In the previous post, I tried to categorize features that exist in many existing card game systems. Some systems, however, are unique or complex enough to not be simply categorized as such. In this post I try to dig deep into them and explore some of the subtle mathematics of each deck. (featured pic: Glyph)
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One of the most famous alternate card systems, the decktet has a large community following. The deck is asymmetrical, both leading to interesting games while frustrating those who try to look for patterns within the deck.
45 cards, composed of:
- ‘1’ (ace), ’10’ (crown) x 6 suits = 12 cards
- [2..9] x 3 cards with two suits each, chosen from 6 suits = 24 cards. The distributions are asymmetric; 3 combinations (e.g. moon-sun) appear three times; most combinations appear twice; 3 combinations appear once, and 3 combinations do not appear at all.
- [‘pawn’] x 4 and [‘court’] x 4; each of these eight cards are triple-suited, again with arbitrary combinations = 8 cards
- One unsuited card, [‘The Excuse’].
- Cards depict either a personality, place, or event ; arbitrary distribution. There is thematic connection between the suits of a card and what is depicted, though – for example, wyrm suit is usually for dangerous or negative scenarios; water suit is literal. Water/wyrm is [‘The Cave’]. Leaf/Moon is [‘The Forest’].
- Three cards depict both a place and an event.
- Suits are always in a defined order; ‘moon’ always comes before ‘sun’.
- Total sum of all number cards per suit is 44.
- Two-suited decks are cool. Can be improved by splitting them into a primary suit and secondary suit, instead of having the suits always in the same order (moon-sun and sun-moon are different cards)
- Many people praised the asymmetry of the deck, but will try to see if deeper patterns can be put in.
- Thematic relationship between character and the suits of the card, making a more coherent deck.
From the description: This is a card deck & game system with each card having a rank and three suits, but the suits are subsets of each other.
Features 54 cards:
- Six suits: [1..9] in 6 suits (Generosity, Honesty, Kindness, Laughter, Loyalty, and Magic); referred to as [A..F]
- The six suits themselves are grouped in two different ways. [A..C] is classed under supersuit M, while [D..F] is under supersuit N.
- Also, [A,B], [C,D], [E,F] are classed under three other supersuits X, Y, and Z.
- One of the only custom decks that have a very clear way of grouping suits into bigger suits in more than one way.
Card game system specifically designed to be a portable way to emulate existing game systems. 98 cards. Good attention to visual design, and avoids the mishmash of visual elements which plague other attempts at multi-use cards.
From the description:
- [0..14] x 6 suits (hearts, crosses, clovers, toadstools, diamonds, horns), paired into three color-suits (red, blue, green)
- [Red, Green, Blue] color-suits are numbered 0-29.
- A, J, Q, K are marked for use in a standard deck.
- Two full sets of six suits (earth, fire, water, air, magic, alchemy). These suits come 1, 2, or 3 to a card. Unknown distribution.
- Secondary suits are numbered 2-9 plus the additional classes ACE, APPRENTICE, MAGICIAN, and WIZARD (see the dots on top of 11 and 12 in the picture).
- Five story suits (WILD, ITEM, EVENT, CHARACTER, and LOCATION). Each card in the deck has a different image that can be used in creative and storytelling games. The story suit also serves as a “Small number” showing either [1, 2, 3, 4, 5] x #2 copies. (See the triangles)
- The deck also contains 8 wild cards that can be organized by color (making 4 groups of 2) or by layout (making 2 groups of 4).
- Very good visual design.
- Green stripe one the whole left side makes a very nice marker when the cards are fanned out or placed on top of one another like the picture.
- Stripe on left ensures that it looks good when fanned out in hand.
- Secondary suits are visible enough but blend in to the background more when they need to be ignored.
- Good story suit design (small unobtrusive triangle)
- 11-14 instead of JQKA. Efficient, but may lose character.
- Doesn’t the Ace/Apprentice/Magician/Wizard of the secondary suit overlap with J/Q/K?
