Several methods have been suggested for random initial positions generation (without a computer). There are two main objectives that need to be addressed :

  • All 960 positions must have an equal probability to come
  • The method must be simple, ie. easy to memorize and follow and not require special material

Another objective might be the “deterministicness” of the method, ie. no step should require repetitively drawing cards or tossing coins or rolling dice etc until a particular set of outcomes is obtained.

For instance, in order to determine the light-squared bishop’s position, which can be one of b1, d1, f1 or h1 (4 cases), a method might use a die and exclude the numbers 5 and 6, thus interpreting the rolls 1 to 4 as the squares b1 to h1. This method would not be deterministic, since there will be an unknown number of die rolls until a convenient number (ie. 1 to 4) comes up.

Most of the methods require use of dice, coins or playing cards. This stuff is pretty much easy to find. There are also methods that need special types of dice (eg. an octahedron) or special printed cards.

The following methods ensure the objectives mentioned :

 

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The castling rules is the single complicated part about Chess960. Going through a couple of examples will make this topic clear. Only White’s castles will be considered, as Black’s are perfectly symmetrical to White’s.

 

The following diagram shows the initial squares of the King and the two Rooks in a random Chess960 starting position :

chess960_white_castlings

 

These would be the final positions for White’s queenside and kingside castles :

chess960_white_queenside_castle_final_positions

chess960_white_kingside_castle_final_position

 

 

 

 

 

 

 

 

The requirements for each castle are as follows :

Queenside castling

All the squares between the King’s initial and final square, including both the initial and final square, may not be attacked by opponent pieces :

chess960_unattacked_squares_queenside

All the squares between the King’s initial and final square, including the final square, must be empty :

chess960_empty_squares_queenside_1

All the squares between the Rook’s initial and final square, including the final square, must be empty :

chess960_empty_squares_queenside_2

 

Kingside castling

All the squares between the King’s initial and final square, including both the initial and final square, may not be attacked by opponent pieces :

chess960_unattacked_squares_kingside

All the squares between the King’s initial and final square, including the final square, must be empty :

chess960_empty_squares_kingside_1

All the squares between the Rook’s initial and final square, including the final square, must be empty :

chess960_empty_squares_kingside_2

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This 3-step method ensures that all 960 starting positions have an equal probability to appear. It is considered to be the simplest method to produce a random Chess960 initial position. It uses 8 playing cards, separated in odds and evens.

Playing_card_club_1 Playing_card_club_3 Playing_card_club_5 Playing_card_club_7

Playing_card_club_2 Playing_card_club_4 Playing_card_club_6 Playing_card_club_8

 

Step 1: Randomly pick one card from each stack. These first two cards are the positions for the two Bishops. 

Obviously there will be one white and one black Bishop. For example, suppose the 5 and the 6 were drawn :

Playing_card_club_6 Playing_card_club_5

 

After placing the two Bishops accordingly :

Chess960 randomly generated position after step 1

Chess960 randomly generated position after Step 1

 

Step 2: Shuffle the remaining 6 cards and draw 3 random cards. These are the positions for the Queen and the 2 Knights.

In our example the remaining cards are 1, 2, 3, 4, 7, 8. Let’s say we drew the 2, 1 and 8, in this order:

Playing_card_club_2 Playing_card_club_1 Playing_card_club_8

 

The new position will be :

bview (2)

Step 3: The remaining empty squares are for Rook, King, Rook, in this order, so that castling is possible both ways.

After placing the last pieces, we get the following position :

Chess960 randomly generated position after step 3

Chess960 randomly generated position after Step 3

 

And the full starting position will look like this :

Chess960 randomly generated position displayed in full

Chess960 randomly generated position displayed in full

 

The BOU.LI.NA. method was devised by Boussios Christos, Likartsis Athanasios and Navrozidis Georgios (hence the name).

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