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'''[[Main Page|Home]] * [[Chess]] * [[Pieces]] * Influence Quantity'''
[[FILE:SamuelBakIntruder.jpg|border|right|thumb|link=http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bd0|[[Arts#Bak|Samuel Bak]] - Intruder <ref>[http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bd0 Chess in the Art of Samuel Bak] [http://chgs.elevator.umn.edu/ Center for Holocaust & Genocide Studies], [https://en.wikipedia.org/wiki/University_of_Minnesota University of Minnesota]</ref> ]]
The '''influence quantity''' of pieces is defined by their number of unique [[Moves|moves]] with respect to their [[Origin Square|from]]- and [[Target Square|to-square]] coordinates, the [https://en.wikipedia.org/wiki/Cardinality cardinality] of the set of all possible moves, or [[Mobility#TheValueofReachingaSquare|potential, global]] [[Mobility|mobility]] <ref>[[Dan Heisman]] ('''1990, 1999, 2010, 2015''').''[http://www.danheisman.com/elements-of-positional-evaluation.html The Positional Elements of Chess]''. Russell Enterprises</ref>. It might be used to enumerate and [[Encoding Moves|encode]] all those moves, i.e. associating each move, per piece and in total, with a unique number for [[Hash Table#MinimalPerfectHashing|minimal perfect hashing]] opposed to intermittent [[Butterfly Boards|Butterfly boards]].
For instance a [[Pawn|pawn]] (including [[Promotions|promotions]]) has 48 (8*6) single pushes and 84 (2*7*6) [[Captures|captures]], plus 8 possible double pushes on each [[Files|file]], which results in a influence quantity of 140 of either white or black pawns.The influence quantities of all pieces are divisible by four times seven (28), excluding pawn and [[King|king]] even by sixteen times seven (112). While obviously the number of [[Queen|queen]] quantities is the sum of [[Rook|rook]]- and [[Bishop|bishop]] quantities, it is at the first glance somehow surprising that the rook quantity is the sum of bishop- and [[Knight|knight]] quantities.
=Moves per Origin=
Following table gives the distinct number of moves per piece and [[Origin Square|origin square]] and their sums from the lower left quarter of a [[Chessboard|board]] (a1-d4) and in total for the whole board:
<pre>
Knight King Bishop Rook Queen
4 6 8 8 5 8 8 8 7 9 11 13 14 14 14 14 21 23 25 27
4 6 8 8 5 8 8 8 7 9 11 11 14 14 14 14 21 23 25 25
3 4 6 6 5 8 8 8 7 9 9 9 14 14 14 14 21 23 23 23
2 3 4 4 3 5 5 5 7 7 7 7 14 14 14 14 21 21 21 21
sum 13 19 26 26 18 29 29 29 28 34 38 40 56 56 56 56 84 90 94 96
84 = 3 * 4*7 105 = 3 *5*7 140 = 5 * 4*7 224 = 8 * 4*7 364 = 13 * 4*7
336 420 560 896 1456
</pre>
==Whole Board Diagrams==
Whole board tables cover pawn, knight, king and sliding pieces, and their [[Files|file]]-, [[Ranks|rank]] and total sums:
<pre>
White pawn total white pawn a2 white pawn d2
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| | | | | | | | | | | | | | | | | | | | | | | | | | |
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | 3 | 3 | 3 | | | 17 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | 3 | 3 | | | | 14 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | 3 | | | | | 11 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | | 20
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | | | | | | 8 | | 3 | 3 | 3 | 3 | 3 | | | 15
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | | | | | | | 5 | | | 3 | 3 | 3 | | | | 9
| 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 30 | 3 | | | | | | | | 3 | | | | 4 | | | | | 4
| | | | | | | | | | | | | | | | | | | | | | | | | | |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
13 19 19 19 19 19 19 13 140 13 15 12 9 6 3 58 6 12 15 19 15 12 9 4 92
Knight King
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 2 | 3 | 4 | 4 | 4 | 4 | 3 | 2 | 26 | 3 | 5 | 5 | 5 | 5 | 5 | 5 | 3 | 36
| 3 | 4 | 6 | 6 | 6 | 6 | 4 | 3 | 38 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 3 | 4 | 6 | 6 | 6 | 6 | 4 | 3 | 38 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 2 | 3 | 4 | 4 | 4 | 4 | 3 | 2 | 26 | 3 | 5 | 5 | 5 | 5 | 5 | 5 | 3 | 36
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
26 38 52 52 52 52 38 26 336 36 58 58 58 58 58 58 36 420
Bishop Rook Queen
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 56 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |21 |21 |21 |21 |21 |21 |21 |168
| 7 | 9 | 9 | 9 | 9 | 9 | 9 | 7 | 68 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |23 |23 |23 |23 |23 |21 |180
| 7 | 9 |11 |11 |11 |11 | 9 | 7 | 76 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |25 |25 |25 |23 |21 |188
| 7 | 9 |11 |13 |13 |11 | 9 | 7 | 80 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |27 |27 |25 |23 |21 |192
| 7 | 9 |11 |13 |13 |11 | 9 | 7 | 80 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |27 |27 |25 |23 |21 |192
| 7 | 9 |11 |11 |11 |11 | 9 | 7 | 76 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |25 |25 |25 |23 |21 |188
| 7 | 9 | 9 | 9 | 9 | 9 | 9 | 7 | 68 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |23 |23 |23 |23 |23 |21 |180
| 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 56 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |21 |21 |21 |21 |21 |21 |21 |168
