Rock, Paper, Scissors, Lizard, Yeast!

The Rock Paper Scissors Dynamic

Zero-sum is a concept that is closely related to games and game design. Formally, it can be described as tripartite nontransitive design-in other words, design comprised of three elements, related in such a fashion as to violate the familiar and logical notion of:

if        A is favoured over B

and     B is favoured over C

then    A must be favoured over C

Instead, a nontransitive design will employ something like this:

if          A is favoured over B

and      B is favoured over C

then     C is favoured over A

This concept is most commonly recognized as the Rock/Paper/Scissors dynamic (or RPSD). Fascinatingly, this design methodology can be found, to varying degrees, in just about every competitive game where a balanced competitive scene is desired. Even more compelling is the evidence suggesting that this phenomenon is nigh omnipresent throughout the natural world. Empirical evidence has been found that identifies the existence of this pattern across an incredibly diverse range of disciplines. From blotched lizards, to marine invertebrates, to strains of E .coli, and even yeast, this phenomenon is truly pervasive in its scope.

“It's the simplest constructed game that involves strategy. You cannot construct a simpler game that would actually involve some element of choice within it … the dynamic that appears in rock-paper-scissors appears everywhere. It appears the ways animals evolve, to the way video games are coded. It appears all over in theories of mathematics, how politics and governments are balanced. The essence of that relationship and that thread of logic appears throughout nature and human behavior. Rock-paper-scissors will never fade away. It's ingrained in our culture, and our being."

- Douglas Walker - President of the World RPS Society

What conclusions, specifically related to the discipline of game development and design, can we draw from these observations? The RPSD is most commonly applied by game designers as a means of creating Zero-sum balance systems. To probe the answer to this question more deeply, we must seek out historic precedents establishing the RPSD as a game mechanic.

History of Rock/Paper/Scissors

Since ancient times, games have been a pervasive element of civilized society. While there is a lack of historical evidence available, there have been references found of a finger or hand- flashing game that is depicted on the walls of the Beni Hasan burial site dating back as far as 2000 B.C.E.

With these murals being suggestive if not conclusive, it was centuries before more concrete evidence of the game was found in China. A book titled Wuzazu authored by Xie Zhaozhi (a Ming-dynasty writer who lived circa 1600 A.D.) mentioned that the game shoushiling (literally: "hand command") dated back to the Han Dynasty, between 206-220 AD.

It is uncertain as to the exact path the game took from there, but it wasn’t until the 17th century that mentions of “sansukumi-ken” (literally: “fist game with a three way deadlock”) or “mushi-ken” (Slug, Frog, Snake) were recorded. The ken style of games were originally drinking games, but exploded in popularity as the concept spread, spawning numerous regional variations.

From there, the game evolved to the more familiar “jan-ken”, establishing the ubiquitous symbolism of modern Rock, Paper, Scissors.

After leaving Asia, the game took on the form of the universally recognizable Rock, Paper, Scissors and has remained popular on a global scale. The Paper Scissors Stone Club was founded 1842 in London, England, and still exists today, in the form of the World RPS Society.

Modern Video Games

It is quite common to see the application of the RPSD to modern FPS, role-playing, and real-time strategy games. The utilization of these interactions often follows the familiar military cycle of real-world warfare, with cavalry defeating archers, archers defeating pikemen, and pikemen defeating cavalry.

Most modern games accommodate some form of this concept in their designs, usually in order to stimulate an interesting competitive scene or as a form of self-balancing. Several games have successfully leveraged the dynamic to create internally complete competitive systems.

Perhaps one of the most widely recognized competitive real-time strategy games is the Starcraft franchise created by Blizzard in 1998. Starcraft redefined the standard for future generations of RTS games attempting to create an internationally competitive scene.

With the three defining races of Protoss, Terran, and Zerg, we encounter an expertly crafted version of the RPSD in modern gaming.

Not only does Blizzard establish these three races in a classic RPS relationship, they extend the dynamic by incorporating this design philosophy into an imperfect, yet still extremely effective version of what I will call the Zero-Sum Web, which I will elaborate upon later.

Inside Starcraft there exist microcosmic echoes of the RPSD, and Blizzard should be lauded for the design and execution of this system. I would like to call attention to the three core units that embody the RPSD within Starcraft.

The Protoss Zealot, the Terran Marine, and the Zerg Zergling are simultaneously icons of the Starcraft franchise, their respective races, and the RPSD as it is present in Starcraft..

