---

---

The Mathematician Who Built a Multiverse

Richard Garfield didn’t just design a game. He designed a new way for games to exist in the world.

Before Magic: The Gathering, tabletop games were objects. You bought a box, you owned the complete experience, you played until you mastered it or got bored. The game was finite, bounded, solved.

After Magic, games could be ecosystems — living systems that expanded indefinitely, generated secondary markets, created communities that fed on novelty and scarcity. The game wasn’t in the box. The game was the relationship between the box and everything around it: the trades, the tournaments, the deck-building sessions, the metagame that evolved faster than any designer could track.

Gygax built the RPG industry. Garfield built the only tabletop phenomenon that rivals it in commercial scale — and he did it by understanding something Gygax never quite grasped: the game that happens between sessions is as important as the game on the table.

---

The Inheritance of Structure

Richard Channing Garfield was born in 1963 in Philadelphia, into a family with innovation in its blood. His great-great-grandfather was James A. Garfield, the twentieth President of the United States. His grand-uncle Samuel Fay invented the paper clip. His father was an architect whose career took the family around the world — Bangladesh, Nepal, elsewhere — exposing young Richard to patterns of structure and design across cultures.

But the formative influence was mathematics.

Garfield earned his bachelor’s degree in computational mathematics from the University of Pennsylvania in 1985, then returned for a Ph.D. in combinatorial mathematics, completed in 1993 under Herbert Wilf. His doctoral thesis examined how large sets of discrete units behave when classified by their remainders after division.

This sounds abstract. It isn’t.

Combinatorics is the mathematics of arrangements — how many ways can you combine elements from a set? How do those combinations interact? What patterns emerge when thousands of discrete units follow simple rules?

A Magic deck is a combinatorial problem. Sixty cards drawn from a pool of thousands. Each card a discrete unit with specific rules. The question isn’t just “what cards should I play?” It’s “how do these cards interact with each other, with my opponent’s possible cards, with the metagame’s current shape?”

Garfield didn’t stumble into game design. He approached it as applied mathematics — and the mathematics scaled.

---

The Constraint That Created an Industry

In 1991, Garfield met Peter Adkison, CEO of a small Seattle company called Wizards of the Coast. Garfield pitched RoboRally, a programming game where players simultaneously chose movement commands for robots, then watched chaos unfold as the commands executed.

Adkison loved the game. He couldn’t afford to make it.

RoboRally required elaborate components — boards with moving elements, complex pieces, significant manufacturing investment. Wizards of the Coast was a startup running on enthusiasm and credit cards. Adkison asked Garfield if he had anything cheaper. Something portable. Something people could play in the long lines at gaming conventions.

Garfield went home and thought about constraints.

He thought about his childhood, trading baseball cards and marbles. He thought about Cosmic Encounter, the 1977 game where each player had asymmetric powers that broke the rules in different ways. He thought about an old prototype called Five Magics he’d built in 1982.

And he thought about what would happen if the game itself were incomplete by design.

---

The Insight

The idea was simple, radical, and unprecedented:

What if you didn’t own the whole game?

Traditional games assumed completeness. When you bought Monopoly, you received every component necessary to play. The possibility space was fixed, known, bounded.

Garfield proposed the opposite. Each player would own a personal subset of a larger card pool. No one would know every card that existed. When you sat down across from an opponent, you couldn’t be certain what they might play — what creatures, what spells, what combinations you’d never seen.

The game wouldn’t just happen on the table. It would happen before you sat down — in the deck-building, the trading, the discovery of new cards, the metagame that emerged from thousands of players exploring the possibility space simultaneously.

This required a new business model. Instead of selling complete games, Wizards would sell randomized booster packs — small packets containing a semi-random assortment of cards. Some cards would be common, printed by the millions. Some would be rare, scarce enough to chase.

The collector’s impulse would fuel the player’s engagement. The player’s engagement would fuel the collector’s impulse. The two drives would reinforce each other indefinitely.