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
56 68 76 80 80 76 68 56 560 112 112 112 112 112 112 112 112 896 168 180 188 192 192 188 180 168 1456
</pre>
==Board Circles==
The [https://en.wikipedia.org/wiki/Concentric concentric] "circles" around the [[Center|center]] with their respective influence sums of sliding pieces:
<pre>
Bishop Circles Rook Circles Queen Circles
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 196 | | 392 | | 588 |
+ +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ +
| | 180 | | | | 280 | | | | 460 | |
+ + +---+---+---+---+ + + + + +---+---+---+---+ + + + + +---+---+---+---+ + +
| | | 132 | | | | | | 168 | | | | | | 300 | | |
+ + + +---+---+ + + + + + + +---+---+ + + + + + + +---+---+ + + +
| | | | 52 | | | | | | | | 56 | | | | | | | | 108 | | | |
+ + + + + + + + + + + + + + + + + + + + + + + +
| | | | 4*13 | | | | | | | | 4*14 | | | | | | | | 4*27 | | | |
+ + + +---+---+ + + + + + + +---+---+ + + + + + + +---+---+ + + +
| | | 12*11 | | | | | | 12*14 | | | | | | 12*25 | | |
+ + +---+---+---+---+ + + + + +---+---+---+---+ + + + + +---+---+---+---+ + +
| | 20* 9 | | | | 20*14 | | | | 20*23 | |
+ +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ +
| 28* 7 | | 28*14 | | 28*21 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
</pre>
<span id="PointValues"></span>
=Quantities and Point Values=
The mentioned move quantities of pawns and pieces only roughly correlate with their [[Point Value|point values]] since the static enumeration of all moves with distinct coordinates does not take into account the reachability of all origin-squares. Only queen and rook can reach any square in at least two moves on the otherwise empty board. Bishop quantities cover all light and dark colored from-squares. While a single bishop is bounded to one square color, its individual influence quantity is therefor divided by two. Also, pawns can only move forward and can not reach each enumerated origin square, which decreases their individual influence accordantly. King and knights can reach every square on the otherwise empty board, but may take more time with respect to [[Distance|distance]] and [[Knight-Distance|knight-distance]].
=Divisibility by Seven=
All influence quantities are divisible by four times seven, thanks to the double pushes. For a rook it is quite obvious, since each of the 64 from squares covers one rank and file each with seven squares left.
{| class="wikitable"
|-
! Piece
! #
! div 4
! div 7
! div 28
|-
! Pawn
| style="text-align:right;" | 140
| style="text-align:right;" | 35
| style="text-align:right;" | 20
| style="text-align:right;" | 5
|-
! Knight
| style="text-align:right;" | 336
| style="text-align:right;" | 84
| style="text-align:right;" | 48
| style="text-align:right;" | 12
|-
! King
| style="text-align:right;" | 420
| style="text-align:right;" | 105
| style="text-align:right;" | 60
| style="text-align:right;" | 15
|-
! Bishops
| style="text-align:right;" | 560
| style="text-align:right;" | 140
| style="text-align:right;" | 80
| style="text-align:right;" | 20
|-
! Bishop
| style="text-align:right;" | 280
| style="text-align:right;" | 70
| style="text-align:right;" | 40
| style="text-align:right;" | 10
|-
! Rook
| style="text-align:right;" | 896
| style="text-align:right;" | 224
| style="text-align:right;" | 128
| style="text-align:right;" | 32
|-
! Queen
| style="text-align:right;" | 1456
| style="text-align:right;" | 364
| style="text-align:right;" | 208
| style="text-align:right;" | 52
|-
! Q | N
| style="text-align:right;" | 1792
| style="text-align:right;" | 448
| style="text-align:right;" | 256
| style="text-align:right;" | 64
|}
<span id="FibonacciSpiral"></span>
=Fibonacci Spiral=
If we only consider pieces with disjoint moves (excluding pawns and king), and the queen as superset of bishop and rook, the influence quantities are even divisible by seven times sixteen, where the remaining quotients from knight to queen are [https://en.wikipedia.org/wiki/Fibonacci_number Fibonacci numbers] as shown by the Fibonacci spiral <ref>[http://library.thinkquest.org/27890/theSeries6a.html The Fibonacci Series - The Series - Fibonacci Spiral In Action]</ref> <ref>The [[Point Value#TheoreticalAttempt|relative piece values]] for {N, B, R, Q} of {3, 5, 8, 15} were mentioned by H. M. Taylor ('''1876'''). ''[http://www.tandfonline.com/doi/abs/10.1080/14786447608639029#.UfEUGXePZlR On the Relative Values of the Pieces in Chess]''. [https://en.wikipedia.org/wiki/Philosophical_Magazine Philosophical Magazine], Series 5, Vol. 1, pp. 221-229 as reported in [[Mathematician#Coxeter|H. S. M. Coxeter]] ('''1940'''). ''Mathematical Recreations and Essays''. pp. 162-165, from the [http://www.gutenberg.org/ebooks/26839 original] by [[Mathematician#WWRouseBall|W. W. Rouse Ball]], [https://en.wikipedia.org/wiki/Macmillan_Publishers Macmillan], as reported by [[Jack Good]] ('''1968'''). ''A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares''. [http://www.doc.ic.ac.uk/~shm/MI/mi2.html Machine Intelligence Vol. 2]</ref> .
