The Wonderful World of Chemistry’

On Jan. 31, Sterling Chemistry Lab hosted "The Wonderful World of Chemistry: A Magic Show." The one-hour interactive lecture drew hundreds of school students from around the community, and introduced basic chemistry concepts through "magic" tricks explained through the lens of science.

The event was sponsored by Yale Pathways to Science, which seeks to to encourage and support promising young scholars to pursue careers in science, technology, engineering, and math (STEM), and opens the door for middle and high school students to explore STEM at Yale.

Pittman Hosts Journalism Guru On “Magic” Show

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This week on Math & Magic: Stories from the Frontiers of Marketing, the iHeart CEO interviewed journalist Ken Auletta. The Columbia Journalism Review declared, "No other reporter has covered the news communication business as thoroughly."

Pittman and Auletta discuss everything from Auletta's profiles of powerful people, to his instincts for industry reporting. We also learn how politics led Auletta to his career in journalism and why he thinks the press can be a motivator for good. Plus, listeners can find out his trick for landing so many high-profile interviews.

You can hear the new episode HERE.

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New OMSI show blends magic and science into ‘impossible’ act

PORTLAND, Ore. (KOIN) -- A towing company employee was injured after being hit in the midst of carjacking, according to Portland police.

Early Wednesday morning, Jack Durrett told KOIN 6 News his son was run over while someone stole a car from inside the 21st Century Towing lot, where his son is employed. Police later confirmed someone broke into a storage lot and stole a vehicle, during which an employee was struck and sustained non-life threatening injuries.

Stalked: Like never before, marketers are using your personal data to tailor their messages

You're being stalked around the clock.

A growing array of electronic devices — including your smartphone, tablets, speakers and smart TVs — are acting as magnifying glasses for companies that pay billions of dollars to get an up-close and personal view of you.

The information is fed into profiles used to target you with ads, classify the riskiness of your lifestyle, help determine your eligibility for a job and much more. Mounds of personal data are flowing to political consultants attempting to influence your vote, government agencies trying to find lawbreakers and scammers trying to trick you.

But the way most people feel the results day to day is through marketing.

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Like never before, marketers are using your personal data to tailor their messages Submitted photo

Christopher Day Submitted photo

Peter Lazarz Submitted photo

Brian McGinnis Submitted photo

Warran Sifre Submitted photo

Christopher Day knows better than most how intrusive technology can be.

He's the founder of an Indianapolis tech company, DemandJump, that uses artificial intelligence to help companies identify customers and send them the right messages to procure sales.

But Day has also been a victim of what he calls annoying and even creepy cyber-marketing — strategies that are different from those employed by DemandJump.

Late last year, Day was thinking about buying a Peloton, a popular indoor exercise bike. He had never searched for nor discussed Peloton online or in emails. He had never contacted the manufacturer or a retailer about the product.

But with his smartphone in his pocket, Day discussed the bike with friends at a holiday party. And he believes his phone — either through the operating system or an app he installed — was listening.

Suddenly, he began receiving digital ads for Peloton across his devices.

"That feels too invasive," Day said. "That made me not want to buy the product. And I didn't."

But despite the marketing fail with Day, many advertisers are relying on these and other cyber tactics to get their products in front of customers — repeatedly.

Everything you do with your electronic devices is monitored, tracked, reported and stored. And all that information is saved indefinitely, ready to be rolled out at a moment's notice to help a company make a sale.

While consumers can take some steps to stem the peeping, it's tough to stop the data gathering completely without going off the grid — a difficult move given that the tools that make life convenient today are the very ones marketers exploit.

Cookie monster

Companies build profiles about customers and track them in a number of ways. But the most important ingredient might be cookies—and not the edible kind.

Cookies are bits of programming that operate in the background of a website, app or device.

The name is derived from the term "magic cookie," which is what programmers in the late 1970s called a packet of data a program picks up from a user's computer and sends elsewhere for identification purposes. Cookies grab what's called an IP address, an identifying number assigned to every device on an internet-connected network. But cookies don't necessarily know the user or owner of that device (although, as you'll see, those dots aren't difficult to connect).

Cookies have some important, practical functions. For example, they let web servers know whether someone is logged into a site, and which account they are logged in with. IBJ uses cookies, for example, to help determine whether a reader on its website is a subscriber.

But programmers have discovered even more valuable marketing uses for cookies. Ever wonder how you can leave an online store — or close your browser or turn off your computer entirely — and come back a few minutes, hours or even days later to find the contents in your shopping cart still there? Or how an airline knows about a reservation you started but didn't complete?

