Collectible Card Games and Card Limits

Written by Curt Adams (curtadams@aol.com).

(This post was written for the Jyhad netgroup (r.c.trading-cards.jyhad) but has been also posted to r.g.trading-cards.misc and r.g.design)

The Jyhad group often discusses whether card limits are good for Jyhad, but that has recently expanded into a broader discussion of whether card limits are good for collectible card games (CCGs) in general. My thesis is that designing for no limits is a practical choice that creates a vastly more flexible and solid game. Anybody designing a game with built-in blanket limits is greatly reducing the potential variety in their game, and probably creating a game that will be broken by somebody if the game succeeds.

This discussion focuses on deck construction, and takes a mathematical bent. Deck construction in the most constant element in different CCGs than play, so a discussion of deck construction is appropriate to all such games.

The things I consider good are:

  1. A large number of different tournament-caliber decks (i.e., one so large that in most tournaments everybody will have a different deck)
  2. A huge number of playable decks (i.e., one so large that if everybody in the world built several decks, they couldn't get them all).
  3. Strong flavor to decks - identifiable themes, even in the best.
These are all desirable goals. Even if not fully attainable, obviously coming closer will make for a better CCG.

When one builds a deck in a CCG, one has to consider how many of each card to put in. Each possible combination of cards can be considered a point in a space of all potential Each combination will have a value, defined as the chance of winning in a given play environment. This allows you to define a "deck power function". For each point in the space of all potential decks, the value of the function is its chance of winning.

The best way for us to visualize that kind of thing is to imagine choosing decks from a 2-dimensional plain of choices. The "power function" will be like a 3-d relief map on the plain. Good decks are the ones high up, on the mountains. The shape of the "power function" can be flat or hilly, mountainous or rolling, and these shapes have profound effects on the variety and style of playable decks.

To examine these effects, consider a design decision between 2 different cards. I've simplified to this situation as I can't really show anything more complex with ASCII text. I've put in some graphs of differing situations for the trade-off between the two cards. In all these situations I've graphed more of one card to be "up" and more of the other "down".

The first situation is "increasing returns to scale". Good is up.

       *      *
       *      *
More   **    ** More
Card   ***  *** Card
A      ******** B
This is the situation, for example, with the Magic cards Bad Moon and Crusade: 8 of either beats 4 of each. This is the situation that card limits are needed for. But this is the least interesting situation! The player wants one of two decks - limit maximum of one or limit of the other - and any deviations from the optimum are severly punished. Typically, one of the two is better than the other, so there's only one good deck. (E.g, White weenie generally beats Bad Moon).

The second is "decreasing returns to scale"

           **
         ******
More    ********  More
Card    ********  Card
A      ********** B
For this situation, card limits are obviously completely unecessary. In some ways it's similar to increasing returns - here there is only one optimal deck. However, variation from the optimal deck is tolerated, as decks close to the optimal balance are still pretty good.

In real games, the tradeoffs are not necessarily so simple. More complicated tradeoffs might create situations in a "decreasing returns" design more like this:

           * **   * 
         ******* ** **
More    ***************  More
Card    ***************  Card
A      ***************** B
Here, because of complex interactions, the situation in the middle range isn't so simple. There's more than one "best deck", when compared to nearby competitors, and, typically, variations on successful decks don't involve much penalty. Card limits are clearly unecessary. The best deck must be determined by a comparison of multiple plausible candidates, each of which has nearby playable variants. In addition, the game's depth need not be limited by the playtesting - if the playtesting indicates that the card balances are of the format above, detailed investigation is not necessary. The game tolerates being played much more than it was tested.

If the designer has an "increasing returns" situation, however, they gain no benefit from this. The peaks at the extremes will dominate all the variation in the middle. Card limits are often introduced to "fix" this. If the card limits are very stringent, the designer can trim off the "degenerate" ends and leave the varied and complex middle. However, this is an intensely fragile situation, and the game design is very difficult. The needed limits will typically differ for each card. In addition, if someone figures out a way to combine cards in ways not anticipated by the playtesters - BOOM! - those increasing returns kick in, and you've got a spoiler deck. Basically, the playtesting has to be more complete than the playing, and for a successful CCG that's obviously impossible.

Now if the tradeoff were just 2 cards, picking the best alternative would be a very simple task. What makes CCGs interesting is the the competition is played out in ENORMOUS spaces. Take Jyhad, with a typical deck size of 80 or less and 328 library cards. The space covered by all possible decks is one face of a 328-dimensional analogue to an octahedron, with a volume of about 10^87. This is considerably larger than the number of particles in the observable universe.

In the view of this truly enormous potential space, thorough playtesting is obviously impossible. The "control with card limits idea " - design a game with a built-in potential for abuse, and then clip off the abuses with card limits - clearly cannot work. The designer and playtesters can't test every possible spoiler deck, and every new idea has a reasonable chance of being a spoiler deck.

The compromise most games have done so far is to use categories (colors in Magic, disciplines in Jyhad, etc.) to restrict potential decks to an extremely small subset of the available decks. They continue to accept the increasing returns to scale. Then they playtest and tweak the game to make the main strategies approximately equal.

The result is a game that appears to work at first glance, but doesn't stand up to detailed examination. First, the only decks that really work are those in the playtested regions (the game had to be designed to make others unplayable). Most themes turn out unviable, no matter how clever the player is at design. Second, although relatively small, these spaces are still enormous. Even with a 60-card deck in an 80-card subset, there are nearly 10^40 decks, which is still an enormous number (around the number of atoms in the ocean, I believe). So inevitably, spoiler decks get missed.

Any game which requires limits to work necessarily carries significant flaws. Initially, the game can look really cool. After a while, though, players find their themes are very strongly constrained and the good decks are all from a repetitive set of spoiler decks. Sound familiar?

If you couldn't make a game without card limits - if a limit-free game were not practical to design - then we'd just have to live with them. But we know you can do without limits. There is at least one game (Jyhad) within clear striking distance of the ideal absolute freedom from card limits. The need for card limits is the choice of the designers, not a limit beyond their ability to avoid.

In its ads, WotC promises "infinite variety" from Magic. A slight exageration, but this prospect is the biggest draw for CCGs - the possibility that you can sit down and create a good, interesting deck that has never been made before. For this players must be able to explore an area of the deck space that has never been explored (and hence never playtested) - and still find plenty of good decks, with no spoilers. If the game needs card limits, it cannot be this kind of game. Only games without limits will yield the pleasures we all seek from CCGs.

A designer who wants to really tap the potential variety in CCGs must design a game which is fundamentally sound. He must have a game that withstands exploration in new areas of decks. If designers want to reach the real potential of CCGs, they will have to design a game which doesn't need limits. If players want CCGs that won't break down or get boring with heavy play, they will have to pick games that don't need limits.


For somewhat related commentary, see Dave's article on the theory of card limits in Jyhad.