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* [[Root|Root Node]] and the [[Leftmost Node|Leftmost Nodes]] are always PV-nodes
* In [[Principal Variation Search]], PV-nodes are defined by <span style="background-color: rgb(229, 229, 229)">beta-alpha>1</span>
* All [[Sibling nodeNode|Siblings]] of a PV-node are expected Cut-nodes
<span id="CUT"></span>
Assuming a constant [[Branching Factor|branching factor]] of 40, this results in following number of leaves:
{| class="wikitable"|+ number {Number of leaves with depth n and b = 40 |-! depth! worst case! best case! PV ! CUT ! ALL |-! n | style="text-align:center;" | b<span style="vertical-align: super;">n</span>| style="text-align:center;" | b<span style="vertical-align: super;">⌈n/2⌉</span> + b<span style="vertical-align: super;">⌊n/2⌋</span> - 1| style="text-align:right;" | 1 | style="text-align:center;" | b<span style="vertical-align: super;">⌈n/2⌉</span> - 1| style="text-align:center;" | b<span style="vertical-align: super;">⌊n/2⌋</span> - 1|-! 0 | style="text-align:right;" | 1 | style="text-align:right;" | 1 | style="text-align:right;" | 1 | style="text-align:right;" | 0 | style="text-align:right;" | 0 |-! 1 | style="text-align:right;" | 40 | style="text-align:right;" | 40 | style="text-align:right;" | 1 | style="text-align:right;" | 39 | style="text-align:right;" | 0 |-! 2 | style="text-align:right;" | 1,600 | style="text-align:right;" | 79 | style="text-align:right;" | 1 | style="text-align:right;" | 39 | style="text-align:right;" | 39 |-! 3 | style="text-align:right;" | 64,000 | style="text-align:right;" | 1,639 | style="text-align:right;" | 1 | style="text-align:right;" | 1,599 | style="text-align:right;" | 39 |-! 4 | style="text-align:right;" | 2,560,000 | style="text-align:right;" | 3,199 | style="text-align:right;" | 1 | style="text-align:right;" | 1,599 | style="text-align:right;" | 1,599 |-! 5 | style="text-align:right;" | 102,400,000 | style="text-align:right;" | 65,569 | style="text-align:right;" | 1 | style="text-align:right;" | 63,999 | style="text-align:right;" | 1,599 |-! 6 | style="text-align:right;" | 4,096,000,000 | style="text-align:right;" | 127,999 | style="text-align:right;" | 1 | style="text-align:right;" | 63,999 | style="text-align:right;" | 63,999 |-! 7 | style="text-align:right;" | 163,840,000,000 | style="text-align:right;" | 2,623,999 | style="text-align:right;" | 1 | style="text-align:right;" | 2,559,999 | style="text-align:right;" | 63,999 |-! 8 | style="text-align:right;" | 6,553,600,000,000 | style="text-align:right;" | 5,119,999 | style="text-align:right;" | 1 | style="text-align:right;" | 2,559,999 | style="text-align:right;" | 2,559,999 |Leaves}}
=Quotes=
[[Robert Hyatt]] on the distinction between [[Node Types#ALL|ALL-]] and [[Node Types#CUT|CUT-nodes]] <ref>[http://www.talkchess.com/forum/viewtopic.php?topic_view=threads&p=398061&t=38317 Re: "CUT" vs "ALL" nodes] by [[Robert Hyatt]], [[CCC]], March 08, 2011</ref>:
=See also=
* [[Alpha-Beta]]
* [[Stephen F. Wheeler#Alpha-Beta Benchmark|Alpha-Beta Benchmark]] by [[Stephen F. Wheeler]]
* [[Enhanced Forward Pruning]]
* [[Internal Iterative Deepening]]
==2000 ...==
* [https://www.stmintz.com/ccc/index.php?id=285939 ALL node definition] by [[Alvaro Cardoso]], [[CCC]], February 21, 2003
* [https://www.stmintz.com/ccc/index.php?id=354012 Fruit - Question for Fabien] by [[Dan Honeycutt]], [[CCC]], March 11, 2004 » [[Fruit]], [[Transposition Table]], [[Principal variationVariation]], [[Principal Variation Search]]
: [https://www.stmintz.com/ccc/index.php?id=354016 Re: Fruit - Question for Fabien] by [[Fabien Letouzey]], [[CCC]], March 11, 2004
* [http://www.open-aurec.com/wbforum/viewtopic.php?f=4&t=171&start=143 Re: Attack table] by [[Zach Wegner]], [[Computer Chess Forums|Winboard Forum]], October 22, 2004 » [[Attack and Defend Maps]]
* [http://www.talkchess.com/forum/viewtopic.php?t=59682 Recognizing PV nodes] by [[Martin Fierz]], [[CCC]], March 29, 2016
* [http://www.talkchess.com/forum/viewtopic.php?t=62890 What is wrong with doing Nulls & ttcuts in a pv node ?] by [[Mahmoud Uthman]], [[CCC]], January 21, 2017 » [[Null Move Pruning]], [[Node Types#PV|PV-Nodes]], [[Transposition Table]]
* [http://www.talkchess.com/forum/viewtopic.php?t=65477 cut nodes] by [[Folkert van Heusden]], [[CCC]], October 18, 2017 » [[Node Types#CUT|Cut-Nodes]]* [http://www.talkchess.com/forum3/viewtopic.php?f=7&t=69510 Pruning at PV nodes?] by [[Mahmoud Uthman]], [[CCC]], January 06, 2019 » [[Pruning]], [[#PV|PV-Nodes]]
=External Links=
=References=
<references />
'''[[Node|Up one Level]]'''
[[Category:Hyatt Quotes]]