That's information the web browser deposited on your computer with a cookie. When you go back to the site, the computer reads the cookie and distills the information from your previous visits.

And that's just the first crumb of what cookies can track. They can tell a site what pages you looked at and for how long, what items you clicked on and even where you put your cursor. Some can even track — through your webcam — where you trained your eyes.

But not every cookie is created — or accessed — equally.

Cookies deposited on your computer by a website operator are called first-party cookies. Generally, first-party cookies can be read — in their entirety — only by the website that deposited them.

Website developers say those kinds of cookies help them customize content to suit you. Think ESPN.com, which uses cookies to track your browsing, reading and viewing, then recommends other stories.

Third-party cookies are another story entirely. They are deposited by ads, online quizzes, games and other content users download or visit. So if you click on, say, a Nike ad and then go to the Nike website, the site will retrieve that cookie to get a better idea of who you are and how you like to shop.

Tracking your every move

But why, after you search for a product or click on an ad, do ads for those and related products begin popping up — no matter where you surf?

Enter data brokers and trackers — a vast and growing network of companies that are not only depositing cookies but also selling that information to a wide range of retailers, service providers and websites. A national or global company might subscribe to a dozen or more data brokers and others services to track current and potential customers.

Say you go to a car dealer's website and then surf to a news site. If those two sites subscribe to the same ad network — or network of networks — then, voila, you'll see an ad for the very vehicle you were researching, even though the story you're reading has nothing to do with cars.

"It's like you once stopped in a car dealership, but now you' re at the grocery store and someone is chasing you around the grocery store yelling at you to see if you want to buy a car," said DemandJump's Day. "In real life, internet marketing methods might be considered harassment."

DemandJump doesn't rely on cookies, Day said. It uses math and artificial intelligence to make sure companies have access to consumers in the "buying mode" of their product. It's a complicated business that relies on programing to recognize the precise wording of search queries.

But thousands of companies use cookies, and so, as you travel from website to website, you are taking on cookies like a well-traveled ship takes on barnacles.

"Your IP address is being collected by every single network you pass through, and that includes services like Netflix," said Warren Sifre, principal consultant for Moser Consulting, an Indianapolis-based information technology company that specializes in business intelligence and advanced analytics.

Free software and apps are huge data-gathering tools.

"There is a reason why things are free," Sifre said. "It wouldn't make much business sense to develop an application that had zero return on investment, whether it be directly or indirectly."

The combination of millions of cookies and huge data brokerages means retailers and other companies can divine within a second of your landing on their website where else you've been on the internet and everything you've clicked on, read, viewed or listened to — sometimes for years, even a decade or more.

"People don't appreciate the permanence of this data," said Brian McGinnis, a partner in the local law office of Barnes and Thornburg and a cybersecurity expert. "There's a reason why some companies are building massive data centers. The internet doesn't forget."

Getting personal

Combine cookies with personal data — your name, birthdate, hometown and more — and the outcomes become very personal.

Among the ingredients is Facebook — and its forerunner, MySpace.

When the first major social network, MySpace, came along in 2003, it seemed like a great way for people to stay connected to family and friends. But marketers — and social media sites themselves—quickly realized the value of the information it was gathering. Then came Facebook, with its worldwide reach, which took personalized marketing to a new level.

Social networks have induced people to voluntarily cough up the information marketers have long coveted: name, residence, age, occupation, nationality, dating status, hobbies, vacation destinations, you name it. And all that information can be easily attached to the IP address of your laptop, tablet or, increasingly, your smartphone.

And Facebook has made a tidy bundle of cash selling that data. Though the company won't disclose the amount, multiple tech sources estimate the world's biggest social media network makes $10 billion annually selling data.

Through your device's IP address, data brokers, trackers and ad networks can not only know all about you, but also where your device is at any given time—almost down to the square foot.

But this treasure trove of data doesn't all come from Facebook.

There is another cadre of companies whose sole mission is to scrape every imaginable piece of your personal information — even some you might not imagine — from online public records and sell it to the highest bidder.

These trackers collect property records, court filings, driver's license and motor vehicle records, census data, birth certificates, marriage licenses, divorce records, state professional and recreational license records, voter registration information, bankruptcy records, and on and on.

They also collect or buy information from commercial sources, snatching up people's purchasing histories, including the dates, dollar amounts, payments used, loyalty cards and coupons used, as well as warranty registration information from retailers and catalog companies.