{|
|-
| [[FILE:chessfibspirale.jpg|none|border|text-bottom|link=http://www.127jupiter.com/]]
| [[FILE:Yupana 1.png|none|border|text-bottom|270px]]
|-
| Fibonacci spiral <ref>[http://www.127jupiter.com/ Peter Orantek: Encyclopedia of Chess-Prehistory]</ref>
| [https://en.wikipedia.org/wiki/Yupana Yupana], counting tool of the [https://en.wikipedia.org/wiki/Incas Incas]
|}
{| class="wikitable"
|-
! Piece
! covers other pieces
! #
! ÷ (7x16)
|-
!Knight
| style="text-align:center;" | -
| style="text-align:right;" | 336
| style="text-align:right;" | 3
|-
! Bishop
| style="text-align:center;" | queen, king and pawn captures
| style="text-align:right;" | 560
| style="text-align:right;" | 5
|-
!Rook
| style="text-align:center;" | queen, king and pawn pushes
| style="text-align:right;" | 896
| style="text-align:right;" | 8
|-
| colspan="2" | possible queen move coordinates
| style="text-align:right;" | 1456
| style="text-align:right;" | 13
|-
! colspan="2" | possible from-to move coordinates
! 1792
! 16
|}
=Analogy in Astronomy=
In his [https://en.wikipedia.org/wiki/Esotericism esoteric] and [https://en.wikipedia.org/wiki/Pseudoscience pseudo scientific] touched ''Encyclopedia of Chess-Prehistory'', Peter Orantek <ref>[http://www.127jupiter.com/Honors.pdf Peter Orantek: Encyclopedia of Chess-Prehistory - Programming Language Chess]</ref> mentions a possible connection to [https://en.wikipedia.org/wiki/Astronomy astronomy], related to the [https://en.wikipedia.org/wiki/Orbital_period orbital period] of [https://en.wikipedia.org/wiki/Earth Earth] and [https://en.wikipedia.org/wiki/Venus Venus]. The influence quantity of a queen is equivalent to about 4 years (4 x 364 days), while the influence quantity of a rook is equivalent to 224 days x 4 Venus rotations.
{| class="wikitable"
|-
| [[FILE:FullMoon2010.jpg|none|border|text-bottom|240px|link=https://en.wikipedia.org/wiki/Moon]]
| [[FILE:Venus-real color.jpg|none|border|text-bottom|240px|link=https://en.wikipedia.org/wiki/Venus]]
| [[FILE:The Earth seen from Apollo 17.jpg|none|border|text-bottom|240px|link=https://en.wikipedia.org/wiki/Earth]]
|-
| [https://en.wikipedia.org/wiki/Moon Moon]
| [https://en.wikipedia.org/wiki/Venus Venus] 224
| [https://en.wikipedia.org/wiki/Earth Earth] 364
|}
In his German text sample <ref>[http://www.127jupiter.com/Example.pdf Peter 0rantek: Encyclopedia of Chess-Prehistory - Decoded prehistorical books of Chess] (pdf text sample)</ref> , Orantek further elaborates that queen quantities of the four [[Center|center squares]] (four times 27) represent four [https://en.wikipedia.org/wiki/Moon earth moon] rotations, while the three concentric rings around the center might related to various [https://en.wikipedia.org/wiki/Orbital_period synodic periods] of the four [https://en.wikipedia.org/wiki/Terrestrial_planet terrestrial planets]. He associates following [https://en.wikipedia.org/wiki/Prime_number prime numbers] with [https://en.wikipedia.org/wiki/Planet planets] or objects orbiting the [https://en.wikipedia.org/wiki/Sun Sun] <ref>[http://www.127jupiter.com/Contents.pdf Peter 0rantek: Encyclopedia of Chess-Prehistory - Decoded prehistorical books of Chess - Contents] (pdf)</ref> :
{| class="wikitable"
|-
! Prime<br/>number
! Piece
! Engine
! Planet<br/>or Objects
! Symbol
! Orbital period<br/>in days
! Synodic period<br/>in days
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/3_%28number%29 3]
| style="text-align:center;" | [[Knight]]
| style="text-align:center;" | [[Black Knight]]<br/>[[White Knight]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Mercury_%28planet%29 Mercury]
| style="text-align:center;" | [[FILE:Mercury symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 87.9691
| style="text-align:right;" | 115.88
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/5_%28number%29 5]
| style="text-align:center;" | [[Bishop]]
| style="text-align:center;" | [[BlackBishop]]<br/>[[The Crazy Bishop]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Venus Venus]
| style="text-align:center;" | [[FILE:Venus symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | '''224.70069'''
| style="text-align:right;" | 583.92
(579–589)
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/13_%28number%29 13]
| style="text-align:center;" | [[Queen]]
| style="text-align:center;" | [[Queen (engine)|Queen]]<br/>[[Terra]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Earth Earth]
| style="text-align:center;" | [[FILE:Earth symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | '''365.256366'''
| style="text-align:right;" |
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/61_%28number%29 61]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Mars Mars]
| style="text-align:center;" | [[FILE:Mars symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 686.971
| style="text-align:right;" | 779.96
(764–811)
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/89_%28number%29 89]
| style="text-align:center;" |
| style="text-align:center;" | [[Anubis]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Asteroid Asteroids]
| style="text-align:center;" |
| style="text-align:right;" |
| style="text-align:right;" |
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/127_%28number%29 127]
| style="text-align:center;" |
| style="text-align:center;" | [[Jupiter]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Jupiter Jupiter]
| style="text-align:center;" | [[FILE:Jupiter symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 4,331.572
| style="text-align:right;" | 398.88
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/167_%28number%29 167]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Charon_%28moon%29 Charon]
| style="text-align:center;" |
| style="text-align:right;" |
| style="text-align:right;" |
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/181_%28number%29 181]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Saturn Saturn]
| style="text-align:center;" | [[FILE:Saturn symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 10,759.220
| style="text-align:right;" | 378.09
|-
| style="text-align:right;" | 307
| style="text-align:center;" |
| style="text-align:center;" | [[Chiron]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/2060_Chiron Chiron]
| style="text-align:center;" | [[FILE:Chiron symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 18,539.000
