Standard Playing Cards
I’ve been thinking about cards a lot recently. Really, for a while. I wanted to lay out a little bit of how I’ve started thinking about them, why I think certain design decisions are common, and what constraints they follow from. While I may present some reasoning as a fait accompli or historical fact, in truth all of the logic here can and should be interrogated.
I've been making little packs of mystery cards for myself to play around with.
So let’s set out to make a deck of playing cards. We want this deck to lend itself to multiple possible games, but we’ve none in mind specifically. These games should support anywhere from one to six or maybe more players. They should be fun games offering risk, decision-making, and replayability.
We’ll make the cards of paper because it’s cheap and receptive to printing. To improve the durability, handling qualities, and visual appeal of the paper, we can finish it with sizing, coating, and calendering. If cost were no object, there may be some advantages to plastic instead of paper, for example variable opacity and increased durability.
Because paper is produced and processed in large rectangular sheets,1 it’s simple and efficient to cut smaller rectangular cards from those. (Other shapes, even if they tessellate, will create waste.) We may exclude squares from consideration because having distinct height and width allows us to encode information from rotation.2 The corners of our cards are the most fragile parts, so we can round them in advance to avoid uneven wear.
How big should the cards themselves be? It should be comfortable to manipulate a card or several cards at once. Conventionally this means they are “palm-sized,” which is to say, the smallest (patience) cards are 67 × 42 mm, while the largest (tarot) cards are 120 × 70 mm. Narrower cards are easier to manipulate, but wider (larger) cards are easier to recognize and more dramatic. Additionally, smaller cards are more portable.
In order to handle well, the cards have some thickness, but this also places limitations on the size of the pack. More than one or two hundred cards becomes difficult to shuffle and manipulate. More than a few thousand becomes difficult to transport. There is some trade-off with size here: packs of smaller cards are more easily (or at least more usually) combined.
At the lower end, we need at least as many cards as players. If we want to support games with up to six players, we’ll need at least six cards. The games that can be played with one card each may be unsatisfying (especially once we try to design multiple games), so perhaps we should double this lower bound to twelve. Even a game with two cards each is likely to be short and repetitive; adding more cards improves replayability and increases the length of a game. Longer games allow more opportunities for decisions and can be more skill-testing.
Because one common way to start a game is to “deal out” the deck, many packs have an abundant number3 of cards in them (although notably, not the 52 card French-suited pack). “Abundance” by itself here is not so important, but is rather an indicator of a number with many divisors. Paper sizes may also play a role in selecting the exact size: the 52-card French-suited pack must be printed as a single 8x7 sheet (with two jokers and two filler cards). Minimizing those filler cards increases printing efficiency, but the bounds of printing technology are currently beyond the scope of this essay.
Front faces, uncut sheet of playing cards.
To facilitate hidden information, and therefore risk-taking, all the cards should have a common back. It’s cheapest to leave them blank, but a “busier” pattern can obscure imperfections and markings on the cards themselves, inject character and visual appeal, and offer an opportunity for branding. To avoid the possibility of information “leaking,” the back faces can be rotationally symmetrical, but given the large number of cards in a pack, this is not always a concern.
Back faces, uncut sheet of playing cards.
Finally, we need to encode information on the front of our cards. This is the single factor that will most enable and shape play. The key feature of information is that it allows interactions between cards.
Let’s start with arbitrary information. Maybe one card has my home address on it, another a picture of a baseball player, a third a short poem. What interactions does this allow? If any of these cards are duplicated, we have the most fundamental relation: matching, or whether two cards are the same or different. This gives us games like Concentration, Spot-It, and Go Fish.
That’s a bit messy though, and somewhat limited. We can import a bunch more interactions at once if we encode an existing system of information on the cards. We could consider letters, words, musical notes. But the most common choice here is numbers.
If each card has a unique number on it, we unlock comparison. That is, not “same” or “different” but “greater than” or “less than.” We also gain arithmetic, or, in order of increasing (mental) complexity: addition, subtraction, multiplication, and division.4
While this is true of any old numbers, we can restrict ourselves to ranks, which are generally a sequence of natural numbers, or easily mapped to them. This preserves all the math above, but now given two cards, we can tell if there are other cards between, above, or below them. This means that two cards can be adjacent and allows us to form “runs” of distinct but adjacent cards.