And, of course, they also exchange or purchase information from one another, then merge the data. Most data brokers have profiles on millions of people, each with thousands of characteristics.

"Some would say those companies know you better than you know yourself," McGinnis said. "And with predictive analytics becoming increasingly sophisticated, they're getting much better at predicting your next move."

The Federal Trade Commission took a hard look at the shadowy world of data brokers seven years ago and released a 110-page report in May 2014. But it stopped short of instituting any sweeping regulations—or even requiring data brokers to reveal what they are collecting about whom and with whom they share it.

It is possible for consumers to opt out of some data collection on some sites, but the process is time-consuming, difficult and needs to be regularly repeated because data brokers keep collecting more. Some brokers pull data from other sites and update automatically. And some data brokers don't remove information even when asked.

People still struggle to understand the nature and scope of the data collected about them. In a recent Pew Research Center study, half of all respondents said they don't know why their data is being gathered and 9% said there's nothing they can do to control it.

"Most have no idea who these companies are and how they got their data on them, and they would be very surprised to know the intimate details that these companies have collected on people," said Amul Kalia, an analyst at the Electronic Frontier Foundation, a global digital rights group based in San Francisco.

The big four

The biggest data gatherers in the game — Amazon, Apple, Facebook and Google—are not in the shadows at all.

The reach of those four behemoths is dizzying. And to expand their reach, the companies have made a multitude of acquisitions.

Collectively, they own websites, operating systems, devices, cloud storage systems and more that gather truckloads of data about you every day.

Google has made more than one acquisition a month for the last decade. In 2014 alone, it purchased a staggering 34 companies. Its acquisitions include YouTube and DoubleClick, companies that expand its reach far beyond its ubiquitous search engine.

Google likely knows everything you've ever searched for on the internet, all the apps you use or have ever used, the YouTube videos you've watched dating back to 2008, many of the events you attended and when, every image you've ever searched for and saved, every location you've ever searched and clicked on, and every news article you've searched for and read. It also has a five-year history of the photos many people have taken with their cell phones.

And all that information is being constantly monitored, stored and backed up in massive data centers.

It's not clear how all the data is used — even among data collectors and buyers. Some in the tech sector say the companies collecting the data don't yet have a use for all the information, but are saving it in perpetuity assuming that technological advances such as artificial intelligence, machine learning and predictive analytics will someday give even the tiniest piece of information value.

The data Google has on most individuals can fill millions of virtual dump trucks. A data collection file on a single person can easily be 5.5 gigabytes, which is 3 million Word documents.

Facebook, meanwhile, collects data on and stores your login location, time and the device used; data on where you are and where you've been; what apps you've installed (plus when you use them and what for); all the devices you've ever used to log in to your account; all the apps you've ever connected to your Facebook account; and every (audio and digital) message, file, emoji and sticker you've sent or been sent.

Facebook also collects and stores all the contacts in your phone, what it thinks you are interested in based on the things you have liked and — maybe most eerie — what you and your friends talk about.

The social network monitors and stores information on the games you play; your photos and videos, music, search and browsing history; radio listening habits; and your emails, call history and files you download.

The company also can access your webcam and microphone.

Facebook data on a single person who uses a computer and social media a moderate amount can exceed 600 megabytes, which is 400,000 Word documents.

Many marketing tech companies — a number of which are in Indianapolis — sit on the shoulders of the Facebooks of the world, said Mark Clerkin, vice president of data science for local venture studio High Alpha.

With the vast tech empires controlled by Google, Facebook, Apple and Amazon, chances are that, most of your waking hours, you're using a device, operating system or website owned or operated — in part or in whole — by one of them.

"If you are using a computer or the web, it's difficult to get beyond their reach," McGinnis said.

Listening in

Apple's 2010 acquisition of Siri Inc. took data gathering to a new level, one that has been elevated by a proliferation of smart speakers and televisions that are always listening.

Introduced in 2011, Siri was touted as an efficient and fun way to search for information. Siri (which has been incorporated into iPhones, iPads and other Apple devices) is a keen listener — even when it's not being addressed. The same is true for Amazon Echo and Google Home.

"There's a lot of uncertainty about what the makers of those devices say, and what those devices actually do," McGinnis said. "The makers of the devices say they don't track the information."

DemandJump's Day isn't buying it. "How else are they reaching out to you when you are not searching online for something?" he said.

He's not alone in his skepticism.

