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R is a common name for a constant or variable signifying depth reduction used in the Null Move Pruning ^[1], Null Move Reductions and independently in Multi-Cut ^[2]. In many null move implementations it is either 2 or 3, the exact formula being depth - R - 1.

Variable Reduction

When R becomes a variable, then we say that a program uses adaptive null move pruning, first described by Ernst A. Heinz ^[3], using R=3 when normal search depth exceeds 6 plies and R=2 otherwise, while more recently most engines account increased search depth with greater reductions ^[4].

Forum Posts

1997 ...

• Null move depth reductions by Tom King, rgcc, February 02, 1997
• Null move reductions by Roberto Waldteufel, CCC, October 04, 1998

2000 ...

• Null move R=2 vs Null move R=2/3 by Tom King, CCC, August 09, 2001
• Null-Move: Difference between R = 2 and R = 3 in action by Omid David, CCC, July 11, 2002
• Smooth scaling -- an explanation by Dann Corbit, CCC, December 30, 2009

2010 ...

• Figuring out the R factor by Michael Sherwin, CCC, January 03, 2010
• How much to reduce ? by Henk van den Belt, CCC, October 03, 2013 » Late Move Reductions
• Reductions by Harm Geert Muller, CCC, May 22, 2016 » Late Move Reductions
• Calculating R value for Null Move by Andrew Grant, CCC, June 23, 2016
• Rethinking r in null move by Michael Sherwin, CCC, August 18, 2017
• Update on null move and LMR by Michael Sherwin, CCC, October 01, 2017 » RomiChess

References

1. ^ Chrilly Donninger. (1993). Null Move and Deep Search: Selective-Search Heuristics for Obtuse Chess Programs. ICCA Journal, Vol. 16, No. 3
2. ^ Yngvi Björnsson, Tony Marsland (2001). Multi-cut Alpha-Beta Pruning in Game Tree Search. Theoretical Computer Science, Vol. 252
3. ^ Ernst A. Heinz. (1999). Adaptive null-move pruning. ICCA Journal, Vol. 22, No 3
4. ^ Rethinking r in null move by Michael Sherwin, CCC, August 18, 2017

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