# [Retros] Total Number of Moves

peufe at tin.it peufe at tin.it
Tue May 15 06:21:26 EDT 2007

>From Franco Fedeli

Italy
Hi friends, I asked myself: " How many different moves in chess?"
I had fun trying to compute them.
Two moves are different if they differ for at least one of these elements:
1) Piece to be moved (K,B,N,R,Q,P)
2) Starting square
3) Final square
4) Piece captured (Nothing, B,N,R,Q,P)
5) Piece promoted (B,N,R,Q)
En Passant captures will be considered different from normal ones.
We must add O-O and O-O-O.
This is my counting:

QUEEN :

Starting Squares (N) Final Squares (F) With Pawn captures (A) No Pawn captures(B) Moves M=N*(6*A+5*B)
(From each one)
Corners
(a1,a8,h1,h8) 4 21 12 9 468

1 and 8 rank
(No corners) 12 21 13 8 1416

a and h file
(No corners) 12 21 17 4 1464

b2,g2,g7,b7 4 23 18 5 532

Boundary
b2>g2>g7>b7 16 23 19 4 2144
(No corners)

c3,f3,f6,c6 4 25 20 5 580

Boundary
c3>f3>f6>c6 8 25 21 4 1168
(No corners)

d4,e4,e5,d5 4 27 22 5 628

--------------
Queen's Total (Q) 8400

ROOK :

1 and 8 rank 16 14 6 8 1216

all the others 48 14 12 2 3936
-----------
Rook's Total (R) 5152

BISHOP :

Corners
(a1,a8,h1,h8) 4 7 6 1 164

1 and 8 rank
(No corners) 12 7 7 0 504

a and h file
(No corners) 12 7 5 2 480

b2,g2,g7,b7 4 9 6 3 204

Boundary
b2>g2>g7>b7 16 9 7 2 832
(No corners)

c3,f3,f6,c6 4 11 8 3 252

Boundary
c3>f3>f6>c6 8 11 9 2 512
(No corners)

d4,e4,e5,d5 4 13 10 3 300
--------------
Bishop's Total (B) 3248

We see that Q=R+B how it must be.

KNIGHT:

a1,a8,h1,h8 4 2 2 0 48

b1,g1,b8,g8 4 3 3 0 72

c1,c8,d1,d8
e1,e8,f1,f8 8 4 4 0 192

a2,a7,h2,h7 4 3 2 1 68

b2,b7,g2,g7 4 4 3 1 92

c2,c7,d2,d7
e2,e7,f2,f7 8 6 4 2 272

a3,h3,a6,h6 4 4 3 1 92

b3,b6,g3,g6 4 6 4 2 136

c3,c6,d3,d6
e3,e6,f3,f6 8 8 6 2 368

a4,a5,h4,h5 4 4 4 0 96

b4,b5,g4,g5 4 6 6 0 144

c4,c5,d4,d5
e4,e5,f4,f5 8 8 8 0 384
------------
Knight's Total (N) 1964

KING:

a1,a8,h1,h8 4 3 2 1 68

1 and 8 rank
(No corners) 12 5 3 2 336

a2,h2,a7,h7 4 5 3 2 112

b2,b7,c2,c7
d2,d7,e2,e7
f2,f7,g2,g7 12 8 5 3 540

a3,a4,a5
h3,h4,h5 6 5 5 0 180

a6,h6 2 5 4 (Ka6xPb7 is illegal) 1 58

Rectangle
b3>g3>g5>h5 18 8 8 0 864

b6,c6,d6
e6,f6,g6 6 8 6 2 276
---------------
King's Total (K) 2434

WHITE PAWN:

Starting Squares (N) Final Squares (F) With captures (A) No captures (B) Moves M=N*(5*A+B)
from each one

a2,h2 2 3 1 2 14

b2,c2,d2
e2,f2,g2 6 4 2 2 72

a3,a4,a6
h3,h4,h6 6 2 1 1 36

b3,b4,b6
c3,c4,c6
d3,d4,d6
e3,e4,e6 18 3 2 1 198
f3,f4,f6
g3,g4,g6 M=N*(6*A+B)

a5,h5 2 2 1 (en passant too) 1 14

b5,c5,d5
e5,f5,g5 6 3 2 1 78

M=4*N*(4*A+B)

a7,h7 2 2 1 (with promotions) 1 40

b7,c7,d7
e7,f7,g7 6 3 2 1 216
------------------

Pawn's Total (P) 668

SUMMARY:

QUEEN: 8400
ROOK: 5152
BISHOP: 3248
KNIGHT: 1964
KING: 2434
PAWN: 668
O-O 1
O-O-O 1
--------------
WHITE: 21868
BLACK: 21868
---------------

TOTAL NUMBER OF CHESS MOVES: 43736

I hope all is correct.
Did you ever play all these chess moves in your playing career?
Maybe no, especially because the unusual underpromotions with captures........
Bye

Franco Fedeli

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