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The Elo rating system is a method for calculating the relative skill levels of players in zero-sum two-player games.

igen's Paradox[edit] Eigen's paradox is one of the most intractable puzzles in the study of the origins of life. It is thought that the error threshold concept described above limits the size of self replicating molecules to perhaps a few hundred digits, yet almost all life on earth requires much longer molecules to encode their genetic information. This problem is handled in living cells by enzymes that repair mutations, allowing the encoding molecules to reach sizes on the order of millions of base pairs. These large molecules must, of course, encode the very enzymes that repair them, and herein lies Eigen's paradox, first put forth by Manfred Eigen in his 1971 paper (Eigen 1971).[1] Simply stated, Eigen's paradox amounts to the following: Without error correction enzymes, the maximum size of a replicating molecule is about 100 base pairs. For a replicating molecule to encode error correction enzymes, it must be substantially larger than 100 bases. This is a chicken-or-egg kind of a paradox, with an even more difficult solution. Which came first, the large genome or the error correction enzymes? A number of solutions to this paradox have been proposed: Stochastic corrector model (Szathmáry & Maynard Smith, 1995). In this proposed solution, a number of primitive molecules of say, two different types, are associated with each other in some way, perhaps by a capsule or "cell wall". If their reproductive success is enhanced by having, say, equal numbers in each cell, and reproduction occurs by division in which each of various types of molecules are randomly distributed among the "children", the process of selection will promote such equal representation in the cells, even though one of the molecules may have a selective advantage over the other. Relaxed error threshold (Kun et al., 2005) - Studies of actual ribozymes indicate that the mutation rate can be substantially less than first expected - on the order of 0.001 per base pair per replication. This may allow sequence lengths of the order of 7-8 thousand base pairs, sufficient to incorporate rudimentary error correction enzymes. A simple mathematical model