- Wondering how the secondary suit distribution matches with the Decktet. What if we make the secondary suit use the same icons as the primary suit?
A system designed to create new games or proxy existing ones. Has several components such as chips and tiles in addition to the 54-card deck. Many mathematical properties, though the game system itself looks bland and abstract.
- 9 ranks: [1 x #3, 2 x #2, and 3, 4, 5, 6 x #1].
- Six symbols (suits), repeated 9 times each. (top to bottom). No two symbols appear on the same rank.
- The suits order themselves based on how they look – ONE drop; TWO hammers; THREE circles; FOUR stacked, the circle(?), and SIX feathers in the arrow.
- The suit-rank combination is written on each corner of the card.
- Three background colors (blue, red, and yellow). Blue has [1, 1, 2]; Red has [1, 2, 3]; and yellow has [4, 5, 6].
- 6 border colors
- The back of the card is asymmetrical, and can be tiled together to form game boards.
- Using the image of the suit icon to rank the suits is cool. Can this be done with regular suits? See Pentology.
- Nice usage of back side of the card. See what patterns can be drawn into it as well.
- Non symmetrical expected value of card when grouped by color. I wonder if we can overlap this, like color1 = [1..5], color 2 = [2..6], color 3 = [3…7], color 4 = [4…8] for combat mechanics or something, so that better colors have a higher, but not 100%, chance to beat lower colors.
- Use of border color
One example design of the ‘mash-up’ card deck, wherein different elements are just put together, splitting the card into smaller usable portions. Here, each card shows a playing card, letter, die result, and a number.
- Example of design not to emulate.
Strange and unique set of playing cards. The artwork is a combination of surreal and caricature, and I don’t really get what it’s aiming for especially compared to the rather geometric layout of values. This symbols are a little hard to understand, but has incredible information density.
- Rank from 2-7
- “Power”, which shows shaded regions in a 3×3 square. The number of shaded regions is equal to the rank. each row and column of the 3×3 square represents a specific attribute, such as ‘mind’ or ‘air’. This shows the strengths and/or weaknesses of a card and can presumably be used by lower-ranking cards to overpower higher-ranking ones.
- Six ‘Clans’, or suits. A bit weird-looking, but each symbol represents a certain number of cells shaded in a 3×3 grid. Total number of shaded areas also range from 2-7, similar to the rank. Suits can also be paired up, shown by having the same color; total ‘suit rank’ is also equal to 9 for each of the three supersuits.
- Actually everything about this deck is cool. The design would have been more interesting to apply to a science / alien-y themed deck, especially when looking at the clan markings.
- The 3×3 matrix is a promising ranking/combat system (left/right/center?), but the lack of labeling makes it hard to grok. Can we use this as some kind of design in the border, for battle/lane defense type games?
- 18 ranks [1..18] x 3 suits = 54 cards + 1 joker = 55 cards. Each of the 18 ranks has a unique color [C1… C18].
- Colors can also be paired as light and dark versions, e.g. light yellow and dark yellow. [C1/C2, C3/C4, … C17/C18]
- Suits are directional; they point in a direction (not sure about the distribution). See picture above; suits are arrows, triangles, and planes.
- 55 unique monster cards with quirky drawings.
- 54 monsters are named after food items (e.g. ‘bacon’, ‘green tea’, ‘bean sprout’) in 9 food groups (e.g. ‘American’, ‘Dessert’). Not sure about distribution of 9 food groups in 3 suits.
- Directional suits are interesting.
- Pairing of light and dark versions of a color to make bigger suits is nice, although tis is also done by the Rainbow Deck.
- Full color bleed looks kinda nice
There’s not a lot of information about this deck, as their website is down. Using wayback machines and a few surviving youtube links, I’ve dug up the basic themes of the deck.
