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Card games are having a huge moment. Marvel Snap is so big that everyone who plays it hates it. Pokemon TCG Pocket is introducing thousands of people to the card game, and raking in millions of dollars. Balatro, one of the best games Ive ever played, hooked people and won GOTY awards with its crazy synergies and repeatable runs.And last year, I got addicted to Solitaire.Why me.During the dark final days of 2024, I was averaging 12 wins per day in Sawayama Solitaire, one of the Solitaires created by developer Zachtronics. Sawayama Solitaire is a variant of Klondike the one thats been bundled into every version of Windows since 1990.Some games of Sawayama Solitaire felt impossible. Some were absurdly easy. Most of them were a satisfying detangling of cards that had me immediately pressing that new game button once I got the win.How was the most basic card game on Earth owning my life like this?I think its because we dont understand playing cards.In 1969, as protests raged against the Vietnam War and counterculture made waves across the nation, a magician named Persi Diaconis went to college.Diaconis had been a professional magician since age 14, and was skilled in sleight-of-hand tricks. But it was probability that fascinated him.He went on to take a degree in statistics. He became a world-renowned mathematician. In 1992, he proved that it takes seven riffle shuffles to truly randomize a 52-card deck, alongside fellow mathematician Dave Bayer. His research on card shuffling has implications for scientific fields as far-flung as the study of glass melting and the creation of magnets.He doesnt know how Solitaire works.One of the embarrassment of applied probability is that we can not analyze the original game of solitaire, he wrote in the abstract for an academic talk called The Mathematics of Solitaire, given at the University of Washington in 1999. The talk has been given several times over the years, and is currently viewable on YouTube. One of his most recent appearances, in 2024, reiterates that despite all the technical advances weve made in science and mathematics, the complexity of cards is still somewhat a black box.Whats the chance of winning, how to play well, how do various changes of rules change the answers? Diaconis wrote. Surely you say, the computer can do this. Not at present, not even close.Its not hard to see the relationship between magic and math. Cards contain limitless possibilities. In fact, math tells us there are more combinations of cards in a 52-card deck than there are atoms on Earth.Writing for Quanta Magazine, Erica Klarreich asked mathematician Ron Graham what that means in practice. He told her, If everyone had been shuffling decks of cards every second since the start of the Earth, you couldnt touch 52 factorial, the number of possible arrangements of a 52-card deck. Klarreich goes on: Any time you shuffle a deck to the point of randomness, you have probably created an arrangement that has never existed before.So thats nuts.Card math is also useful for game devs simulating randomness in prototypes even if theyre not making card-based games.This randomness is probably one of reasons I cant stop playing Solitaire. No two decks of randomized cards are the same. No two rounds of Solitaire are alike.Its difficult for the human mind to comprehend the mathematical probabilities at play in card games. However, one thing we can understand is why that gameplay can keep us hooked. Its called the jerk.In a study from the Japan Advanced Institute of Science and Technology, a team of researchers described the jerk as a sudden change in acceleration. Its mostly used to describe physical sensations your elevator dropping suddenly, a theme park ride jolting you around a corner.But in games, its informational: the balance between certainty and uncertainty in reaching a goal.For example, when you start a round of Overwatch, you dont have a lot of information about the other players: what characters theyve chosen, where theyll attack from, whether youre facing a bunch of randos or a coordinated team. One second youre setting up the next second Pharah is bombarding you with rockets. You have information. And now you need to do something about it.Thats an example of the jerk. And its certainly not relegated to action games. We think of puzzle games as slow-paced and methodical. But the moments that keep us hooked are the ones where you have a sudden revelation, the knowledge of what you need to do.Puzzle games by default require having some kind of an insight, some kind of a realization, Arvi Teikari told me in a video interview. Teikari is the developer behind Baba Is You, a fiendishly clever block-pushing puzzler that netted a ton of accolades in 2019. Depending on what kind of a puzzle game youre making, it can be possible to make that realization in a puzzle into kind of an aha moment, or an insightful moment.Almost all card games center around these aha moments that come when you start to have a bigger picture of the deck. They are, in a sense, puzzles. Think the next card being flipped in Texas Hold em, or filling your hand in Balatro and getting the exact card you need.There are other factors that contribute to games being hooky, like how frequently youre successful and how difficult it is to win. Card games tend to sit in a sweet spot on this scale. One of the researchers in the JAIST study, professor Mohd Nor Akmal Khalid, called them typical incomplete information games.Short, repeatable rounds, chances, and strategizing make them among the most entertaining, even addictive, games, he wrote.The JAIST study focused on Chinese card games like Big