Fischer random chess starting position

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A Fischer random chess starting position is one of 960 possible initial game positions in the chess variant Fischer random chess. The special arrangement of pieces on the players' first ranks is selected randomly before play according to Fischer random chess rules.

Starting position requirements[]

White pawns are placed on the second rank as in standard chess. All remaining white pieces are placed randomly on the first rank, with two restrictions:

  • The bishops must be placed on opposite-color squares.
  • The king must be placed on a square between the rooks.

Black's pieces are placed equal-and-opposite to White's pieces. For example, if the white king is randomly determined to start on f1, then the black king is placed on f8. (The king never starts on the a - or h -files, since this would leave no space for a rook.)

Creating starting positions[]

Usually, the players accept the conditions of the organizer to generate the starting position with software, as it was used in the 2019 World Fischer Random Championship.

If the software is not available or the players don't accept it, there are several procedures for generating random starting positions with equal probability.

There are 4 * 4 * 6 * 10 * 1 = 4 * 4 * 15 * 4 * 1 = 960 legal starting positions:

4 possible squares for the light-squared bishop

4 possible squares for the dark-squared bishop

6 remaining squares for the queen and 5! / ( 3! * 2! ) = 5 * 4 / 2 = 10 ways to place the two (identical) knights on the remaining 5 squares

or

6! / ( 4! * 2! ) = 5 * 6 / 2 = 15 ways to place the two (identical) knights on the remaining 6 squares and 4 remaining squares for the queen

1 way to place the two rooks and king on the remaining 3 squares, since the king must be between the rooks.

Ingo Althofer

In 1998, Ingo Althöfer proposed a method that requires only a single standard die.[1][2] (Re-roll if needed to get values in the range 1–4 or 1–5).

If a full set of polyhedral dice is available (a tetrahedron (d4), cube (d6), octahedron (d8), dodecahedron (d12), and a icosahedron (d20)), one never needs to reroll any dice.[citation needed]

Tossing a coin to create binary numbers and convert them to decimal.

Shuffling objects (cards, pieces, pawns, dominoes tiles, scrabble letters) and use the permutations.

Since all 960 starting positions have been assigned a number (per the Fischer Random Chess numbering scheme) any method that generates a random number between 0 and 959 can be used to generate a starting position.

See also[]

References[]

  1. ^ Althöfer, Ingo (March 1998). van den Herik, Jaap (ed.). "LIST-3-HIRN vs. Grandmaster Yusupov". International Computer Chess Association (ICCA). Universiteit Maastricht. 21 (1): 52–60. ISSN 0920-234X.
  2. ^ Hans Bodlaender (2002-05-10). "Fischer Random Chess: Manual Procedure for Generating Piece Placements". The Chess Variant Pages. Retrieved 2013-01-26.

External links[]

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