Ooh Shiny! The Power of Rarity in Collectible Card Games

One of my favorite types of games is the Trading Card Genre. Few feelings can beat the excitement of opening a new random pack and seeing what is inside. True, most of the cards will probably end up in a dusty box under a bed somewhere, but one card can make it all worth it. Usually that card will be powerful, sometimes shiny, and most important of all, RARE!

Rarity is an incredibly important part of the Trading Card Game experience, both on the consumer and the designer sides, but it is also very misunderstood. Today I am going to take a look at the many different sides of Rarity, including why it exists, how to measure it, and how to design for it.

A Rare Opportunity

The idea of rarity in trading cards goes back over a hundred years, and originated in collectible baseball cards. Some cards were made to be much more difficult to find than others, and therefore much more desirable and valuable on the secondary market. Because of this long history, rarity must have seemed like an obvious element to include in Magic: The Gathering, the first trading card game.

The role of rarity in trading card games is much different than it’s role in regular trading cards, however. Instead of simply being more valuable, these cards were often more powerful in the game than their more common counterparts. This added an additional form of value to these cards, and helped to create a booming secondary market for buying and selling rare trading cards.

Perhaps the biggest role of rarity in TCG’s is to help shape limited play (a form of competition when players are given a small amount of freshly opened cards to build their decks from). When playing a limited format, players have no control over what cards they have to choose from, but they can use rarity to get a reasonable idea of what to expect.

Controlling rarity can also give designers some control over the secondary market for their cards. A card’s price on the secondary market is generally determined by two different factors – the card’s power and desirability, and the card’s rarity. The more desirable and rare a card is, the more expensive it becomes, and by modifying those factors designers can help keep prices in check.

A Pound of Rares

There is no standard for rarity in trading card games – every different game has a different system, and each system can vary wildly. On one side, you have Magic: The Gathering, which only has 4 main rarities – Common, Uncommon, Rare, and Mythic Rare. On the other side, you can have something like Yu-Gi-Oh which has over a dozen different rarities, including Secret Ultra Rare and Ultra Secret Rare, which are legitimately different things.

With all of these different rarities, it can get difficult to know just how valuable some of these cards actually are, especially when trying to compare across different games. Because of this, I have created my own metric to really determine how rare a particular card is – expected packs, or how many different packs of cards you need to open in order to have a 50% chance of opening a particular card.

A Rare Kind of Magic

Let’s start with Magic: The Gathering, as it has a relatively simple rarity system. Every pack has 10 common cards, 3 uncommon cards, and 1 land card. 7 out of 8 packs also have a rare card, while the other 1/8 have a mythic rare instead.

Just looking at those numbers, it may seem that the uncommon cards are about 3 times rarer than the common cards, and the mythic rares are 7 times rarer than the regular rares. While this would be true if there were an equal number of each, in reality each different rarity is pulling from a differently sized pool of cards, which can make the math a little trickier. Instead of just looking at these numbers, I want to create a more objective basis for comparison of how rare a particular card is.

For the rest of this article, I will be using the units of Expected Packs (EPs) to compare how rare a particular card is. An EP number is the number of packs you would have to open in order to have a 50% chance of opening a particular card of a certain rarity. If you are interested in seeing how this number is calculated, continue reading. Otherwise, feel free to skip down to the next section, where I will be presenting my findings for a modern large Magic set.

• Time for some math!

For these calculations I will be using Amonkhet (the most recent Magic: The Gathering set at time of writing) as the basis for my calculations. Amonkhet has 101 common cards, 80 uncommons, 53 rares, and 15 mythic rare cards. Assuming that each card in a pack is truly random aside from rarity (this is not strictly true, but over time it should average out) you can assume that each common that you open has a .99 percent chance of being the particular common that you are looking for (1/101).

That also means that you have a 100/101 chance of a particular common not being the one that you want. If you open a second common card, there is a (100/101) squared chance that neither of them is the card that you are looking for, 3 cards is 100/101 cubed, etc. The more cards you pull, the smaller the chance is that none of them are the particular card you want. Since we are looking for how many packs we have to open to have a 50% chance to open the card we want, let us first find out how many common cards we have to pull to have that same chance that none of them were the one we want.

Every time we open a common card we are raising the exponent of our percentage, and lowering our chances of not having pulled the correct card. Therefore, we just need to find what exponent we need to raise our odds to to get 50%. The fastest way to do this is to use a logarithm, where the base of our logarithm is our odds of not pulling the correct card. If we take Log_(100/101)(0.5), we get 69.7. This means that we have to look at about 70 common cards to have a 50% chance of finding the one you want, which is the same as opening 7 packs. So a common Magic: The Gathering card has an Expected Pack value of 7.