"I'm 100% convinced companies are listening to people through devices, including smart speakers and phones," said Chris Rodgers, a search engine optimization expert based in Denver.

"It's becoming increasingly common that companies are taking audio and translating that into data and storing it," said Rodgers, founder and CEO of Colorado SEO Pros. In addition to programming on the devices themselves, he said, many apps can trigger your gadget's listening device.

"Most of this information is in the privacy policy people agree to," Rodgers said. "But do most people read those agreements? No."

There's good reason companies such as Amazon, Apple, Google and Facebook would want to listen. According to Virginia-based media research firm Comscore Inc., 50% of all searches will be done by voice by the end of this year.

"The technology is certainly there to allow detailed listening-in," McGinnis said. "This is not science fiction."

In fact, it would take only seconds, he said, for a smart-speaker maker to pull up audio from a specific hour — even minute — and replay the discussions and other sounds that occurred in your home or office or wherever you have a speaker.

Devices are even talking to one another. TV programmers and advertisers have been quick to enter audio code designed to reach out and message your smart speaker and phone, so they can send you messages or influence searches on your phone or speaker later.

It's not difficult for a company like Apple, Google or a data broker to figure out which devices are owned by the same person. So when you search for a product with your speaker, you could easily get ads for that or a like product the next time you surf the web on your laptop, tablet or phone.

Location technology

Thanks to global positioning systems — or GPS — and other increasingly sophisticated location technology, big tech companies already know where you are at almost any given time — and with surprising precision. Signals are sent back and forth between one of 27 satellites orbiting the Earth 12,000 miles away and the devices you carry.

Now, technology is in development that is expected to use 3-D models to hone in on where you are within a building.

Google and other companies, tech experts said, will have the capability within a year to know when you're sitting in bed watching TV. And 5G, with its antennas everywhere, will supercharge the power.

Although GPS data can be and is used to locate you in an emergency, location data is also a valuable commodity. It tells marketers if you are in their area. It also lets them know what you might be doing and what you might be in the mode to buy.

According to a report published by India-based research firm MarketsandMarkets, the location analytics market is estimated to grow from $8.2 billion in 2016 to $16.3 billion by 2021. And keep growing.

Companies like Google and Apple have their own location systems, using information from satellites, cell towers, wireless data points, and even weather and barometric pressure. Users can turn off their location devices by app or through a master control on their phone or device. But even then, Apple, Google and Facebook can gather location data. That's spelled out in the phone's privacy policy— which most people never read.

Grandmaster Flash poised to school fans on hip-hop history at U Street Music Hall

Grandmaster Flash will reveal his music-making secrets at U Street Music Hall on Saturday.

Grandmaster Flash recently performed in D.C. at the Smithsonian Folklife Festival. (Courtesy Smithsonian Institution)

WTOP's Jason Fraley previews Grandmaster Flash at U Street Music Hall

He was the first hip-hop artist ever inducted into the Rock & Roll Hall of Fame. Now, he's revealing his music-making secrets.

On Saturday, Grandmaster Flash will hit U Street Music Hall to school fans on the history of the very genre he invented in an event titled "Hip-Hop: People, Places & Things."

"It's a 'jam-ucation' — we're jamming, but I'm giving you an education at the same time," Grandmaster Flash told WTOP. "People need to understand how I came up with a way to manually cut and paste one area of a composition of a different genre to another, on time [and] to the beat, continuously. How did I do it? I have to explain it."

Flash will DJ while an LED screen shows a live feed of his hands on the turntables.

"What my team decided to do was put together a visual presentation while I'm DJing," Flash said. "For example, [the presentation shows] how I created the quick-mix theory and the art of how I manipulate the disc back and forth.

I've tried for decades to explain how important that is to extend the beat so the rappers have a backing track to speak on. … I have cameras on the turntables so you can physically see how I invented this in the '70s."

The video wall also includes footage of important people and places in hip-hop.

"There's also places on the visual presentation of people's places where we used to live before we became famous," Flash said. "I lived in the projects, so did Jay-Z, so did Biggie.

We show all these places on the screen. … That's pretty much what 'Hip-Hop: People, Places & Things' is. 'Things' is turntables, 'places' was in the Bronx, 'people' is various people. I kinda want to just give a visual presentation along with my audio."

Flash was born in Barbados in 1958, but his family moved to New York City. He grew up in the Bronx surrounded by all types of different music playing in his household.

"I would hear a smorgasbord of different types of music on a daily basis," Flash said. "My older sister Violet might play Motown, my other sister Carmetta might play disco, Mom may play Lena Horne, Dad may play Miles Davis.

