Pantheon - An Experiment in Designing
Non-Isomorphic Educational Card Games


By
David S. Blyth
for ET 670

The four categories of card games - Bridge, Rummy, Snap, and Solitaire - are generally played with a single shared, closed, isomorphic and symmetric deck (a CIS deck).

CIS decks are popular with educational card game designers because much educational material can be organized into sets (build a rummy), ranks (build a snap) or patterns (build a solitaire).

But the popularity of Magic The Gathering or Pokemon among children leaves some questions. How do you design an educational card game when there's one open, non-isomorphic, and asymmetric deck per player instead of all players sharing a CIS deck? What type of educational material do you teach? And do card games of this nature represent a new category of card game or another set of categories?

Analysis

This analysis is based on Magic the Gathering (commonly called MTG or just Magic ); the first commercialized asymmetric card game.

Magic uses an open deck. That is, the number of different legal cards (in the thousands) is much larger then the size of any legal deck (between 60 and 80, depending on the tournament). By definition, the game manufacturer is the final arbiter as to what is playable, which leads to a constantly changing card set.

Human nature being what it is, the total number of legal cards has constantly increased for the past five years. Nor is there is any sign that the manufacturer is tired of making money by increasing the card set.

Using an open deck causes the following changes in how the game is played.

Magic takes advantage of the fact that decks can be isomorphic without being symmetric. That is, you can create two (or more) sets with the same number of items per set without requiring the sets to have anything to do with each other ("1,2,3" compared to "Apple, Pencil, Elephant").

Each released edition or expansion set includes five isomorphic card sets. WOTC play tests sets against each other in advance to verify that they have similar levels of power and playability. The sets are called `colors' rather than `suits' because they're orthogonal to each other rather than symmetric.

Colors are loosely based on traditional forms of magic – life and death, fire, water, air and earth.

Each edition or expansion set may also include:

The difference between artifacts and multi-colored cards is determined by the polarity of their response to color-driving cards. For example, a card that affects "Green" cards will also affect Green/Red multi-colored cards but is ignored by artifacts. Colorless cards are not `wild' because they can't be used to replace a colored card.

There's no rule requiring players to build isomorphic decks. Instead, decks may be (and almost always are) composed of haphazard combinations of cards. This makes it difficult to characterize played decks.

Perhaps the simplest explanation is to see any deck as a polyhedron, with each side representing the subset of cards belonging to a pure color, artifact, or multi-color. The size of each side would represent the number of cards in that subset (zero is allowed). In this case, the maximum number of sides of the polyhedron (or card subsets in a deck) is computed by the power series:

Or to write this out in long hand, N!/(N-0)!+N!/(N-1)! + N!/(N-2)! + N!/(N-3)!+N!/(N-4!)+N!/(N-5)!+1 where N is the number of colors in the deck.

For example, a three-color Red/Green/White deck with artifacts can be visualized as an 8-sided die, with the size of each face representing the number of cards belonging to that subset.

Any game can be understood as comparing the power, flexibility and availability of individual cards from random slices of both players' polyhedron decks, given the same meta-rule set.

It is possible to create a card game with orthogonal colors which includes a consistent structure inside each color. For example, three suits in Mille Bournes (Driver Ace, Extra Tank, and Puncture Proof, plus their subsidiary cards) are symmetric to each other and orthogonal to the mileage cards. In addition, the mileage cards are consistent with each other even though that organization is not shared with the other suits.1

But Magic colors are not only orthogonal to each other, the internal structure of each color is asymmetric. The colors can be divided into categories - creatures, spells, and land. However, there is no ordering in how cards go into any category for any color – everything depends purely on the whims of WOTC.

The whimsical nature of Magic means that some cards are naturally more useful or powerful than others. Play balance is maintained by making powerful cards difficult to play. Magic does this by creating a dependency between card categories.

