GoKawiilSummary: People have tried extending rock-paper-scissors to more than 3 options, with some success. If you allow more pairings to be ties, this uncovers a rich garden of different game dynamics and strategies.
As far as a battle of wits go, its hard to find a more balanced game than rock-paper-scissors. Its simplicity means that all strategy is scraped away, and all that’s left is to cold read the other person’s soul. Come, stare into my eyes, and I’ll see the weapon you’ll choose. Your heart says to crush, your mind says to cut, and your hands yearn to smother. I know the future already, and I’ve lined up the perfect parry. Are you ready? Best 2 out of 3, and we’ll go on 3-2-1-shoot. Oh by the way – I always go rock.
Choose Your Weapon
What if we wanted more than 3 options?
This is explored in depth in this wonderful video released yesterday by Fractal Philosophy, which inspired this post. We are going to use that as a jumping off point, and then go further.
If we want to have a game where every weapon is a viable option, then we can’t bump RPS’s 3 to 4. We have to jump all the way to 5 choices with the game Rock – Paper – Scissors – Lizard – Spock. Each weapon beats two others and loses to two. The big downside of this game is complexity – I’m not a Trekkie and have no idea how Spock and Lizard are supposed to relate to the others. The upside is that ties are less common. For RPS 1/3 of all games will be a tie, while for RPSLS this drops to 1/5 – good if you want more decisive outcomes.
Both these games are formally called “paradoxical tournaments”. Tournament means that it’s a game without ties, and paradoxical means that every move can be countered. The video above ends up at the smallest “two-paradoxical tournament”, which means that every pair of moves has a common counter. This doesn’t happen until you get to n=7 moves, but ensures that a game built on these RPS dynamics will have a wide range of viable strategies.
Balancing Act
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