| style="text-align:right;" |
|-
| style="text-align:right;" | 487
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Uranus Uranus]
| style="text-align:center;" | [[FILE:Uranus symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 30,799.095
| style="text-align:right;" | 369.66
|-
| style="text-align:right;" | 499
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/5145_Pholus Pholus]
| style="text-align:center;" |
| style="text-align:right;" | 33,547.410
| style="text-align:right;" |
|-
| style="text-align:right;" | 547
| style="text-align:center;" |
| style="text-align:center;" | [[Neptune]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Neptune Neptune]
| style="text-align:center;" | [[FILE:Neptune symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 60,190.000
| style="text-align:right;" | 367.49
|-
| style="text-align:right;" | 761
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Pluto Pluto]
| style="text-align:center;" | [[FILE:Pluto symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 90,613.305
| style="text-align:right;" | 366.73
|-
| style="text-align:right;" | 1307
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Planets_beyond_Neptune#Planet_X Transpluto]
| style="text-align:center;" |
| style="text-align:right;" |
| style="text-align:right;" |
|}
=See also=
* [[Butterfly Boards]]
* [[Dumb7Fill]]
* [[Encoding Moves]]
: [[Encoding Moves#Enumeration|Move Enumeration]]
* [[Evaluation of Pieces]]
* [[Material]]
* [[Mobility]]
* [[Point Value]]
* [[Table-driven Move Generation]]
=Publications=
* H. M. Taylor ('''1876'''). ''[http://www.tandfonline.com/doi/abs/10.1080/14786447608639029#.UfEUGXePZlR On the Relative Values of the Pieces in Chess]''. [https://en.wikipedia.org/wiki/Philosophical_Magazine Philosophical Magazine], Series 5, Vol. 1, pp. 221-229
* [[Mathematician#Coxeter|H. S. M. Coxeter]] ('''1940'''). ''Mathematical Recreations and Essays''. from the [http://www.gutenberg.org/ebooks/26839 original] by [[Mathematician#WWRouseBall|W. W. Rouse Ball]], [https://en.wikipedia.org/wiki/Macmillan_Publishers Macmillan]
* [[Jack Good]] ('''1968'''). ''A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares''. [http://www.doc.ic.ac.uk/~shm/MI/mi2.html Machine Intelligence Vol. 2]
* [[Dan Heisman]] ('''1990, 1999, 2010, 2015''').''[http://www.danheisman.com/elements-of-positional-evaluation.html The Positional Elements of Chess]''. Russell Enterprises
* Peter Orantek ('''2008'''). ''[http://www.127jupiter.com/ Encyclopedia of Chess-Prehistory - Programming Language Chess]''.
=Forum Posts=
* [https://groups.google.com/d/msg/rec.games.chess/efBhsZU3J1g/fC7rxV5yuycJ Value of the pieces] by Joost de Heer, [[Computer Chess Forums|rgc]], February 01, 1995
* [http://www.open-chess.org/viewtopic.php?f=5&t=171 Material/Mobility] by [[Franklin Titus|kingliveson]], [[Computer Chess Forums|OpenChess Forum]], June 17, 2010
=External Links=
* [https://en.wikipedia.org/wiki/7_%28number%29 7 from Wikipedia]
* [https://en.wikipedia.org/wiki/Seven-day_week Seven-day week from Wikipedia]
* [[Videos#If|If]] - [https://en.wikipedia.org/wiki/If_3 Fibonacci's Number] (1971), [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: {{#evu:https://www.youtube.com/watch?v=GXaefhbtU2k|alignment=left|valignment=top}}
* [[Videos#FrankZappa|Frank Zappa]] and [https://en.wikipedia.org/wiki/The_Mothers_of_Invention The Mothers of Invention], [https://en.wikipedia.org/wiki/Inca_Roads_(song) Inca Roads], 1974, ([https://en.wikipedia.org/wiki/A_Token_of_His_Extreme_(Soundtrack) A Token of His Extreme]), [https://en.wikipedia.org/wiki/YouTube YouTube] Video <ref>[https://en.wikipedia.org/wiki/Clay_animation Clay animation] by [https://en.wikipedia.org/wiki/Bruce_Bickford_(animator) Bruce Bickford]</ref> <ref>[http://adeucefortheskycap.blogspot.com/2007/10/eulogy-for-kelly-lowe-by-michael-king.html Kelly Fisher Lowe] ('''2006'''). ''[http://www.afka.net/Books/lowe.htm The Words and Music of Frank Zappa]''. Praeger Publishers, pp. 119 ''The lyrics to "Inca Roads" are absurdist in the extreme. They veer wildly from spacey - "Did a vehicle / Come from somewhere out there / Just to land in the Andes?," which both [https://en.wikipedia.org/wiki/Ben_Watson_(music_writer) Watson] and [http://www.beefheart.com/tag/kevin-courrier/ Courrier] claim Zappa's satire on the popular-at-the-time book [https://en.wikipedia.org/wiki/Chariots_of_the_Gods%3F Chariots of the Gods?]'' ...</ref> <ref>[https://en.wikipedia.org/wiki/Nazca_lines Nazca Lines from Wikipedia]</ref>
: [[Videos#FrankZappa|Frank Zappa]], [[Videos#GeorgeDuke|George Duke]], [https://en.wikipedia.org/wiki/Napoleon_Murphy_Brock Napoleon Murphy Brock], [https://en.wikipedia.org/wiki/Chester_Thompson Chester Thompson], [https://en.wikipedia.org/wiki/Tom_Fowler_%28musician%29 Tom Fowler], [https://en.wikipedia.org/wiki/Ruth_Underwood Ruth Underwood], [https://en.wikipedia.org/wiki/Captain_Beefheart Captain Beefheart]
: {{#evu:https://www.youtube.com/watch?v=wqp71DOJ3aY|alignment=left|valignment=top}}
=References=
<references />
'''[[Pieces|Up one Level]]'''
[[Category:Samuel Bak]][[Category:Frank Zappa]]
[[FILE:SamuelBakIntruder.jpg|border|right|thumb|link=http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bd0|[[Arts#Bak|Samuel Bak]] - Intruder <ref>[http://chgs.elevator.umn.edu/asset/viewAsset/57f3b6787d58ae5f74bf8ba9#57f3b6d77d58ae5574bf8bd0 Chess in the Art of Samuel Bak] [http://chgs.elevator.umn.edu/ Center for Holocaust & Genocide Studies], [https://en.wikipedia.org/wiki/University_of_Minnesota University of Minnesota]</ref> ]]
The '''influence quantity''' of pieces is defined by their number of unique [[Moves|moves]] with respect to their [[Origin Square|from]]- and [[Target Square|to-square]] coordinates, the [https://en.wikipedia.org/wiki/Cardinality cardinality] of the set of all possible moves, or [[Mobility#TheValueofReachingaSquare|potential, global]] [[Mobility|mobility]] <ref>[[Dan Heisman]] ('''1990, 1999, 2010, 2015''').''[http://www.danheisman.com/elements-of-positional-evaluation.html The Positional Elements of Chess]''. Russell Enterprises</ref>. It might be used to enumerate and [[Encoding Moves|encode]] all those moves, i.e. associating each move, per piece and in total, with a unique number for [[Hash Table#MinimalPerfectHashing|minimal perfect hashing]] opposed to intermittent [[Butterfly Boards|Butterfly boards]].