This deck of say, 100 unique ranked cards, it isn’t very exciting. If the interaction between two cards is comparison, then the difference between any two numbers that are still both greater or both less than a third is negligible. Furthermore, if we’re trying to make a run of adjacent cards, the more ranks there are the less likely this is. In general, the fewer ranks there are, the greater the “impact” of each rank.
Instead of shrinking the deck back down to a possibly unwanted size, we can introduce duplicates of each rank, numbering them say 1-50 twice instead of 1-100. This (roughly) makes each card twice as likely to be relevant in a given situation and also re-introduces matching as a possibility.
If fewer ranks is more “impactful” what happens when we have very few ranks (without shrinking the deck size)? Surely a deck of ranks 1-2 fifty times is maximally exciting? But one reason we may find that it is not is that the more copies of each rank are in a deck, the lower the deck’s variance. Given a deck of 33 rock, 33 paper, and 33 scissors, the odds of drawing a specific card are mostly unchanged between the second draw and the first. Compare to a rock-paper-scissors deck of only two copies each, where the odds of drawing the second copy of a card after the first has been drawn are halved (⅙ from ⅓). These dynamic odds improve replayability.
If fewer ranks are more exciting, and fewer copies of each rank preserve variance (which is also more exciting), then we can also reconsider our deck size. For games with small numbers of players or very short play times, it’s common practice to remove some ranks completely and create a smaller, “stripped” deck. A stripped deck is a perfectly acceptable solution if we relax our initial ideas about how many players a supported game should have, or how long a round should last.
Duplicates add a wrinkle to the comparison operator: the possibly of equal ranks. While some games can be played with rank alone and have rules accounting for the possibility of ties, some games want a way to differentiate between two cards of the same rank. Commonly, these features are suits. What’s important about this additional axis of information is that it isn’t (inherently) hierarchical, else we have just recreated ranks by other names. But suits do give us a second axis on which to evaluate matching.
What the suits are is relatively unimportant. We want them to be visually distinct from each other, but beyond that they are commonly colors 5 or icons. How many do we need? A common psychological rule of thumb is that a person can hold “seven plus or minus two” unrelated pieces of information in their working memory. Since whatever system determines the interactions between suits must be dynamic (that is, mutable from game-to-game), I would propose 9 as an upper bound on this number.6 If we want each card to be unique, this also limits the number of copies of each rank.
We could add further axes of interaction if we like, but they will be subject to the same limitations. It isn’t commonly done,7 perhaps because the two operations we care most about are comparison and matching. Adding a third axis doesn’t immediately add anything novel to care about but does add cognitive overhead.
We now have the technology to begin building poker hands and similar combinations: straights, flushes, pairs, three-of-kind, and so on. These are a novel kind of operation built up from matching, comparison, and adjacency, where the cards interact first to form a construct and then the constructs interact, Voltron-like, in a secondary pre-defined ranking.
As we make these combinations, we will once more run into our limits of working memory: a game where you must consider more than nine or so cards in-hand begins to become unwieldy. We also run in to limits of geometry, as it’s desirable to be able to hold all the cards in a hand (of cards) in one hand (manus), with faces obscured from one side but legible from the other. To facilitate this, modern playing cards use corner indices to identify cards from the corners alone. Rotational symmetry keeps players from having to awkwardly (and perhaps, revealingly) “flip” the cards in their hands, and mirroring the information in both corners allows left-handed players the same convenience. (This pattern occurs even in asymmetrical card designs: the information that is most important to know while a card is held in-hand is moved to the “top” corners.)
Corner indices are also useful in games with very large hands, even if they can’t be easily fanned out, as they allow for quick “searching” if only one card is needed. Conversely, these games may often have heuristics like “following suit” or “matching rank,” where this searching is expected.
While we can now quickly identify cards held closely, we also want to be able to identify cards laid out across the play area quickly and accurately. So the central information on a card should be functionally the same, but at a larger visual scale than the corner indices. This is why colors and icons make good suits. Historically, rank is then represented with pips, repeated visual representations of numbers that transcend language and education. The ability to look at a quantity of things and immediately know how many there are is called subitization, but it stops around four items. Slowing down to count more than four items slows down everything else, but it’s made easier by simple grouping into equal chunks (“two groups of four is eight”) or more broadly by maintaining consistent and distinctive patterns of pips between ranks and across suits. This is because humans are maybe as fast at pattern recognition as at subitization.
