Monday, August 27, 2018

Multiplicative Design

Today I want to dig into a broad design concept called multiplicative design, and look at how we can approach Magic design through that context.

I first heard the phrase "multiplicative design" from a GDC talk. For those who don't know, the Game Developer’s Conference is an annual gathering of game industry professions across many fields, and features an independent games festival, experimental student games, networking opportunities, and perhaps most well-known: the talks. If you’re at all interested in game design (especially digital game design), I highly recommend checking out the hundreds of insightful GDC talks hosted on YouTube. Chances are you’ll find a lot of great lessons from the developers of many of your favorite games.

As an English-speaking conference held in San Francisco, it’s rare that we get to hear from big name studios abroad. It’s exceedingly rare that we get to hear from the notoriously tight-lipped folks at Nintendo. However, in 2017 we were lucky to get a talk from the directors of the then-upcoming (and now smash hit) The Legend of Zelda: Breath of the Wild. The talk is full of great takeaways, but today I’m going to focus on one specific concept brought up by Game Director Hidemaro Fujibayashi: multiplicative design.

Takuhiro Dohta, Hidemaro Fujibayashi, and Satoru Takizawa,
the technical director, creative director, and art director on Breath of the Wild (respectively)
To paraphrase, Fujibayashi describes multiplicative design as an approach to game design that seeks to give players as many options as possible by allowing them to combine game elements in a variety of different ways. To use The Legend of Zelda as an example: a key you use to open a locked door is “additive design”, as those two game elements can only ever interact with one another, and always in the same way. You've only added a single option to the game. Compare this to something like the korok leaf in Breath of the Wild, which creates a big gust of wind that can be used to knock over enemies, fan/extinguish a fire, fill a raft’s sail, launch bombs and other projectiles, etc. The korok leaf multiplies the options available to the player, because of the way it can interact with everything else in the world. This is multiplicative design: creating simple game objects and building gameplay out of the interactions between them.

Now as a Magic player/designer, this might all seem a little familiar to you, and it should. Though we might not call it by the same name as Mr. Fujibayashi, multiplicative design is at the core of what makes Magic the game we know and love. Card games by their very nature necessitate the interaction of many simple game pieces, and Magic design has always focused on maximizing the fun of these interactions. Plus, unlike a digital game, Magic allows us to create and expand new forms of interaction without having to reprogram every element that already exists (though, to be fair, we do still occasionally do that). For example, just think about how many different things you can do with a card as simple as Giant Growth: saving a creature from a removal spell, killing another creature in combat, gaining extra life with a lifelink creature, gaining extra squirrels with a squirrellink creature, dealing 3 points of damage to your opponent with an unblocked attacker, etc. Just like the korok leaf, Giant Growth is simple but can create a wide array of results simply by interacting with other cards.

So how can we as Magic designers optimize the multiplicity of our designs?

Leave the Door Open (Ended)

A simple, straightforward way to increase the multiplicity of your designs is to leave your templating open ended. For instance, in Amonkhet block there were many cards that triggered off of not just cycling (which had been done in the past), but any discarded card. This is an overt attempt to increase the multiplicity of these cards, allowing them to interact and combine with thousands of extra cards throughout Magic's history. You can see the potential in this approach with the rise of BR Hollow One in modern. That deck wouldn't have been possible without making these cards open ended. Revolt is another recent example. It's wording allows it to interact with combat, flicker, sacrifice, bounce, and more. These types of mechanics give you as a designer much more space to play around with support cards, and greatly increase the fun of discovery for your players both inside the set and in casual/constructed play.

As a counter example, cards like Vizier of the Anointed are rigid, additive design: it's a key that only opens one very specific lock. There’s no room for discovery or interaction beyond the one that’s spelled out for you in the card text. Additive design isn’t necessarily bad, but I’d say it makes Magic much less interesting and fun by foregoing the inherent multiplicative nature of the game system. Magic does need cards every now and then that are narrow and explicit like Vizier to help guide newer players to the set’s themes or act as an important reward for draft, but they’re disappointing when viewed alongside alternatives like Anointer Priest or Aven Wind Guide which found ways to play into the same themes without being so restricted. Vizier is necessary sometimes, but cards like that should be the exception more than the rule.

