[Retros] Total Number of Moves

[peufe at tin.it]

>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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