Since Magic: the Gathering first launched 25 years ago, an enormous number of cards have been designed. There are now nearly 19,000 distinct Magic cards in existence. That’s a cause for celebration. Since life without knowledge is death in disguise, today I wanted to share several interesting scientific facts to highlight the diversity, depth, and history of the game.
Multiple Modern Cards are Worth More Than Their Weight in Gold
At the time of writing, one gram of gold is nearly $40. Since a Magic card weighs approximately 1.78 grams to 1.81 grams, this means that any Magic card over $73 is definitely worth more than its weight in gold. Hence, the following Modern cards, according to the prices of their original printings in the ChannelFireball store, are more valuable than gold:
This is an impressive list, but there are plenty of materials that are more expensive than gold, and there are many Magic cards that fetch a higher price than those above.
Take an Alpha Black Lotus, for example. It’s well-known to be one of the rarest and most expensive Magic cards out there. Although its price heavily depends on its condition, one graded 9.5 was recently sold at an auction for $87,000, which would peg it at about $48,000 per gram.
This means that it’s more valuable than gold, rhodium, platinum, heroin, meth, cocaine, LSD, plutonium, and even tritium. An Alpha Black Lotus is indeed one of the most expensive substances in the world.
But Magic cards still have a long way to go when compared to the rarest baseball cards and rarest stamps. In recent years, a T206 Honus Wagner baseball card was sold for $3.12 million, and a British Guiana 1c magenta stamp was sold for $9.48 million. Compared to those numbers, $87,000 for a Black Lotus is nothing.
But all of this expensive cardboard is still a bargain compared to californium, a radioactive chemical element with a price tag of $27,000,000 per gram. And don’t get me started on antimatter, a potential fuel for interplanetary and interstellar travel, whose production is estimated to cost about $25,000,000,000 per gram.
But hey, at least those materials have important practical uses. If you plan to burn a stack of Black Lotuses as spaceship fuel, you won’t be getting very far. Apart from upsetting Magic fans all around the world.
The Number of Unique 60-card Standard Decks is Far Larger Than the Number of Atoms in the Visible Universe
Before giving a lower bound on the number of unique 60-card Standard decks, let me first provide some numerical context by analyzing a singleton Standard deck. Consider a given deck with 60 unique cards. To figure out how many different games you can play with this deck, a natural question is how many different orderings this deck this deck can be shuffled into.
The answer is that the number of different orderings is equal to 60*59*58*…*2*1. In other words, the factorial of 60, written as 60!. In numerical form, it’s 8,320,987,112,741,390,144,276,341,183,223,364,380,754,172,606,361,245,952,449,277,696,409,600,000,000,000,000, and the way to say this number is 8 sexvigintillion 320 quinvigintillion 987 quattuorvigintillion 112 trevigintillion 741 duovigintillion 390 unvigintillion 144 vigintillion 276 novemdecillion 341 octodecillion 183 septendecillion 223 sexdecillion 364 quindecillion 380 quattuordecillion 754 tredecillion 172 duodecillion 606 undecillion 361 decillion 245 nonillion 952 octillion 449 septillion 277 sextillion 696 quintillion 409 quadrillion 600 trillion. Or just 8 sexvigintillion and change.
In scientific notation, we would write it more succinctly as approximately 8.3 * 10^81. This is similar to the number of atoms in the visible universe, for which some estimates range from 10^78 to 10^82 and other estimates peg it at 10^80. So for your 60-card singleton deck, there is approximately one unique way to shuffle it for every atom in the visible universe.
But that only describes the range of possibilities for one deck, and I was originally wondering how many unique 60-card Standard decks there are. Well, this number of decks is far larger.
With the 1281 cards currently in Standard you can build 1281! / ( 1221! * 60! ) = 8.3 * 10^103 different 60-unique-card singleton decks. I’m not even going to try and write out that number. But since it provides a lower bound for the number of unique 60-card decks in Standard, we can conclude that this number is far larger than the number of atoms in the visible universe.
And since the total number of games you could play in this format between singleton decks alone (obtained by multiplying and squaring the above numbers under assumptions of forced mulligans to one and prescribed play patterns) is in the unfathomable order of 10^371, the take-away is that the number of possibilities in Magic is humongous. Truly humongous. But I think that’s exactly one of the main reasons why many of us love the game so much.
A Stack of All Magic Cards Ever Printed Would Easily Hit the International Space Station
With 25 years of history, a lot of Magic cards have been printed. But how many exactly? Can you take a guess?
For the early years of Magic, print numbers are available. According to Volume 1 of the Official Magic: the Gathering Encyclopedia, Alpha had a print run of 2.6 million cards, and Beta had a print run of 7.3 million cards. For Unlimited, at least 35 million cards were printed. Expansions were introduced around that time as well, and their print runs ramped up, with 62 million cards for The Dark.
Moving to 1995, Wizards stopped disclosing the size of print runs. It’s likely that hundreds of millions of cards were printed per set, but that’s based on educated guesses only. It wasn’t until recently when official sources became available again.
One recent publication stated that over 20 billion cards had been printed from 2008-2016, i.e., over 2.5 billion cards per year on average. That number is in line with the Hasbro Investor Day 2017 presentation, which states that 117 million booster packs were produced in the U.S. in 2016, i.e., 1.8 billion cards in one year, excluding production outside the U.S. and Magic Online redemptions.
Combining all these numbers, we have 20.1 billion cards confirmed as a fact, but given Magic’s 25-year history, it seems likely that there are far more Magic cards in existence. Assuming linear growth and taking the 20 billion figure from 2008-2016 for granted, my best guess is 44 billion Magic cards. That’s nearly six cards for every human being alive right now, and that’s probably still an underestimation.
But no matter how many have been printed, let’s suppose we collected them all and want to lay them out side-by-side, as if we’re drawing a ginormous opening hand. Since the width of a Magic card is about 6.3 cm and the distance around the Earth at the equator is 40,075 km, we “only” need 0.64 billion cards to go around the equator. Given that we have probably have at least 44 billion of them, we would be able to make 68 trips around the world. (Disregarding some practical problems with mountainous regions, oceans, collecting all those cards in the first place, and so on.)
But what if we didn’t want to lay out our cards side-by-side but instead wanted to stack them like a huge, tower-like library? Well, since the thickness of a Magic card is about 0.0305 cm to 0.0316 cm and outer space conventionally starts at an altitude of 100 km, we’d “only” need approximately 0.32 billion cards to reach outer space. This, of course, ignores all the physics-related challenges associated with such a stunt, or the issue that the stack might be toppled by a stray Skywhale, but we would almost surely be able to reach it with Guilds of Ravnica alone. In fact, with a slightly larger stack of 1.29 billion Magic cards, which is still lower than the average number of cards that was printed per year, we would be able to build a library that is 400 km tall, which is the average altitude of the International Space Station.
Sadly, for now, the moon remains out of reach. We’d need over a trillion Magic cards stacked on top of each other to reach the moon, and we’re only about 5% of the way there. But give it a few more successful decades, and we might get there. Maybe that’s what Emrakul is waiting for.