The Real Story (and Some of the Math) Behind the Famous “Rock, Paper, Scissors, Lizard, Spock” Game

by klheyman on 14-05-2012 08:00 AM - last edited on 16-05-2012 10:31 PM

One of the running gags on the geek-com The Big Bang Theory is a five-item variant on Rock, Paper, Scissors called, “Rock, Paper, Scissors, Lizard, Spock.” It made its first appearance in 2008, in an episode entitled, “The Lizard-Spock Expansion.”

For fans of the show, hilarity ensued. For software engineer Sam Kass, who’d invented the game along with his wife, technical writer Karen Bryla, life got a little awkward.

When they dated as undergraduates at Carnegie-Mellon, Kass and Bryla were a little too in sync as a couple: Most of their rock-paper-scissors (RPS) shoot-outs ended in ties. “We realized if we had a couple of more hand throws, we’d tie a lot less often,” says Kass.




For a pair of geeks, Spock’s Vulcan Salute was an obvious choice for an additional gesture. But what else could they use? At first they considered another geek favorite, a sock puppet, since it’s easy to mime. They quickly discarded it, because really, a sock against Spock? “We came up with a poisonous lizard,” says Kass, “Lizard Poisons Spock was the first of the new rules, and everything else kind of fell out from there.”

The expanded RPS turned out to serve a secondary role as a “Geek Test,” according to Kass. As he described the rules, he discovered the world is divided into our kind, and those who need to have “Paper Disproves Spock” explained to them.

Why five gestures? To quote Spock himself: “It’s logical.”

“So long as you have an odd number of hand signals, you can create a fully balanced graph where everything is beaten and beats the same number of things,” says Kass, “Four doesn’t work, because one will be unbalanced; but five works.”

Mathematician Alan Yuille explains more details via email. “You select an odd number of objects (e.g., rock, Spock) and arrange them in order on a circle (like numbers on a clock),” writes Yuille. “Say that there are 7 objects. Then you make each object beat the next 3 objects clockwise and lose to the 3 objects counterclockwise (more generally, replace 7 by 2n +1 and 3 by n). This means that each object wins half the time (so no object is favored).”

Following that logic, you can make an RPS game with any number of signs, as animator David Lovelace breathtakingly did. In an effort somewhere on the human achievement scale between climbing Everest and making an Eiffel Tower of toothpicks, Lovelace created a 101 gesture variant, with 5,050 outcomes.

Kass’s version had inspired Lovelace to wonder, “how much more absurd the game could be made.”  As an artist, Lovelace saw the beautiful geometries of RPS. “Sam turned a simple triangle matrix involving one win outcome per each of three gestures, and turned it into a pentagram of two win outcomes for each of five. Most intriguing to me was how the original triangle of RPS, among a few others, could still be found within that new pentagram. Assuming you had the time, patience, and imagination, you could keep going with multiply-stellated septagrams, nonagrams, etc., with the only challenge coming up with logical-sounding relationships between the hand-shaped pictogram gestures you invent,” he explains in an email.

After relatively benign RPS 7, 9, 11, 15 variants, Lovelace designed a memory-defying RPS25 with 300 outcomes. He thought he’d created his magnum opus and stopped, but other people kept giving him new ideas, and he kept coming up with new ones of his own. The compulsion once again took over: In 2006, he announced the sine qua non RPS101. It had taken him an entire year to design, “using pencil-drawn hand gestures on scraps of torn paper, taped to my wall in a massive, nine-foot-diameter circle. They were all numbered, and I'd spend days, weeks, and months staring at them, trying to figure out situations like how in the Hell a ‘Bowl’ could beat ‘Air,’ or what possible relationship Math and a Cockroach could have,” he remembers.

Lovelace writes that some people have complained of 101’s “rampant incorporation of complete bullshit.” His answer is to dare anyone to do better. Unlike Everest, odds are his summit will remain unique.

Kass first put his own RPS version, a mere footstool by comparison, on the Web in the 90s. Kass was learning HTML, and put up a image of the rules in a fully-connected graph as part of the practice for his first webpage.




Years later, a friend at work told him that a show he’d never watched had an upcoming episode called, “The Lizard Spock Expansion.”

“I watched and sure enough, [Sheldon] said all the rules right out,” says Kass, “My Facebook was going crazy and everyone was like, ‘They’re using your game! They’re using your game!’”

Unfortunately, people who didn’t know Kass had searched for the rules online, and were accusing him of plagiarism on his own Web site. Kass had to use the Internet WayBack Machine to defend his honor.

(According to a show insider, the writers hadn’t even considered attributing the rules to anyone in particular. They’d assumed it was a common piece of geek culture with which their characters—and their real-life counterparts—would already be familiar.)

While Kass was fielding accusations on the Web from fans who’d never heard of him, the show’s co-creators, Bill Prady and Chuck Lorre, were fielding questions at various cons  from fans who had.

On February 19th of this year, Prady, a former programmer who waxes nostalgic for PDP-11s, made up for the oversight (er, arguably the copyright infringement) by tweeting “All Hail Sam Kass!” That night’s episode, “The Rothman Disintegration,” also included a scene in which Sheldon (Jim Parsons) declares “All Hail Sam Kass!” before repeating the rules.

Among the millions of people those shout-outs surprised was: Sam Kass.

“The next morning, I go into work, and everybody’s like ‘All Hail Sam Kass!’ Oh boy…” sighs Kass. He still gets teased about it, but he has fun with it too.

To this day, nobody at The Big Bang Theory has ever spoken to Kass, despite the rules being fully recited in two episodes and briefly mentioned in a third. He has no hard feelings. “I was impressed,” he says of star Jim Parsons’ bravura speed-recitations of the rules, “He said them better than I can. I still have to think about who wins.” (Bill Prady recently connected with Sam Kass over Twitter, and extended an invitation to visit the show.)*

Becoming known as He Who Must Be Hailed has had some sweet geek perks: ThinkGeek sent him and Bryla their Rock/Spock t-shirts. It’s also helped drive traffic to Kass’s Café Press site, the only Rock/Spock merchandise that financially benefits the meme’s true creators.

It also led to him and Bryla being asked to officiate at a Rock/Spock competition at a recent Pittsburgh ComicCon. In a perfect ending that even The Big Bang Theory’s writers might not have dared to script, the winner in a field of almost 40 people was a seven year old boy who threw Spock.


*Clarification: Sam Kass tweeted about a show policy that required a "Geek of the Week" visiting guest to have a PhD. That was my misinterpretation. The show has been very open to a wide range of people.


See also:


by Cameron Laird alternate(anon) on 16-05-2012 10:46 AM

Good reporting, Karen.  While on the subject, I think you'll also want to know about Rock-Scissors-Paper Lizard-Sex http://en.wikipedia.org/wiki/Common_side-blotched_lizard#Mating_strategy  Not the same, or even particularly-close, but plenty fascinating in itself, and it sounds like something that would tickle the inmates of fictional Pasadena.

by klheyman on 16-05-2012 02:02 PM - last edited on 16-05-2012 02:14 PM

Happy to report that Bill Prady and Sam Kass spoke over Twitter this morning, and that Prady has invited Sam to the show.

Don't want to leave anyone with a misimpression of Prady. He's always been very generous with his time. Unfortunately, the timeline for this story didn't sync with his schedule.


by klheyman on 16-05-2012 02:05 PM

Thank you Cameron!

Readers, check Cameron's link.It's a very interesting piece of biology/game theory.

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