… I had to figure out a way to [manually] have all these different genres hold hands. Just like in school when the teacher is crossing the street and says, 'Everybody hold hands!' I did that with music."

His dream of combining all genres became a reality via boom boxes in the park.

"Breakdancers is originally what I created this turntable technique for," Flash said. "I had my crappy sound system in the park, I would put a mic [up] to see if there was anybody who could vocalize to this new style of this continuous drum break.

… I would take a track from any group, let's say Thin Lizzy 'Johnny the Fox.' … I would take a Jackson 5 break or a Sly & The Family Stone break on 'Sing a Simple Song.' The drum break is so incredible, but it's so short, so I had to find a way to cut and paste."

Back then, the "cutting and pasting" had to be done manually with elbow grease.

"Back in the '70s, we had no technology, no computers, no studios, no beat machines, no apps, no nothing," Flash said. "So how would the music track be generated?

We had to get duplicate copies of the record and pick the desired section where the drum solo was, which a lot of time was like 10 seconds, then cut and paste it and extend it for three or four minutes so the rapper would have a beat to speak on."

That meant voracious shopping in record stores to find the perfect drum break.

"When I went shopping for records to find that drum break, we went shopping in the pop section of the record store, or the rock section, or the jazz section, or the blues section, or the funk section, or the R&B section, or the alternative section, or the Caribbean section, or the Latin section, just to find that drum break," Flash said.

Let's just say 'Good Times' by Chic … I would listen to that on the turntables and go, 'Wow, this is great for me to play in the gymnasium or the community center next week!'"

Other times, he'd listen to an entire record only to find nothing usable.

"When we go record shopping, it's a crapshoot, but once you break the plastic, you buy it, like it or not," Flash said. "So we would buy records on guessing. I'd bring the record home and play every cut trying to find that drum solo and it would all be crap, so that would go in the crap crate."

However, this discard pile would later come in handy, providing dummy copies for Flash to secretly conceal his art from rival DJs snooping around his turntables.

"One of the biggest jokes of the streets was we would soak the labels off and put the bull-crap label on the hot break … so when a DJ would come on-the-low to stare at my turntables, they would go buy the crap ones. They would go buy the stiffs," Flash said. "We were too prideful to ask, 'What's that break?'

We'd have to send a spy in because we heard about it in the street or heard it on a mixtape. … It's dastardly, it's disgusting, it's funny, but this is how you kept your secrets. It's how we kept our arsenal private."

Now, all these decades later, the magician is finally ready to reveal his tricks.

"I come form a time where we used to keep things a secret because we were in competition with each other in the Bronx," Flash said. "But we're at an information age where sharing is paramount and extremely important.

… I decided to pull the sheet off it and show people how it's done. … These kids want to know. This thing didn't happen by someone just tripping over a wire. This is math, bars and science."

He said hip-hop is such a dominant genre that fans need to appreciate its roots.

"As one of the elder statesmen and one of the architects of the culture, we need to say, 'This is why this is,"" Flash said. "People need to know why this is the big monster that it is today.

It is arguably the biggest cultural musical phenom on the planet, so why is it? I like to go back to the beginning and say it was a bit of pop, a bit of rock, a bit of jazz, a bit of blues, a bit of funk, a bit of R&B, a bit of disco, a bit of Latin."

Just like when he was a kid listening to his parents' records, he insists it's all genres.

"This is a multi-genre, multi-race situation," Flash said. "Music has no color. … Dope music is dope music! … A funky drum break is a funky drum break."

To this day, his deep knowledge of samples sparks fun debates with his kids.

"There'd be a hot song on the radio and I know it's a sample," Flash said. "They'd say, 'Nah, dad. You're old. That ain't a sample.' And I'm like, 'You sure?'

I would go into my collection and I would play the original sample and they'd go, 'Oh!' There's so much to teach the babies today. That's what 'Hip-Hop: People, Places & Things' is."

Hear my full conversation with Grandmaster Flash below:

WTOP's Jason Fraley chats with Grandmaster Flash (Full Interview)

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Column: A horse named Clever Hans who could solve math problems

There's a growing body of evidence that suggests that animals are smarter than people.

Columns share an author's personal perspective and are often based on facts in the newspaper's reporting.

There's a growing body of evidence that suggests that animals are smarter than people.

Clever Hans was more than just clever. He was a brilliant horse who could solve both simple and very complicated mathematical problems. Really! The best scientists in Germany would surround him as the horse did his mathematical magic. Nope. It was not a trick or magic show. This horse truly was a quantitative genius.