For instance a [[Pawn|pawn]] (including [[Promotions|promotions]]) has 48 (8*6) single pushes and 84 (2*7*6) [[Captures|captures]], plus 8 possible double pushes on each [[Files|file]], which results in a influence quantity of 140 of either white or black pawns.The influence quantities of all pieces are divisible by four times seven (28), excluding pawn and [[King|king]] even by sixteen times seven (112). While obviously the number of [[Queen|queen]] quantities is the sum of [[Rook|rook]]- and [[Bishop|bishop]] quantities, it is at the first glance somehow surprising that the rook quantity is the sum of bishop- and [[Knight|knight]] quantities.
=Moves per Origin=
Following table gives the distinct number of moves per piece and [[Origin Square|origin square]] and their sums from the lower left quarter of a [[Chessboard|board]] (a1-d4) and in total for the whole board:
<pre>
Knight King Bishop Rook Queen
4 6 8 8 5 8 8 8 7 9 11 13 14 14 14 14 21 23 25 27
4 6 8 8 5 8 8 8 7 9 11 11 14 14 14 14 21 23 25 25
3 4 6 6 5 8 8 8 7 9 9 9 14 14 14 14 21 23 23 23
2 3 4 4 3 5 5 5 7 7 7 7 14 14 14 14 21 21 21 21
sum 13 19 26 26 18 29 29 29 28 34 38 40 56 56 56 56 84 90 94 96
84 = 3 * 4*7 105 = 3 *5*7 140 = 5 * 4*7 224 = 8 * 4*7 364 = 13 * 4*7
336 420 560 896 1456
</pre>
==Whole Board Diagrams==
Whole board tables cover pawn, knight, king and sliding pieces, and their [[Files|file]]-, [[Ranks|rank]] and total sums:
<pre>
White pawn total white pawn a2 white pawn d2
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| | | | | | | | | | | | | | | | | | | | | | | | | | |
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | 3 | 3 | 3 | | | 17 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | 3 | 3 | | | | 14 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | 3 | | | | | 11 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | | 20
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | 3 | | | | | | 8 | | 3 | 3 | 3 | 3 | 3 | | | 15
| 2 | 3 | 3 | 3 | 3 | 3 | 3 | 2 | 22 | 2 | 3 | | | | | | | 5 | | | 3 | 3 | 3 | | | | 9
| 3 | 4 | 4 | 4 | 4 | 4 | 4 | 3 | 30 | 3 | | | | | | | | 3 | | | | 4 | | | | | 4
| | | | | | | | | | | | | | | | | | | | | | | | | | |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
13 19 19 19 19 19 19 13 140 13 15 12 9 6 3 58 6 12 15 19 15 12 9 4 92
Knight King
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 2 | 3 | 4 | 4 | 4 | 4 | 3 | 2 | 26 | 3 | 5 | 5 | 5 | 5 | 5 | 5 | 3 | 36
| 3 | 4 | 6 | 6 | 6 | 6 | 4 | 3 | 38 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 4 | 6 | 8 | 8 | 8 | 8 | 6 | 4 | 52 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 3 | 4 | 6 | 6 | 6 | 6 | 4 | 3 | 38 | 5 | 8 | 8 | 8 | 8 | 8 | 8 | 5 | 58
| 2 | 3 | 4 | 4 | 4 | 4 | 3 | 2 | 26 | 3 | 5 | 5 | 5 | 5 | 5 | 5 | 3 | 36
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
26 38 52 52 52 52 38 26 336 36 58 58 58 58 58 58 36 420
Bishop Rook Queen
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 56 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |21 |21 |21 |21 |21 |21 |21 |168
| 7 | 9 | 9 | 9 | 9 | 9 | 9 | 7 | 68 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |23 |23 |23 |23 |23 |21 |180
| 7 | 9 |11 |11 |11 |11 | 9 | 7 | 76 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |25 |25 |25 |23 |21 |188
| 7 | 9 |11 |13 |13 |11 | 9 | 7 | 80 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |27 |27 |25 |23 |21 |192
| 7 | 9 |11 |13 |13 |11 | 9 | 7 | 80 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |27 |27 |25 |23 |21 |192
| 7 | 9 |11 |11 |11 |11 | 9 | 7 | 76 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |25 |25 |25 |25 |23 |21 |188
| 7 | 9 | 9 | 9 | 9 | 9 | 9 | 7 | 68 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |23 |23 |23 |23 |23 |23 |21 |180
| 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 56 |14 |14 |14 |14 |14 |14 |14 |14 |112 |21 |21 |21 |21 |21 |21 |21 |21 |168
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
56 68 76 80 80 76 68 56 560 112 112 112 112 112 112 112 112 896 168 180 188 192 192 188 180 168 1456
</pre>
==Board Circles==
The [https://en.wikipedia.org/wiki/Concentric concentric] "circles" around the [[Center|center]] with their respective influence sums of sliding pieces:
<pre>
Bishop Circles Rook Circles Queen Circles
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 196 | | 392 | | 588 |
+ +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ +
| | 180 | | | | 280 | | | | 460 | |
+ + +---+---+---+---+ + + + + +---+---+---+---+ + + + + +---+---+---+---+ + +
