One popular five-weapon expansion is "rock-paper-scissors-lizard-Spock", invented by Sam Kass and Karen Bryla, which adds "Spock" and "lizard" to the standard three choices. "Spock" is signified with the Star Trek Vulcan salute, while "lizard" is shown by forming the hand into a sock-puppet-like mouth. Spock smashes scissors and vaporizes rock; he is poisoned by lizard and disproven by paper. Lizard poisons Spock and eats paper; it is crushed by rock and decapitated by scissors. This variant was mentioned in a 2005 article of The Times and was later the subject of an episode of the American sitcom The Big Bang Theory in 2008.
The majority of such proposed generalizations are isomorphic to a simple game of modulo arithmetic, where half the differences are wins for player one. For instance, rock-paper-scissors-Spock-lizard (note the different order of the last two moves) may be modeled as a game in which each player picks a number from one to five. Subtract the number chosen by player two from the number chosen by player one, and then take the remainder modulo 5 of the result. Player one is the victor if the difference is one or three, and player two is the victor if the difference is two or four. If the difference is zero, the game is a tie.(via en.wiki)
Alternatively, the rankings in rock-paper-scissors-Spock-lizard may be modeled by a comparison of the parity of the two choices. If it is the same (two odd-numbered moves or two even-numbered ones) then the lower number wins, while if they are different (one odd and one even) the higher wins. Using this algorithm, additional moves can easily be added two at a time while keeping the game balanced:
- Declare a move N+1 (where N is the original total of moves) that beats all existing odd-numbered moves and loses to the others (for example, the rock (#1), scissors (#3), and lizard (#5) could fall into the German well (#6), while the paper (#2) covers it and Spock (#4) manipulates it).
- Declare another move N+2 with the reverse property (such as a plant (#7) that grows through the paper (#2), poisons Spock (#4), and grows through the well (#6), while being damaged by the rock (#1), scissor (#3), and lizard(#5)).