Paper, Rock, Scissors.... Lizard, Spock?

We have all played paper-rock-scissors before. In fact, many game mechanics use its core element to achieve balance. But have you ever heard of paper-rock-scissors-lizard-Spock (PRSLS) before? If you are a game designer, than it is more likely you have.

PRSLS is a more complex version of paper-rock-scissors, where Spock destroys rock and breaks scissors, but paper disproves Spock. The lizard poisons Spock and eats paper, but is crushed by the rock and cut by the scissors. When you make all the comparisons, you notice two things. (1.) Every element is weak against half of the remaining elements and is strong against the other half. (2.) Each set of weakness/strengths are unique to each element.

This means that PRSLS is still a completely balanced mechanic in spite of its increased complexity. But can we add more elements and retain the same level of balance. As a matter of fact, you can, as long as the number of elements in the mechanic is odd. I got the following image from the good people of http://www.umop.com. This shows a 25 element mechanic perfectly balanced like paper-rock-scissors.

http://www.umop.com/images/rps25_outcomes.jpg will take you to the breakdown of how

each element interacts with each other. Now this is pretty crazy looking, and as a game designer, I must ask what good is all this? Can this added level of complexity serve a purpose? I've determined that it has some strengths and weaknesses.

One of the most obvious weaknesses is the complexity. How is a player going to remember all the 300 outcomes of this RPS 25? Sure a computer system can keep it all strait, but unless the player knows at least why things are happening, it will likely come across as random outcomes.

One of the biggest strengths of adding more elements in the paper-rock-scissors mechanic is that it reduces the chances of a tie. When playing with the tree elements, there is a 33% chance of a tie. When playing with 25 elements, the chances of a tie are drastically reduced to only 4%. I have come up with another way of organizing this mechanic to reduce the chances of a tie to 11% and keep the complexity to a point where it is very understandable. The following image shows the layout of this design.

As you can see, the elements are embedded in a super-element. Here, any elements found in the brown super-element will defeat any element found in the gray super-element and will be defeated by any found in the white super-element. But if both players chose something from the brown super-element, then the one choosing the brown element will defeat the gray element and will be defeated by the white element.

There is still one more weakness I must discuss when it comes to the paper-rock-scissors mechanic in all the varieties I have covered. Having 3+ players drastically increases the likelihood of a tie (or more appropriately, the cycle of defeat). I remember a time in grade school where six of us got together and played paper-rock-scissors. It took about 15 tries just to get the first person out! Unfortunately increasing the number of elements does not solve this problem. The concept of entering this cycle of defeat may not even be an issue if interactions in you game don't simultaneously consider three or more pieces.

In conclusion, there are ways to increase the number of elements in a paper-rock-scissors mechanic while keeping it perfectly balanced. Doing so increases the level of complexity for better or worse, but reduces the odds of a tie. No matter how many elements are in the mechanic, considering three or more players or units simultaneously will likely lead to an endless cycle of defeat.