The core of the deck is the concept of “progressive position”, or that each of the five (penta, of course) suits is strong against two and weak against two, like a convoluted rock paper scissors mechanism. To aid in the mnemonic, ranking information is encoded in the suits themselves:
The suits are circle, cross, triangle, square, and star, and its ranking is determine by how many strokes it takes to draw: ONE for circle, TWO for an “x”, THREE for a triangle, FOUR for a square, and FIVE for a star (draw it with five lines, not just the outline).
A crowd-designed system to emulate multiple existing systems, similar to Glyph but a much earlier effort. The cards are terribly uninspired and utilitarian, but the mathematics crammed into it is impressive. There is also a ‘deluxe’ version, that includes colored dice and chips to emulate more games.
Decks that the RD can be mapped into, based on description:
- [0..9, J, Q, K] x 12 colorsuits
- Colorsuits can be paired up into icon-suits, with light and dark colors of the same hue pairing up (e.g. red+pink hearts; orange+yellow stars; green+lime clubs; etc) This allows decks to be 26 ranks x 6 suits.
- Each colorsuit is numbered from 0-12, to allow them to be ranked
- Reading the colorsuit number and the rank as a single number allows a sequence of [0..119] to be built
- The deck can be reduced to a double-nine domino set or a pyramidal 12. (See previous post on details)
In addition, the deck has other elements from mashed-up genres like dice and word games. The assignments of these elements seem to be arbitrary, not related to the card’s suit/rank value.
- 12 suits (colour/number) x 2 copies of 1-6 dice values
- 6 suits (icon) x 4 copies of 1-6 dice values
- Letters with values similar to Letter Head
- 6 suits (icon) x 26 letter cards
- n * 26 letter cards + rare letter cards
A Roman-themed deck of cards with standard ranks and suits, but with many other different elements that are in the images, leading to a cramped look.
Structure: 49 ‘regular’ cards (pictured above) + 5 unique special cards (‘Rex’, ‘Dictator’, ‘Consul’, ‘Tribunus Plebis’, ‘Proconsul’). Regular cards can be grouped into a 7×7 grid, showing 7 classes (‘Emperor’, … ‘Slave’; see above) x 7 background colors (three of which are picture above)
- Character, name and symbol (“class”)
- Each regular card has a number from -24 to +24. No identified patterns in sums; this could have easily been arranged as a magic square. See image below.
- Background color (beige, red, blue, yellow, green, white, black). Special cards are striped.
- Roman numeral from 1-7. Shifted around so that for regular cards, each color and each class has I – VII exactly once.
- “Cosmos Mark”: Shifted around so that for regular cards, color and each class has exactly one ‘Sun’, and one ‘Moon’. All special cards have a unique celestial body as well.
- Score value: Each regular card contains a gold, silver or bronze medal. Red and White colors have all silver, while all other rows have 6 bronze and 1 gold. All columns have 4 bronze, 2 silver, 1 gold. No idea why pattern is this way. Instead of medals, all five special cards have drawings of diamonds (1-5).
- Payment value: Regular cards [‘Emperor’… ‘Slave’] have payment values 7, 3, 4, 5, 2, 1, 1 respectively. Arbitrary.
- Dice pips. All cards have white dice, showing [1..6] in 9 copies each = 54 cards. Only 36 out of the 54 cards have black dice, showing a 2D6 roll. The remainder has one keyword shown in the picture below.
- Suit and number, for regular card games.
Medal color and +- Value for all 49 regular cards
Keywords in place of black dice
54-card deck with 4 suits, but with ranks replaced by letters. Leverages the fact that a suit has 13 ranks, while our alphabet has 13 x 2 = 26 letters. I think the distributions can still be changed, but this deck has some interesting concepts.
- Four suits: Lemons, limes, chilis, animals, in that ranking order.
- Lemons rank 1-13 use [A…M]
- Limes rank 1-13 use [N…Z]
- Chilis use vowels in relative language usage distribution. [‘A’ x 3, ‘E’ x 5, ‘I’, ‘O’ x 2, ‘U’ x 1]. The number of pips on the upper left denote rankings between duplicate cards.