Two, Winner, and Fighting the Landlord. Im not a scientist, so take my analysis with a grain of salt here, but I can see how Solitaire fits this framework.Its incredibly easy to repeat a round, and while you start with some information with the cards face up on the board, youre constantly getting little hits of more when you flip the next card or cards from the deck. The moments when you get exactly the card you need, setting off a chain reaction of moves to organize your board, feel so good.But that feeling is not easy to manufacture.I dont enjoy the idea [that] when you deal a deck of cards to play a Solitaire, you might get an impossible hand, Teikari said. I played The Zachtronics Solitaire Collection and noticed myself enjoying it and noticed myself getting ideas for, Oh, what if I tried to design my own Solitaire where you had this kind of a gimmick in it or this kind of detail in it?The result is A Solitaire Mystery, Teikaris collection of 23 Solitaire games that came out on Itch.io last year. A Solitaire Mystery has Teikaris trademark humor and puzzling sensibility, but also a feeling of experimentation.I noticed that my main interest in making games is kind of to surprise the player, Teikari told me. To create some kind of reaction of amazement or amusement or something.The Solitaires of Mystery all have a twist to them. In Chaotic Solitaire, every time you move a card, two random cards swap spots. Or Tap Solitaire, where you can start temporary stacks by tapping cards like in Magic: The Gathering. One of my favorite variants lets you tear cards in half. And 52-Card Solitaire drops all the cards in a pile, and you have to pick them up in order.This is one of the Solitaires that demonstrates how challenging the math behind digital Solitaire can be for game developers.Something like Zachtronics Solitaire Collection actually has systems in place to make sure that every game you play is possible to be beaten, Teikari said, causing a ripple of shame to roll down my spine. I dont know how to do that, but when trying to balance my Solitaire games, it was interesting to notice that inevitably, making a more difficult Solitaire does usually mean that Im also making it more likely that the player can get stuck in it.The 52-Card Solitaire variant is the perfect example of this. Its a wonderful concept, and a very funny joke. But boy, is it difficult, because you can only pick up cards that are not covered by other cards. As in most Solitaires, you can stack cards in descending order and there are some helpful slots on the side where you can store cards for later. But with 52-factorial ways the deck can fall well, lets just say I have yet to beat it.Conversely, a Solitaire can be too easy.It feels more exciting to solve a Solitaire if you know that you might not have solved it, Teikari said. Theres currently one Solitaire in A Solitaire Mystery that people have reported is always solvable no matter what. You cannot get truly stuck. It does feel like a bug. Its a working Solitaire, you can get to the end, but it lacks, kind of, that something.He points to Tap Solitaire and Royal Flush Solitaire as two of the most successful in the collection. Tap Solitaire is the most like a traditional Solitaire, and the tapping mechanic adds complexity, but its also a tool that the player can use to their advantage. In Royal Flush Solitaire, the player makes poker hands to add up to a high score.I think it worked really nicely, and people have commented that they like it quite a bunch, Teikari said.And just think about that: Teikari has created 23 distinct Solitaires for his collection. The Zachtronics Solitaire Collection has nine. There are so many kinds of Solitaire.Depending on your definition of Solitaire, this years biggest game is a Solitaire. Balatro has sold millions of copies and made millions of dollars. Its just a single-player card game but its got incredible complexity because of the different ways the cards can interact with each other and decks can be built.One of the interesting things about Balatro is that while its widely described as a poker variant, its gameplay owes more to Big Two one of the Chinese card games mentioned in that study.Any card game can become a new, even more addictive one with just a twist the possibilities might be infinite, and thats something we simply dont know about playing cards.But also.We dont know where playing cards came from.One of the things that makes games a tricky area of study is that up until very recently, theyve been physical objects that get a lot of use. Dice and game boards are sturdier and might last the test of time; cards are not.Think of how grubby your most-used deck of playing cards is. You might not think twice about tossing it for a new one and future historians are wailing and gnashing their teeth about it, because oh my god, an extant 2024 card deck, depicting popular figure Shrek and his companion, the Donkey?? What an important and unique historical object!Often the game pieces that get preserved are ones that are fancier and decorative. Or ones that were owned by notable people, whose random toy might be considered historically significant.In her book Gaming the Stage: Playable Media and the Rise of English Commercial Theater, Gina Bloom writes that playing cards were mentioned in Spanish antigaming regulations as far back as 1332, but the oldest preserved, complete set, where no cards are missing from the deck, is this one from the Netherlands that dates to the late 1470s (and is now on view at the Met Cloisters). The Met says the cards were hardly used, if at all. It is possible that they were conceived as a collectors curiosity rather than a deck for play.But another old