In this tri-balanced relationship, Blizzard has made it so that in a vacuum, the Zealot (pikemen) can handily defeat two Zerglings (cavalry) through the use of its shields and powerful melee attacks. The Marine (archer) can whittle down the Zealot from afar without needing to engage it directly, and the Zergling can overwhelm the Marine by forcing it to split its fire and subsequently surrounding it.

This relationship is a textbook example of this zero-sum web in action and Blizzard employs this design methodology in the design of the other units for the various factions. This philosophy is carried through to the sequels of the series and is also employed widely within other Blizzard games.

The Zero-sum Web

Finally, with examples of the concept in action we begin to see how this methodology can be applied to games. At the most fundamental level this concept is one of seamlessly interwoven building blocks that are fitted together in a nontransitive way. This idea is flexible and can be applied in a wide variety of ways. This is evidenced through the emergence of the zero-sum pattern in nature, in the design of games, and among other things.

The two game applications I will discuss here are the building of a game from the ground up using the zero sum web methodology and the balancing of game retroactively using the same principles.

Both of these methods require a means of establishing a metric by which to measure the balance of the game. This aspect of the design process is a complex endeavour in and of itself and could easily be the subject of an article of its own. In the interest of brevity and focus on the topic I will be using the tenets of combat, warfare, and decisions from one moment to the next as my guideposts.

As mentioned earlier, the tenets of combat and warfare are especially applicable to real time strategy and FPS games. These are age old and widely recognized. The interrelation between pikemen, archers, and cavalry are familiar and generally intuitive to understand. In the making of a game based on war or combat these are very easily recognizable.

As an example of this within modern games I would ask you to consider the slightly niche genre of fighting games. This type of game is a deeply complex genre that is home to some of the most intricate and skillful designs out there. Fighting games are restrictive in their appeal for a variety of reasons but mostly due to the rather high skill floor and almost limitless skill ceiling. While there will inevitably be skillful interplay between opponents in any competitive situation, fighting games are somewhat unique in that they embody a mix of extremely technical motor control and the ability to know the mind of your opponent with decisions made in a split second.

This fighting game genre, when viewed through the RPSD lens reveals three “strategies” that exist in an nontransitive relationship to each other. Within the context of fighting games these are known as “Aggro/Rushdown”, “Control/Zoning”, and “Hybrid/Grappler”. The origin of these strategies can be traced back to a simplified version of the decisions a person faced with real life combat situation would be presented with.

This ties to the idea of decisions from one moment to the next. In fighting games it is not uncommon for the outcome of a particular exchange to hinge on a single frame of action and when the interplay between combatants is broken down and examined from one frame to the next, three actions emerge as options for a player to choose between. These elements are:

Attack, Defend, or Throw

This tripartite relationship is what establishes the framework for players of fighting games to hone their Yomi (the ability to know the mind of their opponent). In fact, at the highest levels of fighting games, this is usually the skill that decides the winner of the match. When a player is presented with these three options they will generally tend towards one of three based on personal playstyle, context, and experience. This of course opens up the ability for the opponent to recognize when they are being read and counter in turn, ad infinitum. When fighting games are understood and viewed in this way, the matches played by the most masterful players are truly a sight to behold.

These three form the pillars around which character toolkits are designed and it is through their nontransitive dynamics that game balance can be achieved. This can easily be applied to the development and balancing of other games.

The zero-sum approach to game creation begins by designing   three elements related in a nontransitive way and placing them together in a competitive setting. If these elements are designed correctly then a balance, like that found in nature, will emerge and create an interesting gameplay experience for those involved. Of course, with technology continuing to evolve and the tastes of gamers becoming more sophisticated we are no longer able to simply stop there.

The zero-sum web approach to building a game adopts an exponential progression for the addition of mechanics where the game designer creates two additional sets of three nontransitive elements that blend together with the original set of three and form a cohesive whole that is both intuitive and balanced fundamentally.

This process is repeated as many times as the variables can be accounted for. There is a certain threshold where it becomes impossible to accurately predict the behaviours of all the elements. This system is what underlies the majority of the unit interactions in Starcraft and other Blizzard games as well as what guides the design choices behind the creation of fighting game characters and their individual mechanics.

Conclusion

Designing the game in this way offers other benefits than a fundamentally balanced core game. It also provides the development team with a convenient means of creating and fostering a cycle of strategic buffs/nerfs to various abilities/characters in order to prevent the stagnation of a competitive scene. This is a commonly deployed method that can be made easier through zero-sum design.