| | | 132 | | | | | | 168 | | | | | | 300 | | |
+ + + +---+---+ + + + + + + +---+---+ + + + + + + +---+---+ + + +
| | | | 52 | | | | | | | | 56 | | | | | | | | 108 | | | |
+ + + + + + + + + + + + + + + + + + + + + + + +
| | | | 4*13 | | | | | | | | 4*14 | | | | | | | | 4*27 | | | |
+ + + +---+---+ + + + + + + +---+---+ + + + + + + +---+---+ + + +
| | | 12*11 | | | | | | 12*14 | | | | | | 12*25 | | |
+ + +---+---+---+---+ + + + + +---+---+---+---+ + + + + +---+---+---+---+ + +
| | 20* 9 | | | | 20*14 | | | | 20*23 | |
+ +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ + + +---+---+---+---+---+---+ +
| 28* 7 | | 28*14 | | 28*21 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
</pre>
<span id="PointValues"></span>
=Quantities and Point Values=
The mentioned move quantities of pawns and pieces only roughly correlate with their [[Point Value|point values]] since the static enumeration of all moves with distinct coordinates does not take into account the reachability of all origin-squares. Only queen and rook can reach any square in at least two moves on the otherwise empty board. Bishop quantities cover all light and dark colored from-squares. While a single bishop is bounded to one square color, its individual influence quantity is therefor divided by two. Also, pawns can only move forward and can not reach each enumerated origin square, which decreases their individual influence accordantly. King and knights can reach every square on the otherwise empty board, but may take more time with respect to [[Distance|distance]] and [[Knight-Distance|knight-distance]].
=Divisibility by Seven=
All influence quantities are divisible by four times seven, thanks to the double pushes. For a rook it is quite obvious, since each of the 64 from squares covers one rank and file each with seven squares left.
{| class="wikitable"
|-
! Piece
! #
! div 4
! div 7
! div 28
|-
! Pawn
| style="text-align:right;" | 140
| style="text-align:right;" | 35
| style="text-align:right;" | 20
| style="text-align:right;" | 5
|-
! Knight
| style="text-align:right;" | 336
| style="text-align:right;" | 84
| style="text-align:right;" | 48
| style="text-align:right;" | 12
|-
! King
| style="text-align:right;" | 420
| style="text-align:right;" | 105
| style="text-align:right;" | 60
| style="text-align:right;" | 15
|-
! Bishops
| style="text-align:right;" | 560
| style="text-align:right;" | 140
| style="text-align:right;" | 80
| style="text-align:right;" | 20
|-
! Bishop
| style="text-align:right;" | 280
| style="text-align:right;" | 70
| style="text-align:right;" | 40
| style="text-align:right;" | 10
|-
! Rook
| style="text-align:right;" | 896
| style="text-align:right;" | 224
| style="text-align:right;" | 128
| style="text-align:right;" | 32
|-
! Queen
| style="text-align:right;" | 1456
| style="text-align:right;" | 364
| style="text-align:right;" | 208
| style="text-align:right;" | 52
|-
! Q | N
| style="text-align:right;" | 1792
| style="text-align:right;" | 448
| style="text-align:right;" | 256
| style="text-align:right;" | 64
|}
<span id="FibonacciSpiral"></span>
=Fibonacci Spiral=
If we only consider pieces with disjoint moves (excluding pawns and king), and the queen as superset of bishop and rook, the influence quantities are even divisible by seven times sixteen, where the remaining quotients from knight to queen are [https://en.wikipedia.org/wiki/Fibonacci_number Fibonacci numbers] as shown by the Fibonacci spiral <ref>[http://library.thinkquest.org/27890/theSeries6a.html The Fibonacci Series - The Series - Fibonacci Spiral In Action]</ref> <ref>The [[Point Value#TheoreticalAttempt|relative piece values]] for {N, B, R, Q} of {3, 5, 8, 15} were mentioned by H. M. Taylor ('''1876'''). ''[http://www.tandfonline.com/doi/abs/10.1080/14786447608639029#.UfEUGXePZlR On the Relative Values of the Pieces in Chess]''. [https://en.wikipedia.org/wiki/Philosophical_Magazine Philosophical Magazine], Series 5, Vol. 1, pp. 221-229 as reported in [[Mathematician#Coxeter|H. S. M. Coxeter]] ('''1940'''). ''Mathematical Recreations and Essays''. pp. 162-165, from the [http://www.gutenberg.org/ebooks/26839 original] by [[Mathematician#WWRouseBall|W. W. Rouse Ball]], [https://en.wikipedia.org/wiki/Macmillan_Publishers Macmillan], as reported by [[Jack Good]] ('''1968'''). ''A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares''. [http://www.doc.ic.ac.uk/~shm/MI/mi2.html Machine Intelligence Vol. 2]</ref> .
