{"id":1094988,"date":"2026-01-25T17:32:18","date_gmt":"2026-01-25T17:32:18","guid":{"rendered":"https:\/\/www.polygon.com\/?p=506918"},"modified":"2026-01-25T17:32:18","modified_gmt":"2026-01-25T17:32:18","slug":"no-one-understands-how-playing-cards-work","status":"publish","type":"post","link":"https:\/\/arcader.org\/news\/no-one-understands-how-playing-cards-work\/","title":{"rendered":"No one understands how playing cards work"},"content":{"rendered":"
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<\/figcaption><\/figure>\n

Card games are having a huge moment. Marvel Snap<\/em> is so big that everyone who plays it hates it<\/a>. Pokemon TCG Pocket<\/em> is introducing thousands of people to the card game, and raking in millions of dollars<\/a>. Balatro<\/em>, one of the best games I\u2019ve ever played, hooked people and won GOTY awards<\/a> with its crazy synergies and repeatable runs.<\/p>\n

And last year, I got addicted to Solitaire.<\/p>\n

Why me<\/em>.<\/p>\n

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 \u2014 the one that\u2019s been bundled into every version of Windows since 1990.<\/p>\n

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 \u201cnew game\u201d button once I got the win. <\/p>\n

How<\/em> was the most basic card game on Earth owning my life like this?<\/p>\n

I think it\u2019s because we don\u2019t understand playing cards.<\/p>\n

In 1969, as protests raged against the Vietnam War and counterculture made waves across the nation, a magician named Persi Diaconis went to college.<\/p>\n

Diaconis had been a professional magician since age 14, and was skilled in sleight-of-hand tricks. But it was probability<\/em> that fascinated him.<\/p>\n

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<\/em> 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<\/a>.<\/p>\n

He doesn\u2019t know how Solitaire works.<\/p>\n

\"\"<\/p>\n

\u201cOne of the embarrassment of applied probability is that we can not analyze the original game of solitaire,\u201d he wrote in the abstract for an academic talk called \u201cThe Mathematics of Solitaire\u201d<\/a>, given at the University of Washington in 1999. The talk has been given several times over the years, and is currently viewable on YouTube<\/a>. One of his most recent appearances, in 2024, reiterates that despite all the technical advances we\u2019ve made in science and mathematics, the complexity of cards is still somewhat a black box.<\/p>\n

\u201cWhat\u2019s the chance of winning, how to play well, how do various changes of rules change the answers?\u201d Diaconis wrote<\/a>. \u201cSurely you say, the computer can do this. Not at present, not even close.\u201d<\/p>\n

It\u2019s 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<\/a>. <\/p>\n

Writing for Quanta Magazine, Erica Klarreich asked mathematician Ron Graham<\/a> what that means in practice. He told her, \u201cIf everyone had been shuffling decks of cards every second since the start of the Earth, you couldn\u2019t touch 52 factorial,\u201d the number of possible arrangements of a 52-card deck. Klarreich goes on: \u201cAny time you shuffle a deck to the point of randomness, you have probably created an arrangement that has never existed before.\u201d <\/p>\n

So that\u2019s nuts. <\/p>\n

Card math is also useful for game devs simulating randomness in prototypes \u2014 even if they\u2019re not making card-based games.<\/p>\n

This randomness is probably one of reasons I can\u2019t stop playing Solitaire. No two decks of randomized cards are the same. No two rounds of Solitaire are alike.<\/p>\n

\"A<\/p>\n

It\u2019s difficult for the human mind to comprehend the mathematical probabilities at play in card games. However, one thing we can<\/em> understand is why that gameplay<\/em> can keep us hooked. It\u2019s called the jerk.<\/p>\n

In a study from the Japan Advanced Institute of Science and Technology, a team of researchers described the jerk<\/a> as a \u201csudden change in acceleration.\u201d It\u2019s mostly used to describe physical sensations \u2014 your elevator dropping suddenly, a theme park ride jolting you around a corner. <\/p>\n

But in games, it\u2019s informational: \u201cthe balance between certainty and uncertainty in reaching a goal<\/a>.\u201d<\/p>\n

For example, when you start a round of Overwatch <\/em>you don\u2019t have a lot of information about the other players: what characters they\u2019ve chosen, where they\u2019ll attack from, whether you\u2019re facing a bunch of randos or a coordinated team. One second you\u2019re setting up \u2014 the next second Pharah is bombarding you with rockets. You have information. And now you need to do something about it. <\/p>\n

That\u2019s an example of the jerk. And it\u2019s 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.<\/p>\n

\u201cPuzzle games by default require having some kind of an insight, some kind of a realization,\u201d Arvi Teikari told me in a video interview. Teikari is the developer behind Baba Is You<\/em>, a fiendishly clever block-pushing puzzler that netted a ton of accolades in 2019. \u201cDepending on what kind of a puzzle game you’re making, it can be possible to make that realization in a puzzle into kind of an \u2018aha\u2019 moment, or an insightful moment.\u201d<\/p>\n

