Who knew you could change existing games?

I learned the game, Rock, Paper, Scissors years ago, probably back in elementary school.  Last year, I learned the extension, "..., Lizard, Spock"to the game (1, 2).  This is pretty cool, so I taught some of my students as a new way to play (Koreans, of all ages, love Rock, Paper, Scissors).

It wasn't until I taught my son the game that I learned something.  There is no reason to stop at 5 elements to the game.  He quickly suggested adding Cider and Balloon to the game although we were both hazy on how and why they beat or were beaten by the other elements.

As an ESL teacher, I am now very interested in the game and ways to add to it.  It seems clear that you need an odd number of elements so that each element can beat and be beaten by half of the others:

New element beats (n-1)/2

New element is beaten by (n-1)/2

And it helps, I think, to draw a polygon with five, seven, nine or more sides to diagram how each element affect the others.

Diagram from the above Wikipedia link and here, another Wikipedia description I just found which describes the same information as I independently came up with.
As an ESL teacher, it is the last bit that is useful.  We all know:
Rock smashes scissors but is covered by paper.
Paper covers rock but is cut by scissors,
Scissors cut paper but are smashed by rock.
----
In the Lizard, Spock alternative:
Spock uses a laser on scissors and rock, but is disproven by paper and poisoned by lizard.
Lizard eats paper but is crushed by rock and decapitated by scissors.

My students will be making their own additions to the game next semester... and I need to thank my son for reminding me to consider changing established activities.

Time to play CalvinBall (1, 2)