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title: Late Move Reductions

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Samuel Bak - Other Rules [1] Late Move Reductions (LMR),

or its version known as History Pruning and History Reductions [2] , 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 [3] 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.

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. Base reduction depth changes according to depth and move number, with further adjustments being made depending on certain conditions. Here are some sample base formulas can be viewed:

  • Weiss reduces by 0.20 + ln(depth) * ln(move number) / 3.35 for captures and promotions and 1.35 + ln(depth) * ln(move number) / 2.75 for quiet moves.
  • Ethereal reduces by 0.7844 + ln(depth) * ln(moves played) / 2.4696 for quiet moves and 3 (or 2 if the move gave check) for captures and promotions

LMR adjustments

After determining a base value, several adjustments can be made to the reduction depending on certain conditions.

Some common conditions to reduce less:

Some common conditions to reduce more:

  • We are on an expected cut-node
  • Move has a bad history score
  • Our score is not improving (ie our current evaluation is less than or equal to the evaluation from two plies ago)

Re-searches

Classical implementation assumes a re-search at full depth if the reduced depth search returns a score above alpha. However, modern implementations have a triple-search system for PV-nodes and a double search system for non PV-nodes.

Test Results

Some test results related to LMR can be found on

See also

Publications

Forum Posts

2004

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2006

Re: late move reductions by Alessandro Scotti, CCC, March 01, 2006 » Kiwi PHR (Peak History Reduction) idea by Daniel Mehrmann, CCC, March 01, 2006 » Home, Relative History Heuristic

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External Links

References

  1. ↑ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
  2. ↑ History Reductions in Pro Deo by Ed Schröder
  3. ↑ An Introduction to Late Move Reductions by Tord Romstad (Wayback Machine)
  4. ↑ Mark Winands, Erik van der Werf, Jaap van den Herik, Jos Uiterwijk (2004). The Relative History Heuristic. CG 2004, pdf
  5. ↑ Receiver operating characteristic (ROC) from Wikipedia
  6. ↑ LMR - or starters - Advance and Expert by Ed Schroder, CCC, May 01, 2017

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