Almost all card games center around these \u201caha\u201d 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 \u2019em, or filling your hand in Balatro<\/em> and getting the exact card you need.<\/p>\n

There are other factors that contribute to games being hooky, like how frequently you\u2019re 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 \u201ctypical incomplete information games.\u201d<\/p>\n

\u201cShort, repeatable rounds, chances, and strategizing make them among the most entertaining, even addictive, games,\u201d he wrote.<\/p>\n

The JAIST study focused on Chinese card games like Big Two, Winner, and Fighting the Landlord. I\u2019m not <\/em>a scientist, so take my analysis with a grain of salt here, but I can see how Solitaire fits this framework.<\/p>\n

It\u2019s incredibly easy to repeat a round, and while you start with some information with the cards face up on the board, you\u2019re constantly getting little hits of more<\/em> when you flip the next card or cards from the deck. The moments when you get exactly <\/em>the card you need, setting off a chain reaction of moves to organize your board, feel so good. <\/p>\n

But that feeling is not <\/em>easy to manufacture. <\/p>\n

\u201cI don’t enjoy the idea [that] when you deal a deck of cards to play a Solitaire, you might get an impossible hand,\u201d Teikari said. \u201cI played The Zachtronics Solitaire Collection<\/em> 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?<\/em>\u201d<\/p>\n

The result is A Solitaire Mystery<\/em>, Teikari\u2019s collection of 23 Solitaire games<\/a> that came out on Itch.io this year. A Solitaire Mystery<\/em> has Teikari\u2019s trademark humor and puzzling sensibility, but also a feeling of experimentation<\/em>.<\/p>\n

\"A<\/p>\n

\u201cI noticed that my main interest in making games is kind of to surprise the player,\u201d Teikari told me. \u201cTo create some kind of reaction of amazement or amusement or something.\u201d<\/p>\n

The Solitaires of Mystery<\/em> 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 \u201ctapping\u201d cards like in Magic: The Gathering<\/em>. One of my favorite variants lets you tear cards in half. And 52-Card Solitaire\u2026 drops all the cards in a pile and you have to pick them up in order.<\/p>\n

This is one of the Solitaires that demonstrates how challenging the math behind digital Solitaire can be for game developers.<\/p>\n

\u201cSomething like Zachtronics Solitaire Collection<\/em> actually has systems in place to make sure that every game you play is possible to be beaten,\u201d Teikari said, causing a ripple of shame to roll down my spine. \u201cI don’t 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 I’m also making it more likely that the player can get stuck in it.\u201d<\/p>\n

The 52-Card Solitaire variant is the perfect example of this. It\u2019s 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. Like most Solitaires, you can stack cards in descending order \u2014 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\u2026 well, let\u2019s just say I have yet to beat it.<\/p>\n

Conversely, a Solitaire can be too easy.<\/p>\n

\u201cIt feels more exciting to solve a Solitaire if you know that you might not have solved it,\u201d Teikari said. \u201cThere’s currently one Solitaire in A Solitaire Mystery<\/em> that people have reported is always solvable no matter what. You cannot get truly stuck. It does feel like a bug. It’s a working Solitaire, you can get to the end, but it lacks kind of that something.\u201d<\/p>\n

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 it\u2019s 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.<\/p>\n

\u201cI think it worked really nicely and people have commented that they like it quite a bunch,\u201d Teikari said.<\/p>\n

And just think about that: Teikari has created 23 distinct Solitaires for his collection. The<\/em> Zachtronics Solitaire Collection<\/em> has nine. There are so many kinds of Solitaire.<\/em><\/p>\n

Depending on your definition of Solitaire, this year\u2019s biggest game is a Solitaire. Balatro<\/em> has sold millions of copies<\/a> and made millions of dollars<\/a>. It\u2019s just a single-player card game \u2014 but it\u2019s got incredible complexity because of the different ways the cards can interact with each other and decks can be built.<\/p>\n

One of the interesting things about Balatro<\/em> is that while it\u2019s widely described as a poker variant, its gameplay owes more to Big Two<\/a> \u2014 one of the Chinese card games mentioned in that study.<\/p>\n

\"\"<\/p>\n

Any card game can become a new, even more addictive one with just a twist \u2014 the possibilities might<\/em> be infinite, and that\u2019s something we simply don\u2019t know<\/em> about playing cards.<\/p>\n

But also.<\/p>\n

We don\u2019t know where playing cards came from. <\/p>\n

One of the things that makes games<\/em> a tricky area of study is that up until very recently, they\u2019ve been physical objects that get a lot of use. Dice and game boards are sturdier and might last the test of time\u2026 cards are not.<\/p>\n

Think of how grubby your most-used deck of playing cards is. You might not think twice about tossing it for a new one \u2014 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!<\/p>\n

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. <\/p>\n

In her book Gaming the Stage: Playable Media and the Rise of English Commercial Theater<\/em><\/a>, Gina Bloom writes that playing cards were mentioned in Spanish antigaming regulations as far back as 1332, but the oldest preserved, complete<\/em> set, where no cards are missing from the deck, is this one from the Netherlands<\/a> in the late 1470s \u2014 now on view at the Met Cloisters. The Met says \u201cthe cards were hardly used, if at all. It is possible that they were conceived as a collector\u2019s curiosity rather than a deck for play.\u201d<\/p>\n