{|
|-
| [[FILE:chessfibspirale.jpg|none|border|text-bottom|link=http://www.127jupiter.com/]]
| [[FILE:Yupana 1.png|none|border|text-bottom|270px]]
|-
| Fibonacci spiral <ref>[http://www.127jupiter.com/ Peter Orantek: Encyclopedia of Chess-Prehistory]</ref>
| [https://en.wikipedia.org/wiki/Yupana Yupana], counting tool of the [https://en.wikipedia.org/wiki/Incas Incas]
|}
{| class="wikitable"
|-
! Piece
! covers other pieces
! #
! ÷ (7x16)
|-
!Knight
| style="text-align:center;" | -
| style="text-align:right;" | 336
| style="text-align:right;" | 3
|-
! Bishop
| style="text-align:center;" | queen, king and pawn captures
| style="text-align:right;" | 560
| style="text-align:right;" | 5
|-
!Rook
| style="text-align:center;" | queen, king and pawn pushes
| style="text-align:right;" | 896
| style="text-align:right;" | 8
|-
| colspan="2" | possible queen move coordinates
| style="text-align:right;" | 1456
| style="text-align:right;" | 13
|-
! colspan="2" | possible from-to move coordinates
! 1792
! 16
|}
=Analogy in Astronomy=
In his [https://en.wikipedia.org/wiki/Esotericism esoteric] and [https://en.wikipedia.org/wiki/Pseudoscience pseudo scientific] touched ''Encyclopedia of Chess-Prehistory'', Peter Orantek <ref>[http://www.127jupiter.com/Honors.pdf Peter Orantek: Encyclopedia of Chess-Prehistory - Programming Language Chess]</ref> mentions a possible connection to [https://en.wikipedia.org/wiki/Astronomy astronomy], related to the [https://en.wikipedia.org/wiki/Orbital_period orbital period] of [https://en.wikipedia.org/wiki/Earth Earth] and [https://en.wikipedia.org/wiki/Venus Venus]. The influence quantity of a queen is equivalent to about 4 years (4 x 364 days), while the influence quantity of a rook is equivalent to 224 days x 4 Venus rotations.
{| class="wikitable"
|-
| [[FILE:FullMoon2010.jpg|none|border|text-bottom|240px|link=https://en.wikipedia.org/wiki/Moon]]
| [[FILE:Venus-real color.jpg|none|border|text-bottom|240px|link=https://en.wikipedia.org/wiki/Venus]]
| [[FILE:The Earth seen from Apollo 17.jpg|none|border|text-bottom|240px|link=https://en.wikipedia.org/wiki/Earth]]
|-
| [https://en.wikipedia.org/wiki/Moon Moon]
| [https://en.wikipedia.org/wiki/Venus Venus] 224
| [https://en.wikipedia.org/wiki/Earth Earth] 364
|}
In his German text sample <ref>[http://www.127jupiter.com/Example.pdf Peter 0rantek: Encyclopedia of Chess-Prehistory - Decoded prehistorical books of Chess] (pdf text sample)</ref> , Orantek further elaborates that queen quantities of the four [[Center|center squares]] (four times 27) represent four [https://en.wikipedia.org/wiki/Moon earth moon] rotations, while the three concentric rings around the center might related to various [https://en.wikipedia.org/wiki/Orbital_period synodic periods] of the four [https://en.wikipedia.org/wiki/Terrestrial_planet terrestrial planets]. He associates following [https://en.wikipedia.org/wiki/Prime_number prime numbers] with [https://en.wikipedia.org/wiki/Planet planets] or objects orbiting the [https://en.wikipedia.org/wiki/Sun Sun] <ref>[http://www.127jupiter.com/Contents.pdf Peter 0rantek: Encyclopedia of Chess-Prehistory - Decoded prehistorical books of Chess - Contents] (pdf)</ref> :
{| class="wikitable"
|-
! Prime<br/>number
! Piece
! Engine
! Planet<br/>or Objects
! Symbol
! Orbital period<br/>in days
! Synodic period<br/>in days
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/3_%28number%29 3]
| style="text-align:center;" | [[Knight]]
| style="text-align:center;" | [[Black Knight]]<br/>[[White Knight]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Mercury_%28planet%29 Mercury]
| style="text-align:center;" | [[FILE:Mercury symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 87.9691
| style="text-align:right;" | 115.88
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/5_%28number%29 5]
| style="text-align:center;" | [[Bishop]]
| style="text-align:center;" | [[BlackBishop]]<br/>[[The Crazy Bishop]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Venus Venus]
| style="text-align:center;" | [[FILE:Venus symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | '''224.70069'''
| style="text-align:right;" | 583.92
(579–589)
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/13_%28number%29 13]
| style="text-align:center;" | [[Queen]]
| style="text-align:center;" | [[Queen (engine)|Queen]]<br/>[[Terra]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Earth Earth]
| style="text-align:center;" | [[FILE:Earth symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | '''365.256366'''
| style="text-align:right;" |
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/61_%28number%29 61]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Mars Mars]
| style="text-align:center;" | [[FILE:Mars symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 686.971
| style="text-align:right;" | 779.96
(764–811)
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/89_%28number%29 89]
| style="text-align:center;" |
| style="text-align:center;" | [[Anubis]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Asteroid Asteroids]
| style="text-align:center;" |
| style="text-align:right;" |
| style="text-align:right;" |
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/127_%28number%29 127]
| style="text-align:center;" |
| style="text-align:center;" | [[Jupiter]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Jupiter Jupiter]
| style="text-align:center;" | [[FILE:Jupiter symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 4,331.572
| style="text-align:right;" | 398.88
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/167_%28number%29 167]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Charon_%28moon%29 Charon]
| style="text-align:center;" |
| style="text-align:right;" |
| style="text-align:right;" |
|-
