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Playing Strength, (Performance, Skill Level)
of a chess player, or chess playing entity, program or engine, reflects the ability to win against other players, given by a number or other element of an ordered set such as an Elo number.

The ability to solve test-positions, that is, finding the specified, likely one and only best move, might be an indicator for various particular engine skills, but does not necessarily correlate with playing strength. In his Parallelism and Selectivity in Game Tree Search lecture, Tord Romstad introduced the Worst Moves Observation (WMO), which states the practical playing strength is not primarily determined by the quality of the players best moves nor average moves, but by the quality of the players worst moves.
Dragon and Snake on ambos [1]

Measuring

A statistical valid method to measure playing strength within a defined confidence interval is to play an appropriate huge number of games with both sides versus a wide range of different opponents [2] with symmetric time constraints, and to apply match statistics. Performance isn't measured absolutely; it is inferred from wins, losses, and draws against other players or engines. Players' rating depend on the ratings of their opponents, and the results scored against them [3]. While relative playing strength of chess engines is not strictly transmissive over various time controls, the number of games played is more relevant than their duration, the todays de facto standard in measuring playing strength is parallel playing fast chess with (ultra) short time control, such as blitz, bullet or even lightning chess, as for instance used in the Fishtest framework of Stockfish [4].

Strength

The strength of a chess program depends on many things, the quality and efficiency of the algorithms involved to determine the best move of a position, the balance of the so called search versus knowledge tradeoff to evaluate or compare leaf nodes of a search tree, how to shape that tree and to propagate a score up to the root, and time management, that is how to allocate time for searching a move under time control requirements. Time used is roughly proportional to the number of visited nodes of the common depth-first search inside an iterative deepening frame, which grows exponentially by its effective branching factor raised to the power of search depth. Playing strength might be improved over the (playing) time due to learning algorithms.

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References

  1. ^ Photo by Gerd Isenberg, September 18, 2016, detail of the Flottmann gate, Art Nouveau theme of Dragon and Sun designed by Carl Weinhold, art director of blacksmith and foundry Füssmann und Fleeth, Essen, exposed at the industrial and trade exhibition 1902 in Düsseldorf, and baught by Heinrich Flottmann as gate for his jackhammer factory, today adjacent to the exhibition and event space Flottmann-Hallen in Herne, North Rhine-Westphalia, Germany, and part of The Industrial Heritage Trail of the Ruhr area, "The dragon is a symbol of physical strength and intelligence with respect to the snake that symbolizes the tough, glowing wrought iron" from Flottmann-Tor – Hün un Perdün, see also Image by Gerd Biedermann, and Flottmann-Hallen - Historie (German)
  2. ^ A word for casual testers by Don Dailey, CCC, December 25, 2012
  3. ^ Elo rating system - Mathematical details - Wikipedia
  4. ^ Stockfish Testing Framework
  5. ^ Elo's Book: The Rating of Chess Players by Sam Sloan
  6. ^ Bayesian inference from Wikipedia
  7. ^ How I did it: Diogo Ferreira on 4th place in Elo chess ratings competition | no free hunch
  8. ^ Re: EloStat, Bayeselo and Ordo by Rémi Coulom, CCC, June 25, 2012
  9. ^ Delphil 3.3b2 (2334) - Stockfish 030916 (3228), TCEC Season 9 - Rapid, Round 11, September 16, 2016

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