It started simply enough when his owner, William Van Osten, asked him, "What is the sum of 3 plus 2; and the horse carefully tapped his hoof five times. The whole nation was completely mesmerized as Clever Hans went on to solving far more complicated problems.

This amazing horse even began to read detailed instructions on a blackboard and infallibly tapped out the right answers with one hoof every time. There was no question about it. This horse had a brain. The psychologists wondered whether it was even better than a human brain

Finally, a certain Professor Oskar Pfungst, a serious psychologist, found that Clever Hans was not really doing mathematics at all. While so many psychologists were observing him, he was carefully observing them. He was simply observing human behavior. The horse noted subtle, unconscious gestures like nods of the head, the holding of breath, and even the cessation of nodding when the correct count was reached – were accurately read by the horse as cues to stop tapping.

Clever Hans may not have been able to do math, but he certainly knew how to observe and interpret human behavior than humans were at understanding horses or, for that matter, other humans.

Here's another one.

Anybody who lives with a cat can tell you that they have inscrutable minds. Psychology students are familiar with a 1979 study in which cats were placed in a glass-fronted puzzle-box and trained to find their way out by jostling a vertical rod at the front of the box which caused the door to open. Yet, before opening the door, the cats rubbed their heads, and turned in circles, before opening the door.

Scientists pondered whether this magical sequence of motions was necessary before they opened the door.

Later, though, it was discovered that this behavior only occurred when a human being was visible to the cats. Without people around, the cats did nothing but take naps. In the end, the cats were simply coming up with a creative way to greet people.

Consider bees. One study about bees tells the story of two female psychologists who raise honeybees in Northern California. They left their car on a side road, got themselves suited up in protective gear, and walked across the fields to have a look at the hives. For some reason, the bees were in a furious mood that day. The bees attacked in platoons. They settled in them from all sides.

One of the psychologists advised the other to walk very slowly and to the right. The idea was that the bees would give up sooner or later. It turned out to be good advice and they walked and walked until they were bee-free. Then they circled the fields, and went back to the car, and found the bees there, waiting for them.

People aren't always as interesting as animals, but they are also sort of interesting. They say that a human being cannot tell a lie without setting off some kind of smoke alarm. So, does this mean we are a moral specie designed to be truthful to each other?

Come to think of it, animals, even plants, lie to each other all the time. Does this mean that humans have evolved to a point where we can't lie without being detected? Perhaps we would do better to stick to less complicated animals. Have you ever heard the story of a German horse named Clever Hans who could solve complicated math problems?

Frank Mazzaglia can be reached at frankwrote@aolcom.

Legends of Runeterra review

Need to know

What is it? A free-to-play card game based on League of Legends.Expect to pay: FreeDeveloper: Riot GamesPublisher: Riot GamesReviewed on: i7 7700, RTX 2070, 16GB RAMMultiplayer? YesLink: playruneterra.com/

I don't think I can stomach buying another booster pack after playing Legends of Runeterra. It's a necessary part of physical card games where cards often have real-world value, but their prevalence in digital card games is just an excuse to sell the worst kind of lootboxes. It's enough to make anyone cynical. But thanks to a generous reward system that avoids booster packs altogether, Legends of Runeterra is one card game that's easy to love.

You can be forgiven if you roll your eyes at the thought of a free-to-play card game based on League of Legends. The card genre is full of these spin-offs, but Riot Games' take is full of clever innovations and tense duels dictated by your skill rather than how much you spend.

Slinging cards 

I really enjoy the back-and-forth of Runeterra's battles.

With its colorful aesthetic and good-natured charm, it's easy to mistake Legends of Runeterra, which entered open beta last month, for a Hearthstone knock-off. It takes the familiar faces of Riot's enormously popular MOBA and adapts their playstyle and abilities into a game where your primary objective is to build decks and play cards to reduce your opponent's hit points to zero. Though it walks like Hearthstone, Legends of Runeterra talks like a simpler version of Magic: The Gathering. That's to its benefit, as Runeterra avoids cribbing many of Magic's cumbersome rules in favor of faster, more aggressive duels.

For example: there's no summoning sickness. Freshly placed creatures (called followers or champions) can attack immediately after being summoned and aren't tapped out after, letting them still block during your opponent's attack phase. It virtually guarantees that every turn both sides will take losses, making those clever plays where you bait your opponent or save a unit from dying feel extra rewarding.

