Card games are having a immense moment. Marvel Snap is so large 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, 1 of the best games I’ve always played, hooked people and won GOTY awards with its crazy synergies and repeatable runs.
And last year, I got addicted to Solitaire.
During the dark final days of 2024, I was averaging 12 wins per day in Sawayama Solitaire, 1 of the Solitaires created by developer Zachtronics. Sawayama Solitaire is simply a variant of Klondike — the 1 that’s been bundled into all version of Windows since 1990.
Some games of Sawayama Solitaire felt impossible. any were absurdly easy. Most of them were a satisfying detangling of cards that had me immediately pressing that “new game” button erstwhile I got the win.
How was the most basic card game on Earth owning my life like this?
I think it’s due to the fact that we don’t realize 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 7 riffle shuffles to truly randomize a 52-card deck, alongside fellow mathematician Dave Bayer. His investigation on card shuffling has implications for technological fields as far-flung as the survey of glass melting and the creation of magnets.
He doesn’t know how Solitaire works.
“One of the embarrassment of applied probability is that we can not analyse the first 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 respective times over the years, and is presently viewable on YouTube. 1 of his most fresh appearances, in 2024, reiterates that despite all the method advances we’ve made in discipline and mathematics, the complexity of cards is inactive somewhat a black box.
“What’s 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.”
It’s not hard to see the relation 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 all second since the start of the Earth, you couldn’t contact 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 most likely created an arrangement that has never existed before.”
Card math is besides useful for game devs simulating randomness in prototypes — even if they’re not making card-based games.
This randomness is most likely 1 of reasons I can’t halt playing Solitaire. No 2 decks of randomized cards are the same. No 2 rounds of Solitaire are alike.
Sawayama Solitaire, my beloved.Zachtronics
It’s hard for the human head to comprehend the mathematical probabilities at play in card games. However, 1 thing we can realize is why that gameplay can keep us hooked. It’s called the jerk.
In a survey from the Japan Advanced Institute of discipline and Technology, a squad of researchers described the jerk as a “sudden change in acceleration.” It’s mostly utilized to describe physical sensations — your elevator dropping suddenly, a subject park ride jolting you around a corner.
But in games, it’s informational: “the balance between certainty and uncertainty in reaching a goal.”
For example, erstwhile you start a circular of Overwatch you don’t have quite a few information about the another players: what characters they’ve chosen, where they’ll attack from, whether you’re facing a bunch of randos or a coordinated team. 1 second you’re setting up — the next second Pharah is bombarding you with rockets. You have information. And now you request to do something about it.
That’s an example of the jerk. And it’s surely 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 abrupt revelation, the cognition of what you request to do.
“Puzzle games by default require having any kind of an insight, any 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 you’re 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 erstwhile you start to have a bigger image 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 also factors that contribute to games being hooky, like how frequently you’re successful and how hard it is to win. Card games tend to sit in a sweet place on this scale. 1 of the researchers in the JAIST study, prof. 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 survey focused on Chinese card games like large Two, Winner, and Fighting the Landlord. I’m not a scientist, so take my analysis with a grain of salt here, but I can see how Solitaire fits this framework.
It’s incredibly easy to repeat a round, and while you start with any information with the cards face up on the board, you’re constantly getting small hits of more erstwhile you flip the next card or cards from the deck. The moments erstwhile 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 don’t enjoy the thought [that] erstwhile 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 plan my own Solitaire where you had this kind of a gimmick in it or this kind of item in it?”
The consequence is A Solitaire Mystery, Teikari’s collection of 23 Solitaire games that came out on Itch.io this year. A Solitaire Mystery has Teikari’s trademark humor and puzzling sensibility, but besides a feeling of experimentation.
Royal Flush Solitaire from A Solitaire MysteryHempuli
“I noticed that my main interest in making games is kind of to surprise the player,” Teikari told me. “To make any kind of reaction of amazement or amusement or something.”
The Solitaires of Mystery all have a twist to them. In Chaotic Solitaire, all time you decision a card, 2 random cards swap spots. Or Tap Solitaire, where you can start temporary stacks by “tapping” cards like in Magic: The Gathering. 1 of my favourite variants lets you teardrop cards in half. And 52-Card Solitaire… drops all the cards in a pile and you gotta choice them up in order.
This is 1 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 certain that all game you play is possible to be beaten,” Teikari said, causing a ripple of shame to rotation down my spine. “I don’t know how to do that, but erstwhile trying to balance my Solitaire games, it was interesting to announcement that inevitably making a more hard Solitaire does usually mean that I’m besides making it more likely that the player can get stuck in it.”
The 52-Card Solitaire variant is the perfect example of this. It’s a wonderful concept, and a very comic joke. But boy, is it difficult, due to the fact that you can only choice up cards that are not covered by another cards. Like most Solitaires, you can stack cards in descending order — and there are any helpful slots on the side where you can store cards for later. But with 52 factorial ways the deck can fall… well, let’s just say I have yet to beat it.