It was a perpetual motion machine for revenue. It was also — and this is why Garfield matters beyond commercial calculation — a genuinely new form of gameplay.

---

Solving the Rich Kid Problem

Garfield understood the danger immediately.

If rare cards were simply more powerful, players with money would dominate players with skill. The game would become a wallet-measuring contest. Competitive integrity would collapse.

He called this “rich kid syndrome,” and he attacked it from multiple angles.

First: common cards had to be genuinely playable. The foundation of any deck needed to work with cards everyone could acquire. Rarity could provide options, flexibility, specialized tools — but not automatic victory.

Second: the color pie. Garfield divided Magic’s mechanics into five philosophical and functional categories — White (order, protection), Blue (intellect, control), Black (power, sacrifice), Red (chaos, speed), Green (nature, growth). Each color had strengths and weaknesses. No single color could answer every threat.

Third, and most radical: the ante system. In early Magic, players wagered a random card from their deck on each game’s outcome. Garfield’s logic was that expensive decks faced higher stakes. The ante system didn’t survive contact with reality — players hated losing cards, legal concerns about gambling emerged. But the problem it tried to solve — competitive integrity in a collectible system — remains central to every game that followed Garfield’s model.

---

The Mechanics

Strip away the business model and examine what Garfield actually built:

The Mana System. Every spell requires resources. Resources come from lands. You can play one land per turn. This single rule creates the entire tempo structure of Magic. Early turns feature small plays; late turns unleash devastating powers. The curve from setup to climax emerges organically from resource constraints.

The Stack. Spells and abilities don’t resolve immediately — they enter a queue where players can respond. I cast a creature. You cast a spell to kill it. I cast a spell to protect it. You cast a spell to counter my protection. The interaction depth approaches chess while remaining accessible to beginners.

Cards as Rule-Breakers. The base rules of Magic are simple. Cards override those rules. A creature with “flying” can only be blocked by other fliers. A spell with “can’t be countered” ignores Blue’s primary defense. Each card is a localized exception to the general system, creating combinatorial explosion as exceptions interact.

The Color Pie as Philosophy. The five colors aren’t just mechanical categories — they’re worldviews. White believes in community and law. Black believes in individual power at any cost. Green believes in natural order. These philosophies create not just balance but meaning. The colors tell stories.

If a standard deck contains sixty cards, the number of possible two-card combinations is 1,770. When the card pool reaches 20,000 unique cards — as Magic has — the combinatorial space becomes effectively infinite. No human could explore every interaction. The metagame becomes necessary simply to navigate the possibilities.

This is Garfield’s combinatorial training made manifest. He built an engine that generates complexity faster than anyone can consume it.

---

The Launch

Magic: The Gathering debuted at Gen Con in August 1993. Wizards of the Coast brought 2.5 million cards, expecting them to last through the fall convention season.

They sold out in six hours.

Players who had never heard of the game an hour earlier returned to buy more packs, then more, then everything remaining. The buzz spread across the convention floor. By the end of the weekend, Magic was the only thing anyone was talking about.

The first print run — ten million cards — sold out within weeks. Within a year, Magic had generated more revenue than the entire rest of the hobby gaming industry combined.

---

The Platform Philosophy

Garfield understood something most game designers miss: the “game” extends far beyond the table.

What happens between sessions — building decks, trading cards, discussing strategies, watching tournaments — isn’t separate from gameplay. It is gameplay, extended across time and community. The metagame is as important as the game.

This insight shaped everything Garfield designed afterward.

Netrunner (1996) pushed asymmetry further than Magic had dared. One player is a Corporation protecting data servers. The other is a Runner hacking in. They don’t just have different cards — they have different rules, different victory conditions, different relationships to information. The Corporation plays cards face-down; the Runner plays cards face-up. The asymmetry is total. The original underperformed commercially. Fantasy Flight’s 2012 reboot became one of the most acclaimed card games of its era — proof that Garfield’s designs sometimes need time for audiences to catch up.

