MVV-LVA

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MVV-LVA (Most Valuable Victim - Least Valuable Aggressor), is a simple heuristic to generate or sort capture moves in a reasonable order. Inside a so called find-victim cycle, one first look up the potential victim of all attacked opponent pieces, in the order of the most valuable first, thus queen, rook, bishop, knight and pawn. After the most valuable victim is found, the find-aggressor cycle loops over the potential aggressors that may capture the victim in inverse order, from pawn, knight, bishop, rook, queen to king. The heuristic is easy to implement and covers a lot of simple cases, such as PxR before BxP. It is used in various move generators build in hardware, such a Belle and more recently in FPGA approaches such as Brutus and MBChess. However the heuristic may fail, if victims attacked by more valuable attackers are defended, in such cases most programs rely on attack tables, set-wise pawn attacks (defends) on the fly to perform a static exchange evaluation.

=See also=
 * Belle | Hardware Move Generation
 * Mater
 * Move Generation
 * Quiescence Search
 * SEE - The Swap Algorithm with Bitboards
 * Static Exchange Evaluation

=Forum Posts=

1995 ...

 * mvv/lva vs SEE capture ordering test results by Robert Hyatt, rgcc, August 10, 1995
 * MVV/LVA vs SEE move ordering - more test results by Robert Hyatt, rgcc, August 25, 1995
 * Re: MVV/LVA vs SEE move ordering - more test results by Brian Sheppard, rgcc, August 27, 1995

2000 ...

 * Fast BB move generation by Bas Hamstra, CCC, May 08, 2000
 * MVV/LVA or SEE - liability? by Severi Salminen, CCC, November 29, 2000 » Static Exchange Evaluation
 * MVVLVA sorting does not help for move ordering by Scott Farrell, CCC, September 21, 2002

2005 ...

 * Sorting captures by Pablo Vazquez, CCC, August 02, 2008
 * Effect of MVV/LVA by Mathieu Pagé, CCC, Sepember 14, 2008
 * MVV/LVA. Or should it be LVV/MVA? by Harm Geert Muller, CCC, March 31, 2009

2010 ...

 * LVA MVV with relative Pin by Clemens Pruell, CCC, February 16, 2011 » Pin
 * MVV/LVA sorting by Harm Geert Muller, CCC, June 05, 2013

2015 ...

 * DarkThought sorts MVV/LVA without looking at any moves? by Rob Williamson, CCC, April 25, 2015 » DarkThought
 * MVV/LVA by Folkert van Heusden, CCC, October 02, 2015
 * Sorting Captures by David Cimbalista, CCC, August 03, 2016
 * A smarter MVV/LVA by thevinenator, OpenChess Forum, December 28, 2016
 * MVV LVA by Vivien Clauzon, CCC, July 01, 2018
 * correct way to score promotions using MVV-LVA by Mahmoud Uthman, CCC, June 06, 2019 » Promotions

=External links=
 * MVV/LVA from Bruce Moreland's Programming Topics
 * Micro-Max 4: Quiescence Search by Harm Geert Muller
 * The Dorf feat. FM Einheit und Caspar Brötzmann - Massaker, Grammatikoff, Duisburg, May 17, 2014, YouTube Video

=References=

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