Rough Edges Make Good Handholds

Elegance is something we often strive for in Magic design, but when it comes to multiplicative design it can often be stifling. There's a concept in Magic I like to call "smoothness", which refers to how clean and contained a mechanic is. For example, Kicker is a very "smooth" mechanic. It's simple and straightforward, immediately grokkable from a mechanical and strategic level. However, that very same "smoothness" is what makes Kicker hard to work with. There are basically no ways to reference or interact with kicker without explicitly calling it out. Again, there's nothing wrong with that, but as we spoke about above it diminishes Kicker's multiplicity.

On the other hand, "rough" mechanics can be excellent for multiplicative design. I consider Vehicles (and "Crew") to be "rough": there's a lot of minutia in there around instant speed timing, non-creatures becoming creatures temporarily, the potential for over-crewing or crewing multiple times, etc. But Vehicles are an excellent example of a "rough" mechanic that has a lot of avenues for interaction: artifacts matter, high power creatures, small creature armies, "becomes tapped" triggers, plus all the stuff in the game that interacts with creatures by default (i.e. most of it). These many different avenues of approach creates a huge possibility space to play and design in.

For another recent example, take a look at Treasure from Ixalan block. While it looks pretty simple on the surface, the designers found ways to use almost every part of it. We've got cards that care about: having treasure, when you sacrifice treasure, artifacts generally, etc. We have extra sacrifice outlets for your treasure, and even the entire Ascend mechanic plays into treasure giving you extra permanents. All of this adds into the natural use of treasure (both ramping and fixing your mana) to create far more access points than might appear at first glance.

It's important to remember that if you're making a set with this kind of mechanic, you need to actually include these interactive elements in order to showcase the possibilities. Your players can't make fun discoveries if you haven't hidden the Easter eggs yet. For example, Landfall isn't a very multiplicative mechanic on it's surface, but it becomes a lot more interesting when the format is full of ways to play multiple lands a turn, or drop them at instant speed. Treasure would have been a lot less interesting if all of the treasure-interaction cards had been cut.

Turn Lines Into Webs

Finally, let's talk about linear mechanics. For anyone unaware, "linear" is a term we use to describe mechanics that work better or require other specific cards to function properly, most often with cards of the same type or with the same mechanic. Linear mechanics include some fan favorites, like tribal, but can end up feeling too restrictive if executed poorly. You might expect that linear mechanics don't lend themselves well to multiplicative design. After all, doesn't making cards that specifically work better with one another and worse alone directly conflict with the whole point? While we do often see linear mechanics fall prey to this, the past few years have been great to us in showing how to avoid this pitfall.

The prime example of creating linear mechanics that are also multiplicitive is Unstable. All three of Unstable's mechanics (dice rolling, contraptions, and host/augment) are linear to varying degrees, but they're also all incredibly multiplicative. Dice rolling, the least linear of the three, has a variety of different support effects (re-rolling dice, modifying results, rolling extra dice, caring about high numbers) split between different colors (blue, black, red, and green respectively) which creates tons of different combinations between them using the same basic mechanic. Contraptions are a bit more focused (in blue and red), but are designed to play off of one another and can be assembled in a myriad of ways. Host/Augment, the most linear of the three mechanics, also happens to be the most multiplicative. Not only does the mechanic literally offer you thousands of potential card combinations, but each augment offers you another trigger which you can build and play around. In black border world, we also have Energy. Similar to Host/Augment, Energy offers a variety of different generators and outlets (oftentimes on the same card) which allow players to discover their own combinations and explore the world of possibilities.

It seems to me there are two keys to good multiplicative design for linear mechanics: volume and diversity of interactions. Volume (as in, the amount of space a mechanic takes up in a set) is important to allow players enough room to explore. All of the mentioned mechanics are featured in 4 or 5 colors, which means color combinations alone will guide players towards different possibilities. Without volume, both limited and constructed players simply won't have enough game elements to perform any meaningful multiplicative gameplay. Diversity of interactions is important to ensure that your cards don't end up additive. It doesn't matter how many cards you make if they all interact with eachother identically (like if every single sliver gave +1/+1). If your linear cards will only ever multiply among themselves, it's up to you as the designer to ensure those multiplications are as varied and awesome as possible. You need to weave a web of connections between your cards, not just have them stack on top of one another.