Category behaviors depend largely on the quirky behavior of individual cards. It's worth examining a few cards in detail. Card behaviors can be modified by other cards by 5 characteristics (at least) plus 3 scales:

Creatures are the only cards that can include all eight items and will always include the category (creature), a mana cost, power, and toughness. The Kird Ape below shows how this data is crammed into one card.

The difference between a creature's `additional attribute' and any `additional rule' is commonality rather than function. An `additional rule' starts by applying only to one card and becomes an attribute if it spreads among future cards. In this case, the `additional rule' is assigned a one-word attribute and the meta-rules are modified to describe the behavior of that attribute. WOTC may also design new attributes in advance.

Spell cards are used to modify the current game conditions and include only two card characteristics - the cost to play the card and the effect it has on the game. Spells are subdivided by when they can be played.

The Army of Allah card below shows a typical Instant.

Playing instant cards back-to-back (or sometimes even just one) can have a drastic affect on the current game conditions. For example, playing Army of Allah on your opponent's turn will increase the damage you take while playing `Reverse Damage' next converts the damage to health.

The Tetravus card shows a typical artifact creature (it is both an artifact and a creature).

Tetravus is an example of a token generating card -the +1/+1 Power/Toughness counters can be swapped for +1/+1 creatures. Tokens must be killed separately from the card that created them. Thus, a player could pull tokens off Tetravus , deliberately kill Tetravus, somehow recycle the card then pull off more tokens.

Magic resembles Nomic 2 in that each card is a self-contained rule and players are looking for ways to combine rules in order to reach a desired end. The game deviates from Nomic in that the rules cannot be changed midstream by mutual agreement with your opponent(s).

As a game, Magic represents complex relationships in a rapidly changing combat environment. Players are given a lot of control over how rules are applied and player creativity is rewarded. The game complexity causes a steep learning curve but creates a rewarding and highly addictive playing environment.

Educationally, Magic provides a constructivist's dream. Players are literally required to construct a mental model that they believe will thrive in a difficult and unstable environment.

It may be necessary to develop another set of categories rather than assigning non-isomorphic card games to a single category, given the plethora of possible designs.

The customizability of Magic or similar card games does make them difficult to analyze. However, you can develop additional card game categories by examining different ways in which to make card games asymmetric. Customizable card games can be designed by (at least):

There is no shortage of ways by which decks can be unbalanced. However, Magic and Pokemon both show that balanced play is still possible with unbalanced decks, given the proper rule set.

Design

Given the number of school-aged children playing Pokemon, unbalanced card games are probably not too complex for educational purposes (unlike Bridge). So what type of subject can you teach or reinforce with an unbalanced card game?

The first topic that came to mind was law, especially criminal trial law. Consider that:

This idea was rejected primarily because I don't know a thing about law. The ideal topic to teach must fall somewhere in a Csikszentmihalyi flow - easy enough for a game designer to supply and hard enough to make it fun and challenging. This is unfortunate because several other complex and highly ordered fields (such as particle physics) might be good candidates for a Magic.

Network system administration, business competition, and history were also considered. I seriously thought about designing an unbalanced Cold War game because:

These topics were eliminated because the game design seemed too complex, given the time constraints.

I was about to give up and participate in someone else's board game design when Dr. Dodge suggested Greek Mythology. This seemed odd at first but some research convinced me to adopt the idea because:

The game designer decided to develop a prototype game to model Greek myths and call this Pantheon. The drawback is that a full-scale version requires mixing a board game with a card game because Greek quest and relationship myths are tightly integrated. For example:

Full-scale realistic simulations such as God I hate this were not considered in lieu of a board game because:

Due to time constraints and the proposed game size, Pantheon focuses strictly on Analysis and Design. A sample board game is discussed below. However, I focused more on the card game and the connection between the card and board games because:

A typical layout would be a square around-the-board game where the object is for the hero to return home with the quested item. The sample Greek quest game below is based on the myth of Perseus killing Medusa.

The myth states that Persus could not kill Medusa without first finding a mirror, a Zeus-blessed weapon, a magic pouch, a pair of winged sandals, and Hades' Helm of Darkness (note that these are all artifacts). The winner of the game is the first person who returns home with any Gorgon's Head (one Gorgon per player).

