THE NEW HOT SPORT.

author=Tau link=topic=2183.msg36871#msg36871 date=1223610393
How does paper beat rock ???

Expected number of rounds to determine a winner

The expected value for the number of rounds required to decide a winner, given that px is the probability of reaching round x, is

\sum_{n=1}^\infty n(p_n -p_{n+1}). In each round of RPS there is a 1/3 probability of a tie, so this equals
\sum_{n=1}^\infty n((\tfrac{1}{3})^{n-1} - (\tfrac{1}{3})^n). Regrouping (which is permitted since terms converge to zero) then leads to the geometric series
\sum_{n=0}^\infty 2n(\tfrac{1}{3})^n, which converges to 1.5.

Non-transitivity

RPS is also often used as an example of the mathematical concept of non-transitivity. A transitive relation R is one for which a R b and b R c implies a R c. A reflexive, antisymmetric, and transitive relation on a set is known as a partial ordering, from which notions of "greater" and "less" follow. A game option which is "greater" than another is closer to being optimal, but such a notion does not exist in RPS: The relation used to determine which throws defeat which is non-transitive. Rock defeats scissors, and scissors defeat paper, but rock loses to paper. In fact, RPS could be called "intransitive" because A is greater than B, and B is greater than C, yet A is not greater than C.

http://www.worldrps.com/index.php?option=com_content&task=view&id=13&Itemid=28

Rei
It wraps and... suffocates it?