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.
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 :
After placing the two Bishops accordingly :
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:
The new position will be :
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 :
And the full starting position will look like this :
The BOU.LI.NA. method was devised by Boussios Christos, Likartsis Athanasios and Navrozidis Georgios (hence the name).