The winner of the board game receives a 500$ cash bonus. All players may now choose to buy cards or tokens usable in the card game from the price list. Players choose items in the order in which they finished the board game (the winner spends all their cash first, the first runner-up chooses second, and so on).

All players currently start with identical Pantheon decks and use the items below to destabilize their decks. Thus, the longer the list of buyable items and the cheaper the prices, the easier it is to customize a deck and the more decks tend to separate from each other. Pantheon should include a long list of items to pick.

Items purchased can only be used in the card game once (you must play the board game again in order to re-earn the same extra cards or tokens). However, players are allowed to save cash won from either the card or the board game. This allows trailing players to hoard cash while they suffer through a few more loses then blow it all at once in an effort to catch up.

Card/Token Cost Description
Unique Artifacts Players may purchase only one artifact. These tokens are unique (buying it prevents other players from getting it).

Medusa's Head token $700 Place token on any god or mortal during upkeep. Cards with this token automatically:
  • kill any mortal they block or are blocked by before any other damage is assessed.
  • tap any god they block or are blocked by. Gods tapped in this fashion can only be untapped by Zeus and do not uptap during the untap phase.
Ares' Sword token $500 Mortals or gods with this token can attack without tapping.
Trojan Horse token

$500 Place on mortal and mortal cannot be blocked. May only attack every other turn (hey, Odysseus took his time building it).
Hermes Sandals token $400 Target mortal or god gains flight. Flight should probably be rarer than it is in this game, as this token is in addition to the Hermes Winged Sandals card in the deck.
Unique Cards The cards below go into your hand at the beginning of the card game and do not count towards hand limits. These cards are unique. Limit one card below per player.
+1/+1 Nymph card $400 Costs 3 mana. Banding. Can be tapped once only to tap Zeus, and once one other to tap any other god.

+1/+3 Dionysus card $300 Played free during combat. No gods or mortals take damage the turn Dionysus is played. All players must drink a liquid when Dionysus shows up or take 3 hits of damage. The controller of Dionysus must drink a liquid each turn Dionysus exists or Dionysus is removed from the card game to wander off to the next party. Dionysus may be tapped to cause any mortal to be tapped.
+5/+5 Achilles card $500 Mortal, but doesn't take damage unless Achilles rolls a 1 on a six-sided die. Also immune to Zeus's Thunderbolt unless he rolls a 1. "I already have one foot in the grave".
+1/+3 Charon Card

$300 Tap to retrieve a mortal from the graveyard. 3-use limit until Hades catches him and removes him from the game.

Regular cards There is an unlimited supply of these cards. Players may purchase up to 4 of any one card. These cards are shuffled into the deck at the beginning of the game then removed from the deck at the end of the game.

+3/+4 Argonaut (2) $500 Banding. Must buy 2 Argonauts at a time.

+4/+3 Trojans (2) $500 Rampage 2. Must buy 2 Trojans at a time.

+0/+6 Stone Wall $200 Cannot attack. Costs 2 mana. Immune to Medusa or Medusa's Head. "No. I don't remember what she looked like."
Counters The counters below may be purchased freely and there is an unlimited supply.

+1 power counter $100 Place on creature during upkeep to increase power
+1 toughness counter $100 Place on creature during upkeep to increase toughness

+1/+1 power/toughness $200 Same as above, but simplifies bookkeeping.
2 +1 Javelins $300 Place a Javelin on any creature during upkeep. Remove Javelin from creature to cause 1 point of damage to any target at any time.
1 extra mana point $100 Play any time to gain 1 extra mana
1 life point $300 Gain 1 life any time.

Rampage 1 counter $200 Creature gains Rampage 1.
Rampage 2 counter $300 Creature gains Rampage 2.
Banding counter $300 Creature gains banding (More expensive than buying Argonauts, but lets you control who gets banding).

A large amount of tweaking is anticipated, to say the least.