- Animals are all face cards, each with different pip icons. Letters are the most common letters of the english alphabet.
The 13-rank vs 26-letter coincidence is interesting enough that I want to explore this Connection. If I’d put my own distribution though I’d probably change it up a little. Using the Scrabble tile distribution, getting the equivalent distributions to a 52 card deck, and trying to match the distribution. Changes from the Scroker deck are:
- -1 ‘E’, +1 ‘I’ in the vowel suit (though I’ve always felt there were too many I’s in Scrabble, so this may not necessarily be a good choice)
- +1 ‘C’, ‘H’, and -1 ‘M’, ‘P’. The twelve most common letters are ETOAIN SHRDLU, and C is the next most populous letter as opposed to M and P.
Card deck that has four dimensions: Rank, Shape, color, and direction (direction arrow). It’s not very obvious from the picture, but the direction arrow also appears in the small suit indicator on the upper-left side.
Since there are only 50 cards, it won’t be comprehensively exhaustive with its combinations; looking at the picture below, again there doesn’t seem to be any holistic pattern to the arrangement.
- 12 cards of each color, plus two black “wild” cards in the star suit (with directional arrows pointing to all four directions)
- Ranks [1..5] x #2 copies each
- Increasing order is red-blue-yellow and repeat, and the arrows move in a clockwise direction.
A very strange card deck. The website is hard to understand, full of his own made-up terms. It looks like it was written by either a genius, an alien, or someone having a stroke. (See this conversation between a user and the author). Distributions are based on two gaussian bell curves (with a mean of 6, so we can’t even use it to simulate 2D6, which have a mean of 7). There’s probably some nice math hidden underneath there, but if your card logic is obtuse, there’s no point.
- 60 cards: 54 “basic deck faces” and 6 “top card faces”
Top Card Faces:
- one rank “zero”, four rank ‘1’s, and one ‘2’ = 6 cards. Is this supposed to be a mini bell curve?
- Zero is colored black in all four quadrants. Two colored white in all four quadrants. Ones have three quadrants colored black, and one quadrant colored white. Why? I have no idea.
- Basic deck “denominations” (ranks) from [3..9]. Again, gaussian distribution: [3 x #2, 4 x #6, 5 x #12, 6 x #14, 7 * #12, 8 * #6, 9 * #2] = 56 cards
- The rank is colored either white or black.
- Basic deck center ring “The lens” in three colors: red, green and blue. Red = 1 point, green = 2 points; blue = 3 points. Adding the score of the colors makes it equal to the rank. (1 + 2 + 3 = 6). Not sure what determines which colors go in which part of the circle.
- Center ring colors is mirrored in the three dots on the upper left side.
- The “Scope” (upper left triangle) is in three possible colors, showing its deviation from the mean. White is +-0; Purple is +-1; Orange is +-2; Blue or Red is +-3.
- Some cards have ‘Archaic Icons”, as shown on the upper right side.
Here’s the dumb distribution.
Kickstarter project. Suit choices are made in an attempt to ascribe meaning or mechanical relevance to the image.
- 5 suits (infinity, dot, plus, minus, 4dots), with each rank having [1..3] x 3 copies, and one  and  = 11 ranks x 5 suits = 55 cards.
- Each set of [1..3] is split into three different colors, [yellow, blue and red].  and  are all colors.
- Each suit was chosen to represent a certain mechanical action. As per the description:
- Art (+) = Card Gain (draw cards, play more cards, etc)
- Change (-) = Card Loss (destroy card, force discard, etc)
- Favors (4 dots) = Play State Change (global effect that affects everyone, such as change of scoring or hand modifications)
- Great Zont (1 dot) = Immunity to power (ignoring effects of other cards when played)
- Giglets (infinity) = Wild power (copies the ability of cards under or beside it)