Like Magic, though, my opponent always gets a chance to respond after I make a move. It's hilarious (and devastating) to cast Deny thinking I'm about to cancel my opponent's fatal spell only to have them cast Deny on my Deny. I really enjoy the back-and-forth of Runeterra's battles.

When interactions between cards get complicated, Runeterra has a clever feature called the Oracle's Eye that shows you what the board will look like after a certain attack phase or spell has resolved. Not having double-check your math or worry that a certain chain of abilities and spells plays will play out a certain way is a godsend.

Some genius twists to combat further distinguish Runeterra from the pack. Most card games, for example, punish me for not spending all your mana in a given turn. In Legends of Runeterra, however, up to three points of my unspent mana are preserved for the next round to be used exclusively on spells. This one change feels as substantial as The Elder Scrolls: Legends having two separate playing boards. Being able to play cards on a turn where it should be impossible to play them because I stored mana earlier is one obvious benefit, but I also like that I'm not as harshly punished by a bad opening hand. It keeps Legends of Runeterra feeling unpredictable and dynamic, instead of one player snowballing due to bad luck.

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(Image credit: Riot Games) Most valuable players 

It's satisfying as hell to trick an enemy into a position that levels up your own champion or destroys theirs.

By far the most unique part of Legends of Runeterra's combat are champions. Each of the initial set of 24 is modelled after a character in League of Legends, adapting their playstyle to fit inside the rules of a card game. Braum, for example, regenerates health and gets to choose which enemy unit blocks him, making him a great tank. Each one also levels up after meeting certain conditions, often gaining more power and new abilities that make them formidable.

Champions are often more powerful than regular followers, but they're far from some kind of game-winning trump card. Knowing when to play them and how to keep them alive is especially rewarding because you just know your opponent is doing everything they can to kill them. With champions in play, Runeterra feels like a true battle of wits, each player trying to outsmart or bait the other. It's satisfying as hell to trick an enemy into a position that levels up your own champion or destroys theirs. 

Champions also add welcome flavor to well-understood deck types. A control deck loaded with spells that stun and force cards back into your opponent's hand becomes far more sinister when paired with Yasuo, who deals damage to stunned or recalled units. If you pull that trick off six times and level him up, he'll start killing stunned units outright. It's terrifying.

Even if you're not a big fan of League of Legends, its charming cast of anarchist nutjobs, stoic samurai, and horrifying specters bring so much life and humor to each battle. I love hearing Jinx laughing maniacally when I use one of her related spells to destroy an enemy unit, or seeing my adorable Lonely Poro transform when I summon another Poro unit. The card art is often so pretty that I frequently sneak a peek using the inspect button during my opponent's turn.

As nice as the art is, the layout of the main menu and deck builder could use a lot of work. Information is poorly laid out and feel, forcing me to navigate to menus just to get information I need when trying to build a deck. It feels like it was developed for mobile, with oversized buttons and interface elements. It's beyond annoying that I have to go to the Store window just to see what crafting resources I have, or that there's not better options for sorting and organizing my collection.

Boosters be gone 

Though its combat is a lot of fun, where Legends of Runeterra sets a new standard is in its economy and rewards. Booster packs are gone entirely—good fuckin' riddance—and replaced with a layering of weekly chests and several free battle passes that constantly dole out crafting materials, cards, and Wildcards, which can be redeemed for any card of a corresponding rarity. Being able to pick which cards I want to add to my collection is refreshing. Though rarer Wildcards come infrequently, I've already built a few decks that feel powerful and highly competitive instead of cobbling together whatever I can. 

It's exciting to play a card game with so few barriers and so little segregation between its players.

Earning the maximum amount of possible rewards each week isn't a brutal grind either. Playing a few hours every day, completing quests and Draft modes, puts me close to capping my rewards, but I could easily play much less and still reap some good loot. Hardcore players might lament running out of things to do if they invest too much time, but I'm happy that a competitive game from a major publisher, for once, isn't trying to take over my life.

Since launch, I've played in Ranked mode almost exclusively. Though I've lost more than I care to admit, I'm motivated to keep playing because fights almost always feel fair—even if their deck is much better than mine. It's one of the less obvious benefits of not being overtly pay-to-win like pretty much any other card game. You can still buy Wildcards, but there's has a weekly cap on them so even hardcore spenders won't outpace us filthy casuals. It's fantastic. Duels feel like a true test of strategy (and a little luck) instead of who is playing the most expensive meta deck.

