The Evaluation of Tournament Results as a Maximization Problem in Probability Theory

  • E. Zermelo
Part of the Springer Series in Statistics book series (SSS)


Chess tournaments are of late always arranged so that each player meets every other player k times, where k is fixed (usually k = 2, with alternate colors) . The ranking of the players is then determined by the number of games won, where an undecided (“drawn” ) game is counted as half a win for each of the partners. This method of calculation treats all games equally, regardless of the order of play, and consequently reduces chance effects to a minimum. Apparently the procedure has worked very well in practice if only a ranking is of interest, but it fails completely for broken-off tournaments (in which the number of games played is not the same for each participant).


Playing Strength Irreducible Case Alternate Color Regular Tournament Usable Evaluation Method 
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  1. (1).
    E. Landau. On the distribution of prizes in tournaments. Ztschr. f. Math. u. Phys. 63, p. 192 (1914)MATHGoogle Scholar
  2. (4).
    This result is only apparently paradoxical, since no player could do worse, however low his playing strength. Cf. Landau, loc. cit., p. 201.Google Scholar

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© Springer Science+Business Media New York 2001

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  • E. Zermelo

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