I think a lack of linear multiplicity is what led to many enfranchised player's disappointment with Ixalan tribal component. Unlike Lorwyn, a tribal block that used changelings and crossover cards to create multiplicity between tribes, Ixalan forwent any crossovers in favor of four purely linear tribes. However, none of these tribes had enough multiplicity to create engaging gameplay. The two smaller tribes, Merfolk and Vampires, lacked the volume to offer up interesting choices. The larger tribes, Pirates and Dinosaurs, had volume and diversity of effects, but not diversity of interactions. For instance, RW Aggro Dinosaurs and GW Ramp Dinosaurs are two different dinosaur decks, but you can't really mix components from the two together in a cohesive way. So instead of creating multiplicity inside of a linear tribe, it felt more like different linear decks that shared the same creature type. (For what it's worth, I think Rivals of Ixalan improved on this quite a bit).

The Product

To recap:

  • Multiplicative design is an important part of Magic, and it's something we should work to maximize
  • Look for ways to leave mechanics open ended, allowing for a broadest range of interactions possible
  • Utilize the rough edges of a mechanic to maximize its avenues of approach, and make sure to give your players tools to use those avenues
  • For linear mechanics, make sure the mechanic has a high enough volume to allow for multiplicative gameplay, and make their interactions diverse

I think many of us naturally try to utilize multiplicative design without actively thinking about it, but it's always good to dig deep into a fundamental of design and increase your awareness. While too much multiplicative design risks overloading your sets with complexity or overwhelming players with options, it's still an essential part of what makes Magic great.


  1. That was a good read, thanks Chris :) I think most of us on an unconscious level already try to make our designs multiplicative, but not consciously. This is definitely something I am going to try to be more conscious about going forward.

    How do you feel about the relation between multiplicative design and lenticular design?

  2. This is great, Chris.

    Looking further through this lens, I see subtractive/divisive design, largely in the form of cards/mechanics that invalidate others. When hate cards are too strong/efficient, they hurt entire decks, and decrease the diversity and possibility space of the metagame.

  3. Fantastic article! I especially like the point on 'rough edges'. I definitely have a tendency to oversimplify mechanics, but it's so important to encourage lots of ways to interact with a singular mechanic. I think many people's favorite formats are ones that encourage multiplicity to the maximum, and I'd personally say that I most feel multiplicity's positivity when it comes to rough edges.

    Ideally, we can find ways to interact with simple mechanics in lots of ways - like landfall - but rough edges are at least something to not offhandedly dismiss!

    So much to think about. Your point about bringing unconscious design philosophy into conscious design principles is also wonderful.

    1. I wanted to ask, Chris, how do you differentiate between smoothness and elegance?

    2. I'm excited to hear what Chris has to say as well. Personally, I'd say that something can be elegant without being smooth, necessarily. To use an abstract analogy, I'd call a gear an 'elegant' shape, but it obviously has lots of roughness to it, ways to interact and connect to it.

      Elegance, to me, is harmony of the parts. In other words, it's where each part makes sense with each other part, and has clear and intuitive function and reason to be there. There's no 'extraneous' bits, no parts where you ask, "Why is this here?" It's easiest to achieve elegance with simplicity - as you have less parts to work with, of course - but it's not necessary.

      A gear is a good example for a few reasons. It has rotational symmetry, and follows a clear pattern. Someone only has to look at part of a gear to 'get' the gear. Two, it's very easy to explain. It's a disc with a central axle and teeth evenly spaced around its surface. When you see it in motion, too, each individual part of it makes sense. The teeth click together, the axle lets it revolve, etc.

      A gear is elegant, but it isn't smooth, because the axle and the teeth allow for points of contact that other items can use in a system. It doesn't have an incredible amounts of points of contact, but you can do some very interesting things with just a few gears, you know?

      Likewise, let's look at a mechanic like Landfall. Landfall is elegant because it looks to a very natural event in the game - playing a land - and rewards you for doing so. Players will get, "Cool, this works about once a turn, maybe a bit less!" I'd call this elegant without being smooth, however, as it isn't a sterile cleanroom of a mechanic, as Chris discussed in the article.

      Personally, I'm now considering whether 'smooth' and 'rough' are apt descriptors for this. I think there's a connotation there that implies smooth is better, and rough is worse. Even in the article, Chris notes smoothness is "clean" and "contained", but I feel like "clean" might not be right either. I'd focus more on a distinction between closed vs. open, regarding the number of 'points of contact' the mechanic has with the rest of the game.

      I look forward to hearing Chris' thoughts! Great question, Jay.

    3. Nice analogy.

      Perhaps shallow/deep, simple/complex, smooth/multifaceted?

      I'd love to see examples of smooth-elegant, smooth-inelegant, and multifaceted-inelegant things / mechanics.

  4. I feel like you would like my custom cube, I tried to put in lots of overlapping synergy (and vehicles!)