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Rolling them bones
On GoogleFacePlusBook, Jeff [1] linked to an article about non-transitive
dice [2]—three dice where, on average (meaning—many rolls) die A will win
over die B, die B will win over die C, but die C will win over die A (kind of
like rock-paper-scissors [3]). Even weirder, if you double the dice, two A's
against two B's against two C's, the order reverses! (And the accompanying
video shows a series of five dice with an even weirder dual-non-transitive
ordering).
This page remineded me of a set of “go-first-dice [4]”—a set of twelve sided
dice where, say, four people each have a ¼ chance of rolling the highest
number, a ¼ chance of rolling the second highest number, a ¼ chance of
rolling the third highest number and a ¼ chance of rolling the lowest number.
In this case, the dice form a strict ordering (there is no chance of a tie).
[1]
http://spinthecat.blogspot.com/
[2]
http://boingboing.net/2013/03/15/weird-probabilities-of-non-tra.html
[3]
http://en.wikipedia.org/wiki/Rock-paper-scissors
[4]
http://www.ericharshbarger.org/dice/#gofirst_4d12
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