But another old deck may contain clues toward understanding card evolution. It\u2019s this deck from the Mamluk sultanate<\/a> in what is now Egypt, on display at the Topkap\u0131 Palace Museum in Istanbul. It\u2019s younger than the Dutch deck \u2014 it dates from around 1500 \u2014 but, as Tor Gjerde points out on this immaculate personal website<\/a>, these cards mark the high card of each suit, similar to Chinese money cards and \u201csome\u201d Persian ganjifa cards.<\/p>\n

Andrew Lo\u2019s \u201cThe Game of Leaves: An Inquiry into the Origin of Chinese Playing Cards<\/a>\u201d puts 1294 in China as the earliest reliable <\/em>date that the existence of cards has been recorded, ever, in all of history, but we don\u2019t 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.<\/p>\n

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<\/em>) numbers.<\/p>\n

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<\/a>.<\/p>\n

On the other hand, ganjifa cards came from what was then Persia and are recorded as far back as the 14th century. Like most historical playing cards, the number of cards in a deck can vary \u2014 but some ganjifa decks can have 96 cards and eight suits<\/a>. Fancy versions of these cards were popular in the Mughal courts of India during the 1500s, where they would\u2019ve been made of shells or ivory.<\/p>\n

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 \u201cchess\u201d and \u201calgebra.\u201d The Spanish word for playing card, \u201cnaipe,\u201d has been traced to the Arabic \u201cna’ib,\u201d the viceroy cards in the Mamluk deck.<\/p>\n

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<\/a>. The Dutch deck that I referenced earlier is a custom hunting-themed deck. The Met describes its suits as \u201chunting horns, dog collars, hound tethers, and game nooses.\u201d 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 wouldn\u2019t get their reputation for divination until the late 1700s<\/a>.<\/p>\n

\"A<\/p>\n

What changed, of course, was the French.<\/p>\n

French card makers standardized the suits \u2014 tr\u00e8fles, carreaux, c\u0153urs, and piques. They simplified the colors, paring the designs down to red and black. They became much easier to block print and stencil<\/a>, and so playing card production shifted its centers of power to France. French playing cards took over Europe. And, gradually, the world.<\/p>\n

For 400-something years, the four suits and the 52-card deck have only become more<\/em> globally ubiquitous. All those popular Chinese card games that were part of the study on addictiveness \u2014 they\u2019re played with this deck.<\/p>\n

That adds a dimension to the question of why<\/em> playing cards are so compelling. As Gina Bloom wrote in Gaming the Stage,<\/em> \u201cWe 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.\u201d<\/p>\n

\u201cI feel like it mostly comes down to playing cards being something that almost all people are kind of intimately familiar with,\u201d Teikari told me. \u201c[…] They have a surprising number of both mathematical and otherwise kind of utilities. But I would maybe say that that simplicity could be \u2014 or not simplicity, but the familiarity would be the kind of major thing that might draw people.\u201d<\/p>\n

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 we\u2019re all using \u2014 more or less \u2014 the same deck. That\u2019s kind of magic. <\/p>\n

One quality shared by most of the card-based video games that I\u2019ve played is that they evoke the physical act of touching cards<\/em>. You can\u2019t make a digital card game without good card sounds<\/em>, or good card feel.<\/p>\n

\u201cModern 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,\u201d Balatro <\/em>developer LocalThunk told Rogueliker<\/a>, in the same interview where they discussed Big Two. \u201cPeople 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.\u201d<\/p>\n

The intimacy and familiarity is kind of a cheat code. You\u2019re already connected to the game \u2014 because you\u2019re connected to the cards. <\/p>\n

\u201cWhen 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,\u201d Teikari said. \u201cI’ve seen people comment on A Solitaire Mystery<\/em> 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.\u201c<\/p>\n

One of the things that tickled me most about A Solitaire Mystery<\/em> is that Teikari indicates whether or not each Solitaire can be played with a physical deck. For a lot of them\u2026 yeah, it\u2019s possible! You might be tearing your cards in half and you can really only do that once, but\u2026 it\u2019s possible! <\/p>\n

Playing cards are associated with everything from clownery to gambling to magic to childhood play. So, one thing we do understand about them\u2026 is that their appeal is infinite.<\/p>\n

Source<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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 I\u2019ve 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 \u2014 the one that\u2019s been bundled into every version of Windows since 1990. Some games of Sawayama Solitaire felt impossible. Some were absurdly easy.…<\/p>\n

Read More…<\/a><\/p>\n","protected":false},"author":1,"featured_media":1094989,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[],"class_list":["post-1094988","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-polygon"],"yoast_head":"\nNo one understands how playing cards work | Arcader News<\/title>\n<meta name=\"description\" content=\"Card games are having a huge moment. Marvel Snap is so big that everyone who plays it hates it. 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