Even Legends of Runeterra's Draft mode, called Expeditions, is overly generous. Like most Draft modes, in order to play you have to spend either a few dollars, spend a draft token you earn from various rewards, or surrender a large sum of crafting resources. But Runeterra's Draft mode lets you play twice per entry, building a new deck each time and then using whichever run was more successful to determine your rewards. Even if you do terribly, you'll still receive a champion card equal to the value of your admission, but winning all seven games showered me with several very rare cards and more than enough crafting resources that I was immediately able to Draft a second time.

It's exciting to play a card game with so few barriers and so little segregation between its players. And because I don't feel like a filthy, second-class casual for not buying cards, Legends of Runeterra has quickly wormed its way into my daily routine. Though its deck building menus could use a lot of work, Legends of Runeterra is a welcome alternative in a genre where how competitive you are is too often related to how much money you spend.

Sneaky Trick Uses Math Magic to Guess Your Cards

Maths is basically magic. So it's no surprise that a clever use of the Fibonacci numbers — a series of numbers (1, 2, 3, 5, 8, etc.) where each number is the sum of the two preceding numbers — and a super-slick shuffling method can combine for a card trick that makes it impossibly easy to guess the number and suit of the two cards you're holding.

Watch as "mathemagician" Colm Mulcahy explain his Little Fib card trick below. The idea is simple: arrange a deck of cards so that five or six Fibonacci numbers (with suits that you memorised) are on top. Ask them to pick two cards and to tell you the sum of their cards (Aces are one, Kings are 13). Shuffle the cards back in randomly. Select their cards from the deck since you know the two cards that were added together because they were the Fibonacci numbers and each sum is unique to only two specific numbers (or in this case, cards). Genius!

Unrelated: I love watching goofy mathematicians use their prowess in numbers for silly things like card tricks.

Colorado’s new graduation requirements could be a hurdle for Denver Public Schools students

Denver Public Schools still has work to do if students are going to meet the state's new graduation requirements, but the problem isn't as severe as numbers released in December suggested.

The December data showed only 9% of juniors in DPS on track to meet three different district and state requirements.

But Mike Ramirez, Denver's deputy superintendent of schools, said 57% of students currently are poised to clear what he considers the highest barrier to graduating: proving competency in math and English. If students can do that, he said he doesn't anticipate a problem meeting the district-level requirements.

Statewide, this year's juniors will be the first class that has to show they've learned enough English and math to be ready for college or a career before they can get a diploma.

Students have up to 11 options to prove they've learned enough, including getting certain scores on tests like the ACT, passing a college-level class or completing a capstone project. Not all districts will accept all options as proof of competency.

Students who demonstrate competency should be able to get into a freshman-level college class without needing remediation, according to the Colorado Department of Education. That suggests the new requirement could be a problem for some students, because at least one-third of college-bound students in Colorado have tested into remedial classes in recent years.

To graduate in DPS, students also need to complete 24 credits and 16 online lessons about college and career planning. The December numbers showed that only one in 10 students, and one in 25 black students, was on track to complete both of those requirements and to demonstrate competency in math and English.

About 70% of DPS students graduated within four years in the most recent school year.

Ramirez said part of the reason the initial 9% figure looked so low is that district officials didn't have full data on how many students had completed their assigned college and career exploration. The December data had shown only about 17% of students were on track with online lessons, while 60% were on track to earn enough class credits to graduate. Black and Hispanic students were less likely to be on track for all three requirements.

Tamara Acevedo, deputy superintendent of academics, said the central office is working with each high school to support students who may not be on track. Schools are embedding activities into classes that will count toward a student's capstone project, making it easier for some to show competency that way, she said.

Ramirez compared the current situation to halftime at the Super Bowl, saying students still have a year and a half to complete everything they need to do. Some tests that could demonstrate competency aren't given until spring.

"That number's going to continue to go up," he said.

Brandon Pryor, a longtime DPS critic and one of the founders of the Michelle Obama STEAM Academy, a high school that has board approval but hasn't yet opened, said he's worried that predictions that few black DPS students would meet the competency requirements will prove correct. The district needs to do more to provide equitable resources to schools serving mostly students of color, and needs to hire more teachers who come from the same culture as their students, he said.

Even if the district follows through on commitments to do more for students of color, that won't help those who fell behind over the past 12 years, Pryor said.

"They're asking the junior and senior (level) teachers to perform magic tricks to catch these kids up," he said. "They're passing kids through so they hit the world with zero viable skills."