Conversely, a Solitaire can be besides easy.
“It feels more breathtaking to solve a Solitaire if you know that you might not have solved it,” Teikari said. “There’s presently 1 Solitaire in A Solitaire Mystery that people have reported is always solvable no substance 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.”
He points to Tap Solitaire and Royal Flush Solitaire as 2 of the most successful in the collection. Tap Solitaire is the most like a conventional Solitaire, and the tapping mechanic adds complexity, but it’s besides a tool that the player can usage to their advantage. In Royal Flush Solitaire, the player makes poker hands to add up to a advanced score.
“I think it worked truly nicely and people have commented that they like it rather 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 year’s biggest game is simply a Solitaire. Balatro has sold millions of copies and made millions of dollars. It’s just a single-player card game — but it’s got incredible complexity due to the different ways the cards can interact with each another and decks can be built.
One of the interesting things about Balatro is that while it’s widely described as a poker variant, its gameplay owes more to large Two — 1 of the Chinese card games mentioned in that study.
Image: LocalThunk
Any card game can become a new, even more addictive 1 with just a twist — the possibilities might be infinite, and that’s something we simply don’t know about playing cards.
We don’t know where playing cards came from.
One of the things that makes games a tricky area of survey is that up until very recently, they’ve been physical objects that get quite a few 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 fresh 1 — and future historians are wailing and gnashing their teeth about it, due to the fact that oh my god, an extant 2024 card deck, depicting popular figure Shrek and his companion, the Donkey?? What an crucial 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 emergence 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 1 from the Netherlands in the late 1470s — now on view at the Met Cloisters. The Met says “the cards were barely used, if at all. It is possible that they were conceived as a collector’s curiosity alternatively than a deck for play.”
But another old deck may contain clues toward knowing card evolution. It’s this deck from the Mamluk sultanate in what is now Egypt, on display at the Topkapı Palace Museum in Istanbul. It’s younger than the Dutch deck — it dates from around 1500 — but, as Tor Gjerde points out on this immaculate individual website, these cards mark the advanced card of each suit, akin to Chinese money cards and “some” Persian ganjifa cards.
Andrew Lo’s “The Game of Leaves: An enquiry 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 don’t have anything left of the cards themselves. any 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 possible precursors for our modern playing cards, since money cards developed 4 recognizable suits.
On the another 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 — but any ganjifa decks can have 96 cards and 8 suits. Fancy versions of these cards were popular in the Mughal courts of India during the 1500s, where they would’ve been made of shells or ivory.
Whether or not the ganjifa cards were based on Chinese cards originally, cards came to Europe through the mediate East, alongside specified silly pastimes as “chess” and “algebra.” The Spanish word for playing card, “naipe,” has been traced to the Arabic “na’ib,” 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 customized suits and decks with varied numbers of cards. Germany utilized acorns, leaves, hearts, and hawkbells. The Dutch deck that I referenced earlier is simply a customized hunting-themed deck. The Met describes its suits as “hunting horns, dog collars, hound tethers, and game nooses.” Many Spanish and Italian decks utilized the suits that we might admit present as tarot suits: cups, coins, swords, and what were then called batons. Tarot, of course, was just another game, and the cards wouldn’t get their reputation for divination until the late 1700s.
Playing Card, ca. 1470–80The Cloisters Collection, 1983
What changed, of course, was the French.
French card makers standardized the suits — trèfles, carreaux, cœurs, and piques. They simplified the colors, paring the designs down to red and black. They became 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 4 suits and the 52-card deck have only become more globally ubiquitous. All those popular Chinese card games that were part of the survey on addictiveness — they’re 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 due to the fact that we usage fundamentally 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 acquainted with,” Teikari told me. “[…] They have a amazing number of both mathematical and otherwise kind of utilities. But I would possibly 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 velocity 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’re all utilizing — more or little — the same deck. That’s kind of magic.
One quality shared by most of the card-based video games that I’ve played is that they evoke the physical act of touching cards. You can’t make a digital card game without good card sounds, or good card feel.
“Modern playing card games are so pervasive in almost all culture in the planet that I think there is something peculiar about standard playing cards themselves as a average for emergent game design,” Balatro developer LocalThunk told Rogueliker, in the same interview where they discussed large 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. You’re already connected to the game — due to the fact that you’re connected to the cards.
“When it comes to cards, digital implementations of card games, and video games that usage card games, can manage to recreate any of the tactile feel or the satisfyingness of playing cards that be in real world,” Teikari said. “I’ve seen people comment on A Solitaire Mystery of like, yeah, the sounds that play erstwhile you decision the cards around are satisfying. So they get any 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 quite a few them… yeah, it’s possible! You might be tearing your cards in half and you can truly only do that once, but… it’s possible!
Playing cards are associated with everything from clownery to gambling to magic to childhood play. So, 1 thing we do realize about them… is that their appeal is infinite.
