Search Statistics

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Search statistics refers to counting various appearances of interest inside the search or evaluation routines and to analyze their relationships to eventually spot bugs or unfavorable conditions in move ordering.

=Node Statistics= Of interest is the appearance of searched nodes inside an iterative deepening framework and the ratio of quiescent nodes, per depth and/or aggregated, in conjunction with effective branching factor (EBF) and of course nodes per second.

Cutoffs
Inside Alpha-beta- or PV-search it is of particular interest to count how often a node failes high or not, in relation to its node types, that is expected cut-Nodes or expected All-nodes. If a fail-high occurs, it is illuminative to know whether the fail-high move it was tried first, early or late and what move ordering classification like move from the transposition table, winning captures, killer moves, etc. was applied.

Re-Searches
At PV-nodes inside a alpha-beta- or PV-search the number of re-searches does concern, and how often a re-search does improve alpha (or even performs a cutoff) or not.

Root Statistics
The Root as distinguished PV-node specially with aspiration window often has its own statistics related to how much relative time (nodes) of the whole iteration is performed per each root-move, and how often another best move was found. In conjunction with static move properties, score graph by searched depth so far, etc., these statistic based informations may be considered in time management to possibly decide about a new iteration.

Selectivity
Counting the various extensions, reductions and forward pruning decisions in relation with effective branching factor might also spot some deficiency inside the search. =TT Statistics= Statistics of the transposition table covers number of probes and stores, fill level, and number of probe hits, likely differentiated by sufficient draft and type of stored node.

=See also=
 * Profiling
 * Match Statistics

=Publications=
 * Hermann Kaindl (1988). Useful Statistics from Tournament Programs. ICCA Journal, Vol. 11, No. 4 » Merlin

=Forum Posts=

1994 ...

 * COMPUTER CHESS: statistics by Deniz Yuret, rgcc, October 27, 1994
 * Cutoff Statistics by Roland Pfister, CCC, December, 18, 1997

2000 ...

 * A matter of statistics by Tijs van Dam, CCC, January 26, 2000
 * Re: The Scalable Search Test / Results of "Der Bringer" by Gerrit Reubold, CCC, June 18, 2000
 * Faster, deeper and more of such... by Ed Schröder, CCC, September 14, 2000 » Diminishing Returns
 * Hash table efficiency by Miguel A. Ballicora, CCC, December 05, 2000 » Gaviota, Transposition Table
 * Hash table statistics by Andrew Wagner, CCC, April 08, 2004
 * What is the Ideal Output for Understanding a Chess Engine? by Rick Fadden, CCC, April 07, 2008
 * Search statistics by henkf, CCC, May 04, 2009

2010 ...

 * make and unmake stadistics by Fermin Serrano, CCC, February 28, 2012
 * Probabilistic approach to optimize search tree by Sergei S. Markoff, CCC, September 22, 2012
 * Search statistics by Robert Pope, CCC, October 30, 2013
 * pruning statistics by Jon Dart, CCC, January 27, 2014 » Pruning
 * Best move statistics by Matthew Lai, CCC, September 12, 2016
 * Move ordering statistics by Sander Maassen vd Brink, CCC, February 26, 2017 » Move Ordering
 * Testing for Move Ordering Improvements by Cheney Nattress, CCC, March 25, 2017 » Move Ordering
 * Komodo 11.2.2 - Initial position until depth 54 by Andreas Strangmüller, CCC, January 15, 2018 » Komodo, Initial Position
 * Stockfish 8 - Initial position until depth 59 by Andreas Strangmüller, CCC, January 16, 2018 » Stockfish

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