A Chess960 starting position is one of 960 possible initial game positions in the chess variant Chess960. The special arrangement of pieces on the players' first ranks is selected randomly before play according to Chess960 rules, and can be generated either by a computer program, or using dice, coin, cards, etc.
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:
Black's pieces are placed equalandopposite 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.)
There are several procedures for generating random starting positions with equal probability.
Dr Ingo Althöfer


A common method for selecting a starting position is one proposed by Ingo Althöfer in 1998, which requires only a single cube die. The position of White's pieces is determined as follows:
This leaves three empty squares. Place the king on the middle empty square, and the rooks on the remaining two squares. Place the white and black pawns on their usual squares, and Black's firstrow pieces to exactly mirror White's. (So, Black should have on a8 the same piece type White has on a1.)
The above procedure uses an average of 6.7 die rolls. Note that one of the random positions (rolled by 23323 or 23342) is the standard chess starting position, at which point a standard chess game ensues.
On average, the single die procedure uses 6.7 die rolls. An optimal procedure would use on average log(960)/log(6) = 3.83 die rolls. It is straightforward to reduce the average number of dice rolls to 6.2. Instead of rerolling 5s and 6s until something else comes up, reroll once and (4/36) use the following scheme:
With polyhedral dice shaped like each of the five Platonic solids, one never needs to reroll any dice.


Roll all the dice in one throw and place White's pieces as follows:
Place the white pawns and mirror the position for Black.
Two coins (small and large) are used to randomly generate numbers with equal probability. Tails on the smaller coin counts as 0, tails on the larger coin counts as 1, and heads on either coin counts as 2. To create numbers in the range 1 through 4, toss both coins and add their values together. To create numbers in the range 1 through 3, do the same but retoss whenever 4 is the result. To create numbers in the range 1 through 2, just toss the larger coin (tails is 1, heads is 2).
There is a way of using coins and making all starting positions equally likely. It uses a third coin for which tails counts as 0, and heads counts as 4. Tossing all three coins generates the values 1 through 8 with equal probability. The method follows the piece placements used for a die. Two coins are used for the bishops as before. Then six squares are available for the queen. All three coins are tossed and retossed until a number in the range 16 comes up. Then five squares are available for the first knight. Now the three coins should be tossed and retossed until a number in the range 15 shows up. For the other knight, only a fourway choice is needed, so a single toss of two coins suffices. The average number of tosses needed for this method is 5 + 14/15.
A similar cointossing method uses one coin to generate all starting positions with equal probability. Toss the coin four times and record the results. If the four coin tosses are all tails, start again. Otherwise toss the coin an additional six times and record the results. Then convert the sequence into a binary number counting heads as 0, tails as 1. The resulting number is a number between 0 and 959 that can then be converted into a starting position using the Chess960 numbering scheme. For example, if the tosses are T, H, T, T, H, H, H, H, T, T this converts to the binary number 1011000011, or 707, which in the Chess960 numbering scheme is the starting position BRKQNNRB.