History Heuristic

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Alfred Agache - La Fortuna, 1885 [1]

History Heuristic,
a dynamic move ordering method based on the number of cutoffs caused by a given move irrespectively from the position in which the move has been made. The Heuristic was invented by Jonathan Schaeffer in 1983 [2] and works as follows: on a cutoff we increment a counter in a special table, addressed either by [from][to] (the Butterfly Boards) or by [piece][to] [3] . The added value is typically depth * depth or 2 ^ depth, based on the assumption that otherwise moves from the plies near the leaves would have to much impact on the result. Values retrieved from that table are used to order non-capturing moves. This simple heuristics performs usually better than domain-dependent heuristics, though it may be combined with them. For example, in Rebel only a few non-captures are ordered by history heuristics, then a piece-square approach is used [4] . In the literature, history heuristic is often presented as depth-independent generalization of the killer moves. It is also said to reflect long-term plans in a position.

Random Noise?

However, all of those statements were made at the time when typical search depth was much lower than today. Nowadays some authors say that given enough search depth, history heuristic produces just a random noise [5] , whereas Ed Schröder, advocated not taking into account the cutoffs from the last couple of plies.


This is how the history array may be updated, if a beta-cutoff occurs:

   if ( score >= beta ) { // cutoff
      if ( isNonCapture (move) )
         history[side2move][move.from][move.to] += depth*depth; // 1 << depth
      return score;

Counter Moves History

A combination of the History Heuristic in conjunction with the Countermove Heuristic, proposed by Bill Henry in March 2015 [6] , as already used by Álvaro Begué in his Checkers program 20 years before [7] , was implemented by Stockfish contributor Stefan Geschwentner [8], further tuned and improved by the Stockfish community, and released in Stockfish 7 in January 2016, dubbed Counter Moves History and mentioned to gain some Elo points [9]. Stockfish's History and Countermove arrays are piece type and to-square based, not butterfly based. Each entry indexed by a previous move, is a complete history table with counters indexed by the move refuting that previous move. Pushing the idea further, Stockfish applies Follow Up History (FUH) tables, indexed by two consecutive moves of the same side [10].

See also

Late Move Reduction Test Results

Selected Publications

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Forum Posts

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External Links


  1. Alfred Agache - Alegoria da Fortuna, 1885, Palais des Beaux-arts, Lille, Category:Alfred Agache - Wikimedia Commons
  2. Jonathan Schaeffer (1983). The History Heuristic. ICCA Journal, Vol. 6, No. 3
  3. Jos Uiterwijk (1992). Memory Efficiency in some Heuristics. ICCA Journal, Vol. 15, No. 2
  4. Move Ordering in Rebel by Ed Schröder, also available as pdf
  5. Re: LMR: history or not? by Robert Hyatt from CCC, December 13, 2007
  6. Improving History Tables by Bill Henry, CCC, March 02, 2015
  7. Re: Improving History Tables by Álvaro Begué, CCC, March 02, 2015
  8. Followup moves by Stefan Geschwentner, FishCooking, January 12, 2014 » Counter Moves History
  9. Re: Stockfish 7 progress by Lucas Braesch, CCC, January 17, 2016
  10. Re: CMH question by Lucas Braesch, CCC, December 09, 2019
  11. Negative Plausibility Move Ordering by Alessandro Damiani, CCC, July 09, 2009

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