In real life we have situations such as: Rock > Scissors, Scissors > paper and Paper > Rock. Is there a type of math to deal with this?
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GeorgeGee (
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September 10th, 2010
There’s no conflict in the game of rock-paper-scissors to say that each could beat another, there is no single greatest. But in standard math, that would be nonsense. How do we reconcile this?
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6 Answers
In Modular Arithmetic the numbers wrap around. That might be a good place to start to define the rules mathematically.
As a kid we played rock, paper, scissors, bomb,. Symbol for bomb was fist with thumb extended. Scissors cuts fuse. Bomb destroys rock, etc. .... Mod 4
Rock, paper,scissors, lizard, Spock would be Mod 5
@worriedguy So then there’s no difference between Rock, Paper, Scissors and Nuke, Foot, Cockroach?
Rock, paper, scissors, lizard, Spock is the best.
What do Spock, foot, lizard and cockroach do and how do you make them
Transitivity is the property of a relation R such that if there are 3 elements a, b, & c and if (aRb) and (bRc) are both true, then (aRc) is also true.
For example if R is “equals” then a=b and b=c implies that a=c. Likewise if R is “greater than” then a>b and b>c implies a>c. Transitivity is not a property of all relations, however & it’s easy to find counterexamples.
In rock-paper-scissors the 3 elements are set up to be non-transitive with respect to which prevails over which. Another example of a non-transitive system is certain kinds of elections, where there are at least 3 candidates and a plurality wins. Then it’s possible that A beats B and B beats C, but C beats A.
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