| style="text-align:right;" | [https://en.wikipedia.org/wiki/181_%28number%29 181]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Saturn Saturn]
| style="text-align:center;" | [[FILE:Saturn symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 10,759.220
| style="text-align:right;" | 378.09
|-
| style="text-align:right;" | 307
| style="text-align:center;" |
| style="text-align:center;" | [[Chiron]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/2060_Chiron Chiron]
| style="text-align:center;" | [[FILE:Chiron symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 18,539.000
| style="text-align:right;" |
|-
| style="text-align:right;" | 487
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Uranus Uranus]
| style="text-align:center;" | [[FILE:Uranus symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 30,799.095
| style="text-align:right;" | 369.66
|-
| style="text-align:right;" | 499
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/5145_Pholus Pholus]
| style="text-align:center;" |
| style="text-align:right;" | 33,547.410
| style="text-align:right;" |
|-
| style="text-align:right;" | 547
| style="text-align:center;" |
| style="text-align:center;" | [[Neptune]]
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Neptune Neptune]
| style="text-align:center;" | [[FILE:Neptune symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 60,190.000
| style="text-align:right;" | 367.49
|-
| style="text-align:right;" | 761
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Pluto Pluto]
| style="text-align:center;" | [[FILE:Pluto symbol.svg|none|border|text-bottom|x32px]]
| style="text-align:right;" | 90,613.305
| style="text-align:right;" | 366.73
|-
| style="text-align:right;" | 1307
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | [https://en.wikipedia.org/wiki/Planets_beyond_Neptune#Planet_X Transpluto]
| style="text-align:center;" |
| style="text-align:right;" |
| style="text-align:right;" |
|}
=See also=
* [[Butterfly Boards]]
* [[Dumb7Fill]]
* [[Encoding Moves]]
: [[Encoding Moves#Enumeration|Move Enumeration]]
* [[Evaluation of Pieces]]
* [[Material]]
* [[Mobility]]
* [[Point Value]]
* [[Table-driven Move Generation]]
=Publications=
* H. M. Taylor ('''1876'''). ''[http://www.tandfonline.com/doi/abs/10.1080/14786447608639029#.UfEUGXePZlR On the Relative Values of the Pieces in Chess]''. [https://en.wikipedia.org/wiki/Philosophical_Magazine Philosophical Magazine], Series 5, Vol. 1, pp. 221-229
* [[Mathematician#Coxeter|H. S. M. Coxeter]] ('''1940'''). ''Mathematical Recreations and Essays''. from the [http://www.gutenberg.org/ebooks/26839 original] by [[Mathematician#WWRouseBall|W. W. Rouse Ball]], [https://en.wikipedia.org/wiki/Macmillan_Publishers Macmillan]
* [[Jack Good]] ('''1968'''). ''A Five-Year Plan for Automatic Chess - Appendix F. The Value of the Pieces and Squares''. [http://www.doc.ic.ac.uk/~shm/MI/mi2.html Machine Intelligence Vol. 2]
* [[Dan Heisman]] ('''1990, 1999, 2010, 2015''').''[http://www.danheisman.com/elements-of-positional-evaluation.html The Positional Elements of Chess]''. Russell Enterprises
* Peter Orantek ('''2008'''). ''[http://www.127jupiter.com/ Encyclopedia of Chess-Prehistory - Programming Language Chess]''.
=Forum Posts=
* [https://groups.google.com/d/msg/rec.games.chess/efBhsZU3J1g/fC7rxV5yuycJ Value of the pieces] by Joost de Heer, [[Computer Chess Forums|rgc]], February 01, 1995
* [http://www.open-chess.org/viewtopic.php?f=5&t=171 Material/Mobility] by [[Franklin Titus|kingliveson]], [[Computer Chess Forums|OpenChess Forum]], June 17, 2010
=External Links=
* [https://en.wikipedia.org/wiki/7_%28number%29 7 from Wikipedia]
* [https://en.wikipedia.org/wiki/Seven-day_week Seven-day week from Wikipedia]
* [[Videos#If|If]] - [https://en.wikipedia.org/wiki/If_3 Fibonacci's Number] (1971), [https://en.wikipedia.org/wiki/YouTube YouTube] Video
: {{#evu:https://www.youtube.com/watch?v=GXaefhbtU2k|alignment=left|valignment=top}}
* [[Videos#FrankZappa|Frank Zappa]] and [https://en.wikipedia.org/wiki/The_Mothers_of_Invention The Mothers of Invention], [https://en.wikipedia.org/wiki/Inca_Roads_(song) Inca Roads], 1974, ([https://en.wikipedia.org/wiki/A_Token_of_His_Extreme_(Soundtrack) A Token of His Extreme]), [https://en.wikipedia.org/wiki/YouTube YouTube] Video <ref>[https://en.wikipedia.org/wiki/Clay_animation Clay animation] by [https://en.wikipedia.org/wiki/Bruce_Bickford_(animator) Bruce Bickford]</ref> <ref>[http://adeucefortheskycap.blogspot.com/2007/10/eulogy-for-kelly-lowe-by-michael-king.html Kelly Fisher Lowe] ('''2006'''). ''[http://www.afka.net/Books/lowe.htm The Words and Music of Frank Zappa]''. Praeger Publishers, pp. 119 ''The lyrics to "Inca Roads" are absurdist in the extreme. They veer wildly from spacey - "Did a vehicle / Come from somewhere out there / Just to land in the Andes?," which both [https://en.wikipedia.org/wiki/Ben_Watson_(music_writer) Watson] and [http://www.beefheart.com/tag/kevin-courrier/ Courrier] claim Zappa's satire on the popular-at-the-time book [https://en.wikipedia.org/wiki/Chariots_of_the_Gods%3F Chariots of the Gods?]'' ...</ref> <ref>[https://en.wikipedia.org/wiki/Nazca_lines Nazca Lines from Wikipedia]</ref>
: [[Videos#FrankZappa|Frank Zappa]], [[Videos#GeorgeDuke|George Duke]], [https://en.wikipedia.org/wiki/Napoleon_Murphy_Brock Napoleon Murphy Brock], [https://en.wikipedia.org/wiki/Chester_Thompson Chester Thompson], [https://en.wikipedia.org/wiki/Tom_Fowler_%28musician%29 Tom Fowler], [https://en.wikipedia.org/wiki/Ruth_Underwood Ruth Underwood], [https://en.wikipedia.org/wiki/Captain_Beefheart Captain Beefheart]
: {{#evu:https://www.youtube.com/watch?v=wqp71DOJ3aY|alignment=left|valignment=top}}
=References=
<references />
'''[[Pieces|Up one Level]]'''
[[Category:Samuel Bak]][[Category:Frank Zappa]]