Vampire: The Eternal Struggle (1994) explored multiplayer politics in the collectible card format. Five players sit in a circle. You can only attack the player to your left; you can only be attacked by the player to your right. The “prey and predator” structure creates shifting alliances, temporary truces, inevitable betrayals.

King of Tokyo (2011) proved Garfield could design for the mass market. Giant monsters fighting over Tokyo. Dice chucking. Simple, colorful, family-friendly. It sold millions of copies and introduced Garfield to audiences who’d never heard of Magic.

The range matters. Garfield isn’t a one-trick designer who got lucky with a single system. He’s a theorist whose principles manifest differently depending on the constraints.

---

The Keyforge Experiment

In 2018, Garfield attempted something radical: eliminate deck-building entirely.

Keyforge uses a proprietary algorithm to generate unique decks. Each deck is procedurally created — no two identical decks exist anywhere in the world. You buy a deck, you play that deck, you never modify it. The intent was to recapture the “wild jungle” of early Magic playtesting, when players didn’t have access to every card and had to win with whatever they happened to own.

The execution was rocky. In September 2021, Fantasy Flight announced a hiatus — the deck-generation algorithm had broken and required complete reconstruction. The IP transferred to Ghost Galaxy, which rebuilt the system and relaunched through crowdfunding in 2022.

Keyforge proved that Garfield’s experimental instincts remained sharp even after thirty years. Whether it proved those instincts were commercially viable remains an open question.

---

The Digital Friction

Garfield’s transition to digital platforms has been troubled.

Artifact (2018), developed with Valve, attempted to bring his design philosophy to Steam. A complex three-lane card game with cards that had real monetary value — tradeable on the Steam Marketplace. Players revolted. The $20 entry fee plus card pack costs felt regressive compared to free-to-play competitors. The complexity overwhelmed digital audiences expecting quicker gratification. Review bombs buried the game within weeks.

Garfield defended the model philosophically. He argued that free-to-play games are “Skinnerware” — exploiting psychological manipulation, preying on whales, using loot box mechanics that provide no return value. The argument had merit. The audience didn’t care. Artifact died.

Vanguard Exiles (2025) continues exploring digital-native design. Early Access reviews praise the mechanical depth and criticize the technical polish. The pattern holds: Garfield’s designs are often ahead of their platforms.

---

The Honest Assessment

The old scoring gave Garfield Mastery 11. The new methodology caps at 10 and asks a specific question: does every design show deliberate control?

No. Artifact was a commercial disaster. Keyforge’s algorithm broke and required complete reconstruction. The Star Wars TCG was forgettable. Some middle-period designs — Filthy Rich, BattleBots — are minor works. The range is impressive, but the hit rate isn’t 100%.

More importantly: Garfield’s body of work is substantial but not vast compared to the scale the methodology measures at 10. His catalog is maybe 15–20 original designs over 32 years. That’s deliberate — he’s a theorist who designs when he has something to say, not a prolific factory. But the “vast solo-authored body of work” criterion for Mastery 10 doesn’t quite fit.

At Mastery 9 — “Master craftsman: deep sustained excellence, clear refinement over time, substantial personally-authored work, others study methods” — the fit is precise. Magic alone demonstrates mastery at the highest level. The color pie is one of the most elegant philosophical/mechanical frameworks in gaming history. Netrunner’s asymmetry shows a different kind of mastery. King of Tokyo shows he can design for mass audiences. Keyforge shows experimental ambition even 25 years into his career. Clear design voice — every Garfield game explores emergent complexity from modular rulesets. Others study his methods universally. Hall of Fame.

But the catalog is relatively small, some designs failed commercially or mechanically, and the “vast body of work” requirement for 10 isn’t met. Garfield is a master craftsman who works precisely, not a grandmaster who produces at overwhelming volume and consistency.

Mastery 9. Down from 11. The methodology is honest about the difference between brilliant and prolific. Knizia’s 700 solo-designed games with Swiss-watch precision is what 10 looks like. Garfield designs like a sniper, not a machine gunner. Both are lethal. Only one produces a vast body of work.

