Random starting position in chess

The rules

A random starting position in chess is played as the classic starting position but the pieces behind the pawns are placed randomly. This variant was proposed because the players can play from the classic starting position with multiple moves by memory or by repeating a previous game, without thinking and without spending time. Thus, in the beginning of the game, there is an equation of players independent from their capacity. These moves are studied in advance in-depth so that a very good player cannot discover into practice sometimes. Moreover, these moves establish the foundations for the future plans of the player that are not necessary to be discovered. Also, because of the deep knowledge of the opening, sometimes the game can have a very fast final result.

In order for the change of the game not to be very drastic from the classic starting position, the pieces are placed with the following restrictions:

· The bishops must be placed on opposite-color squares.

· If the rights for castle exist, then after castling with the nearest rook to the column:

o "h", the king will be in column "g" and the rook will be in column "f".

o "a", the king will be in column "c" and the rook will be in column "d".

·  Black's pieces are placed equal and opposite to White's pieces.

The variant without the limitation of symmetry of the white pieces to the black ones, with the bishops on opposite-color squares and without castling rights was proposed in 1978 by Maxwell Lawrence under the name transcendental chess. It implies that this variant includes the classic starting position without castling rights. Due to the fact that inequalities may arise because of the asymmetry in the starting position, the proposal includes the same starting position one game with white and one game with black for each player.

If the only restriction that exists is the symmetry of the white pieces to the black ones, then the starting positions are 5040. This variant with random starting position is known to be very old. Two games exist in a book of the year 1851. La Rιgence: journal des ιchecs, Volume 3, La partie aux piθces dιplacιes (p. 299-301)

If the restriction for the bishops is on opposite color square, then the starting positions are decreased in 2880.

If the king should be placed in one square between the rooks, then the starting positions are decreased in 960. This variant was proposed officially by the former world champion Robert Fischer, on 19 June 1996 in Buenos Aires (Argentina), called "Random Chess". The rules were approved of the 77th Congress of FIDE (World Federation) in Dresden (Germany), November 2008 and were placed in force on 1 July 2009.

If the rights for castle do not exist, then because of the symmetry, the starting positions substantially are decreased in half, that is to say in 2520, 1440, 480 respectively.

Draw with equal probability for all starting positions

The draw is made by shuffling marked identical objects (cards, pawns, scrabble letters) and using the permutations.

The number of permutations:
in the 8 positions only with bishops without restrictions = 8!/(6!*2!)=7*8/2=28,
of which in squares of different colors = 4*4=16
and in squares of the same color = 28-16=12,
of the remaining 6 pieces in the 6 positions = 6!/(1!*1!*2!*2!)=180,
of the 8 pieces without restrictions = 28*180=5040,
with the bishops on squares of the same color = 12*180=2160,
with the bishops on squares of different colors = 16*180=2880 or 5040-2160=2880
and of those with the king on a square between the 2 rooks = 16*(6!/(1!*2!*3!))=16*(720/4)/3=2880/3=960.

For the draw to be correct, the number of possible permutations must be a common multiple of 5040 and 2880, such as:
8!=40320=8*5040=14*2880 or 40320/2=20160=4*5040=7*2880.

The method of transformation
from a permutation with bishops on squares of the same color
to a permutation with bishops on squares of a different color
is based on the relations 3*16=4*12=2*24.

8 marked cards are shuffled ♘, ♗, ♕, ♔, ♝, ♞, ♖, ♖.

In the random permutations below, if the bishops were on squares of a different color (4/7) we would go to the last step,

♖

♖

♘

♗

♕

♝

♔

♞

♖

♖

♞

♗

♕

♝

♔

♘

a

b

c

d

e

f

g

h

a

b

c

d

e

f

g

h

otherwise (3/7) we move on to the next step:

if the white knight is (in position Nw)
before/after the black knight (in the position Nb),
then the black bishop (in the position Bb)
is swapped with the piece which is respectively in the
next/second next square of a different color
(if it does not exist then the 8 squares are considered in a circle)
[new position Bb] = mod(Bb+1+2*(Nw>Nb);8).

♖

♖

♘

♗

♕

♔

♝

♞

♝

♖

♞

♗

♕

♖

♔

♘

a

b

c

d

e

f

g

h

a

b

c

d

e

f

g

h

Last step. All pieces become the same color. If the king must be between the two rooks (chess960 or Fisher random) then is swapped with the nearest rook.

♖

♔

♘

♗

♕

♖

♗

♘

♗

♖

♘

♗

♕

♔

♖

♘

a

b

c

d

e

f

g

h

a

b

c

d

e

f

g

h

Horizontal symmetry

6 marked cards (♔, ♗, ♘, ♖, abcd, efgh) are shuffled and placed randomly in two rows of pieces and letters. The first letter card shows where the pieces are placed. The remaining pieces (♕, ♗ ♘, ♖) are placed so that they are the same (king=queen) in the columns a=h, b=g, c=f, d=e. Possible starting positions 48. If the king must be on a square between the two rooks, then is swapped with the nearest rook as is the queen. Possible starting positions 16.

For a random generator click here