Once we run out of convenient patterns of pips, we may turn to illustrations, which make use of the same pattern-recognition without being limited by simple and distinctive arrangements. Illustrations don’t lend themselves as well as pips to numbers, but by evoking existing hierarchies can still intuitively represent ranks. Additionally, illustrations can have emotional responses and greater detail, increasing the sense of value of a card as a physical object. This is how we get face cards.8
Since an opponent and I may be sitting opposite each other, symmetrical arrangements of pips and illustrations will once again aid in rapid recognition. However, especially if the card backs are rotationally symmetrical, an asymmetrical front face can also facilitate further rotational encoding of information, as with a “reversed” tarot card in divination.
This detail on the face card gives rise to colloquial names of cards, like “the one-eyed jack” and “the suicide king.” Games may start to assign these functions divorced from their rank or suit. Similarly, we may imagine “suitless” cards, like trumps and jokers, which must be assigned function (or removed), but which nonetheless open up new design space for games. (Trumps still have rank, while jokers have neither rank nor suit.)
If the special functions of these cards proliferate, we may assign them mnemonics explicitly.9 While these are nominally “information” like any other words, instructions do tend to limit the games that can be played with a deck, so we will not consider them further.
So, starting with some broad assumptions and intentions about games, humans, and printing technology, we can effectively re-derive many features of the “standard” deck of playing cards. What’s important here is that each of these postulates can be interrogated. What if we want circular cards? They may not be ideal for holding in hand, but the lack of corners improves durability, and might give us something like Skull. If a group of three friends consistently wants to play a quick game, perhaps using a stripped deck can shorten play time and preserve excitement. If we find our house rules getting out of hand, perhaps it’s time to dedicate a deck of cards to that game by writing reminders and instructions on the cards themselves. What if our “cards” aren’t even material? A digital “card” could have three faces, visible to three different players or at three different times. More than explaining how the current standard designs are perfect for the games they play, I hope that thinking about the “why” in every facet of card design can open up new areas of exploration.
Bibliography
The Playing Card Platform by Nathan Altice, Analog Game Studies, 2014. This scholarly article really made a lot of my work here redundant, and is in many respects more organized.
Cheapass Games in Black and White: A Retrospective by James Ernst, Greater Than Games, 2019. In his commentaries, Ernst repeatedly highlights how new design space is made by questioning fundamentals and how unexamined limitations shape play. Also offers insight into the card production process and what effects follow from it.
The Seven Deadly Sins of TCG Design! by Kohdok, YouTube, 2020-present. This series explores both negative and positive TCG design patterns and examines historical experiments with the form.
As best I can tell, the reasons for this are both historical and industrial.↩︎
Technically, we could rotate any shape: a square could be “corner up,” for example. But the smaller the degree of rotation between positions, the less “stable” it will feel on a surface and the less obvious it will be at a glance.↩︎
An abundant number is less than the sum of its proper divisors. Loosely, it’s a way to pick out numbers with more divisors than their neighbors.↩︎
Multiplication and division can have such high cognitive load that it’s common enough to only use doubling and halving. However this isn’t usually an interaction between two cards, but an ad-hoc modification of a single value.↩︎
There is a case to be made, I think, that the colors of magic can be considered as suits.↩︎
Why do we not limit ranks in the same way? The ranks are all related pieces of information. “Indeed, the deep point of Miller’s work is to suggest strategies, such as placing information within a context, that help extend the reach of memory beyond tiny clumps of data.”—Edward Tutfe, The Cognitive Style of PowerPoint↩︎
“Color” in a classical French-suited deck might feel like a third thing, but it maps so closely to suit that it isn’t functionally independent. The set deck might be a counter-example, which really cares only about matching.↩︎
Face cards do lose convenient access to the arithmetic operations, as the mapping from ranks to numbers needs to be explicitly clarified.↩︎
As in the rest of this post, the reasoning here is not intended to imply cause and effect. For example, there is some evidence that the first playing cards recorded were simple instructions, and that abstract cards developed later.↩︎