---

The Criticisms

Magic’s model has generated legitimate concerns that Garfield’s defenders must acknowledge:

The gambling question. Randomized booster packs tap psychological mechanisms similar to slot machines. Research shows correlation between physical card pack spending and problem gambling. Garfield designed a system that exploits collector psychology. Whether that exploitation is acceptable depends on how you weigh entertainment value against addiction risk.

The pay-to-win problem. Competitive Magic rewards players who can afford more cards. The best tournament decks cost hundreds or thousands of dollars. Skill matters, but access matters too. Garfield’s “rich kid syndrome” solutions mitigated the problem without eliminating it.

The environmental cost. Thirty years of Magic has produced billions of cards. Most cards printed are never played — bulk commons filling landfills. The collectible model generates waste by design.

These criticisms don’t erase Garfield’s achievement. They complicate it. He invented something powerful. Powerful things have consequences.

---

The Scoring Case

---

The Parallel

Gygax and Garfield arrive at identical scores through identical profiles:

Gygax — 39 points (1971): Inv 10 / Arch 10 / Mast 9 / Adj +10
Garfield — 40 points (1993): Inv 10 / Arch 10 / Mast 9 / Adj +11

Both invented a category. Both built architecture that became industry infrastructure. Both were masters who weren’t quite grandmasters — brilliant but imperfect, with failures alongside triumphs. Both triggered every standard adjustment in the system. Garfield’s formal academic teaching earns the field stewardship bonus, giving him the single point that separates them.

Year tiebreaker no longer applies — Garfield now leads by one point. The methodology says: the mathematician built an engine for generating infinite strategic depth, then walked into classrooms to teach others how to build their own.

One point short of the theoretical maximum. The missing point is Mastery 9 instead of 10 — because Garfield designs like a sniper, not a machine gunner, and the methodology values both precision and volume. The sniper is deadly. The body count is smaller.

---

The Hidden Pattern

Richard Garfield sees games as ecosystems, not objects.

The object sits on a shelf. You own it completely. You master it or abandon it. The relationship is finite.

The ecosystem surrounds you. You participate in it. You trade within it, compete within it, evolve with it. Other players shape your experience. The designers keep adding territory. The metagame shifts beneath your feet. The relationship continues as long as you want it to continue.

This is why the collectible model works despite its apparent wastefulness. You’re not buying cards; you’re buying access to a relationship. The next booster pack is the next chapter of an ongoing story. The new expansion is a reason to reconnect with friends who also play. The game is an excuse for human connection, and humans will pay indefinitely for that.

Gygax understood something similar — D&D campaigns are relationships, not products. But Gygax couldn’t build a business model around it. TSR sold rulebooks; once you owned the Player’s Handbook, you didn’t need another one.

Garfield made the ongoing relationship the product itself. You don’t “finish” Magic. You can’t “complete” your collection. The game continues as long as you want the relationship to continue.

The mathematician built an equation that solves for engagement over time. The solution has no upper bound.

---

What Remains

Magic: The Gathering has generated over $10 billion in lifetime revenue. An estimated 50 million people have played. The competitive scene offers million-dollar prize pools. The secondary market treats rare cards as alternative investments. Thirty years after launch, the player base continues to grow.

But Garfield’s influence extends beyond Magic.

Pokemon and Yu-Gi-Oh built on his template. Hearthstone digitized it. Legends of Runeterra refined it. Every game with randomized content drops, every system with evolving metagames, every design that treats incompleteness as a feature rather than a flaw — all inherit from the framework Garfield established in 1993.

The combinatorialist built an engine for generating infinite strategic depth. The engine is still running.

The games keep expanding. The metagames keep evolving. The possibilities keep multiplying.

Total: 40 points. Year: 1993.

---

40 points. 1993. The highest score in the registry.

Somewhere, a mathematician is smiling.