Home * Search * Selectivity * Reductions * Late Move Reductions

Late Move Reductions (LMR),
or its version known as History Pruning and History Reductions [1] , save search by reducing moves that are ordered closer to the end of likely fail-low nodes. Typically, most schemes search the first few moves (say 3-4) at full depth, then if no move fails high, many of the remaining moves are reduced in search depth. The technique has been used for many years in various forms, but it became very popular in 2005 after Fruit and Glaurung [2] used open source implementations based on the History Heuristic. LMR can often reduce the effective branching factor to less than 2, depending on the reduction conditions.
Samuel Bak - Other Rules [3]

Common Conditions

Most programs do not reduce these types of moves:

Less Common Conditions

Less common conditions on moves not to reduce:

Reduction Depth

Classical implementation reduces by one ply only. Yet modern programs, most notably Stockfish, allow reductions of more than one ply and increase them for later moves. Reduction depth changes according to expected node type (being typically smaller in pv nodes), depth and move number. Here some sample formulas can be viewed:
  • Senpai reduces by one ply for the first 6 moves and by depth / 3 for remaining moves.
  • Fruit Reloaded uses formula: uint8( sqrt(double(depth-1)) + sqrt(double(moves-1))); for non-PV nodes. In PV-nodes it reduces by 2/3 of this value.


Classical implementation assumes a re-search at full depth if the reduced depth search returns a score above alpha.

Test Results

Some test results related to LMR can be found on

See also


Forum Posts


2005 ...


2010 ...


2015 ...


External Links

Late Move Reductions



  1. ^ History Reductions in Pro Deo by Ed Schröder
  2. ^ An Introduction to Late Move Reductions by Tord Romstad
  3. ^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
  4. ^ Mark Winands, Erik van der Werf, Jaap van den Herik, and Jos Uiterwijk (2006). The Relative History Heuristic. Computers and Games, Lecture Notes in Computer Science (LNCS 3846) (eds. Jaap van den Herik, Yngvi Björnsson, and Nathan S. Netanyahu), pp. 262-272. pdf
  5. ^ Receiver operating characteristic (ROC) from Wikipedia
  6. ^ LMR - [for starters] - [Advance] and [Expert] by Ed Schroder, CCC, May 01, 2017

What links here?

Up one level