deck may contain clues toward understanding card evolution. Its this deck from the Mamluk Sultanate in what is now Egypt, on display at the Topkap Palace Museum in Istanbul. Its younger than the Dutch deck it dates from around 1500 but, as Tor Gjerde points out on this immaculate personal website, these cards mark the high card of each suit, similar to Chinese money cards and some Persian ganjifa cards.Andrew Los The Game of Leaves: An Inquiry into the Origin of Chinese Playing Cards puts 1294 in China as the earliest reliable date that the existence of cards has been recorded, ever, in all of history, but we dont have anything left of the cards themselves. Some researchers point to very old Chinese tile-based games like dominos and mahjong as precursors to cards.And there are lots of different kinds of cards in China. Domino tiles became domino cards. There are chess cards, money-suited cards, and cards with (gasp) numbers.The money cards are the ones that historians point to as potential precursors for our modern playing cards, since money cards developed four recognizable suits.On the other hand, ganjifa cards came from what was then Persia and are recorded as far back as the 14th century. As with most historical playing cards, the number of cards in a deck can vary but some ganjifa decks can have 96 cards and eight suits. Fancy versions of these cards were popular in the Mughal courts of India during the 1500s, where they wouldve been made of shells or ivory.Whether or not the ganjifa cards were based on Chinese cards originally, cards came to Europe through the Middle East, alongside such silly pastimes as chess and algebra. The Spanish word for playing card, naipe, has been traced to the Arabic naib, the viceroy cards in the Mamluk deck.Early European playing cards were not uniform. As cards traveled north from Spain and Italy, European countries developed custom suits and decks with varied numbers of cards. Germany used acorns, leaves, hearts, and hawkbells. The Dutch deck that I referenced earlier is a custom hunting-themed deck. The Met describes its suits as hunting horns, dog collars, hound tethers, and game nooses. Many Spanish and Italian decks used the suits that we might recognize today as tarot suits: cups, coins, swords, and what were then called batons. Tarot, of course, was just another game, and the cards wouldnt get their reputation for divination until the late 1700s.What changed, of course, was the French.French card makers standardized the suits trfles, carreaux, curs, and piques. They simplified the colors, paring the designs down to red and black. This made them much easier to block print and stencil, and so playing card production shifted its centers of power to France. French playing cards took over Europe. And, gradually, the world.For 400-something years, the four suits and the 52-card deck have only become more globally ubiquitous. All those popular Chinese card games that were part of the study on addictiveness theyre played with this deck.That adds a dimension to the question of why playing cards are so compelling. As Gina Bloom wrote in Gaming the Stage, We can know something of what it felt like for early moderns to play or watch others play these games because we use essentially the same gaming materials they did.I feel like it mostly comes down to playing cards being something that almost all people are kind of intimately familiar with, Teikari told me. [] They have a surprising number of both mathematical and otherwise, kind of, utilities. But I would maybe say that that simplicity could be or not simplicity, but the familiarity would be the kind of major thing that might draw people.I grew up playing Spoons and War and Speed and Go Fish and Bullshit and, yes, Solitaire with these cards. Back in the 16th century they were playing Maw, and Romestecq, and Noddy, and Gleek (really.) The universality of playing cards has resulted in a seemingly limitless number of games to play. But were all using more or less the same deck. Thats kind of magic.One quality shared by most of the card-based video games that Ive played is that they evoke the physical act of touching cards. You cant make a digital card game without good card sounds, or good card feel.Modern playing card games are so pervasive in almost every culture in the world that I think there is something special about standard playing cards themselves as a medium for emergent game design, Balatro developer LocalThunk told Rogueliker, in the same interview where they discussed Big Two. People love to hold a set of cards in their hand, organize and arrange them, think about which cards make sense to play and which they might want to hold on to.The intimacy and familiarity is kind of a cheat code. Youre already connected to the game because youre connected to the cards.When it comes to cards, digital implementations of card games, and video games that use card games, can manage to recreate some of the tactile feel or the satisfyingness of playing cards that exist in real world, Teikari said. Ive seen people comment on A Solitaire Mystery of like, Yeah, the sounds that play when you move the cards around are satisfying. So they get some of that kind of enjoyment of moving cards around.One of the things that tickled me most about A Solitaire Mystery is that Teikari indicates whether or not each Solitaire can be played with a physical deck. For a lot of them yeah, its possible! You might be tearing your cards in half and you can really only do that once, but its possible!Playing cards are associated with everything from clownery to gambling to magic to childhood play. So, one thing we do understand about them is that their appeal is infinite.