The Results

Magic: The Gathering Large Set

Common:  7 EPs

Uncommon: 18 EPs

Rare: 42 EPs

Mythic Rare: 80 EPs

Magic: The Gathering Small Set

Common: 5 EPs

Uncommon: 14 EPs

Rare: 33 EPs

Mythic Rare: 64 EPs

Yu-Gi-Oh (Maximum Crisis)

Note: In Yu-Gi-Oh a particular card can often be available in multiple different rarities.

Common: 4 EPs

Rare: 14 EPs

Super Rare: 13 EPs

Ultra Rare: 40 EPs

Secret Rare: 62 EPs

Pokemon

Who the heck knows?

I had originally planned to include real numbers for the Pokemon TCG, but I had a very difficult time finding reliable data for that particular game (If anybody knows the pull rates for the recent sets please let me know).

A Rare Stroke of Insight

So, now that we have the numbers, what does it mean? First, we notice that even though Magic: The Gathering always has the same 4 rarities, cards in a large set tend to overall be more rare than those in a small set (although the ratios between rarities stay pretty similar).

The second thing that I learned putting together this table is that Yu-Gi-Oh has made adjustments to their rarity system since I started playing that make it much more reasonable for collectors. There used to be very extreme rarities, such as Ghost Rare, with an EP value of 200! However, in the last year or so they have modified their rarity system to bring their EPs in closer to Magic: The Gathering.

Now that we have this data, how can we use it? At the very least, I believe that this sort of data can be used to set a reasonable ceiling on prices on the secondary market. Suppose you are in the market for a particular Secret Rare card for your Yu-Gi-Oh deck, but it costs $200 dollars on the secondary market. You know that to have a 50% chance of pulling that card if you open 62 packs. It would be more economical to instead buy 3 booster boxes, which would only cost $219 for 72 packs. However, if the price of that same card drops to $100, then purchasing it directly would be the better option.

Knowing a card’s EP can also help you when preparing for a limited format, such as Magic: The Gathering draft. If you are drafting a particular strategy, you can workout how likely you will open a particular card or set of cards that will support your deck, and you can estimate how often you will encounter a particular opposing threat.

Designing for Rarity

As important as understanding rarity is for players, it is even more essential for designers. Crafting a proper system of rarity is essential for creating a good limited-play environment that players keep coming back to. This not only improves your game and extends the life-span of your set, but can lead to higher sales as every new draft is dozens of packs that would likely not have been sold otherwise.

There is a common belief that rarity is directly connected to power – the less common a card is, the better it is. While there may be some truth to this, designing for rarity is about much more than simply putting the good cards in rare.

While rare cards can often be considered the “face” of the set, it is really the commons that determine what a set is about. Common cards are the cards that players are going to see the most, so they have to do most of the heavy lifting in explaining the flavor, story and mechanical themes of the set.

Common cards also play a huge role in introducing a new player to the game. While a more experienced player might hand pick their deck full of powerful and expensive rare cards, most of the cards a new player encounters will be common. Because of this, common cards tend to be simpler to read and understand than other rarities. In Magic: The Gathering this concept is known as “New World Order“, which outlines what kinds of complexity can and cannot be at common, to help make the game more approachable to newer players without overwhelming them with complicated effects and board states.

Finally, common cards provide the foundation for limited play. Most cards in a pack will be common, so they should be the types of cards that work well in a limited environment. That means that they should work well with the other cards in the set without requiring too much support, and in general should be able to stand on their own. They should be able to fit in a variety of different types of decks, but they tend not to determine the structure of the deck.

Rare cards, on the other hand, have much different constraints. Rares can be the kinds of cards that would be problematic in limited play, either because they are too powerful in that type of environment or because they require a significant amount of deck-building support. Rare cards should be exciting to open, and should strongly pull a player’s deck in a certain direction. Rare cards play a much bigger role in Constructed (pre-built) decks than limited ones, and for this reason they can be much more complicated and niche than commons.

Rare, But Well Done

That’s about all that I have for this week! I hope you enjoyed this introduction to rarity in trading card games.  There is a lot more on the topic that I could cover, so if there is anything about rarity that you would like me to cover in the future, let me know in the comments down below. If you enjoyed the article, consider signing up for email updates so that you can be notified every time I write a new post! And please join me next week, when I will be talking an in-depth look at the game design of “Vanilla Yu-Gi-Oh”!