How many starting positions does Chess960 have?

Exactly 960. Place the light-square bishop on one of 4 squares, the dark-square bishop on one of 4, the queen on any of the 6 squares left, and the two knights on any 2 of the last 5, which is C(5,2) = 10 ways. The final three squares then hold the rooks and king in exactly one legal order. 4 x 4 x 6 x 10 = 960.

Why is it called Chess960?

Because 960 is the number of legal starting positions the shuffle can produce. Three constraints apply: the bishops go on opposite colours, the king stands between the two rooks, and Black mirrors White. Without those constraints there would be 5,040 arrangements.

Which Chess960 position is normal chess?

Position 518 is RNBQKBNR, the ordinary chess array. The positions are numbered 0 to 959 using the scheme Reinhard Scharnagl set out, and the same number means the same position on Lichess, on chess.com and in FIDE material. Checking that a generator gives RNBQKBNR for 518 is the quickest test that its numbering is honest.

Why 960? Counting the Chess960 starting positions

Q: Why must the king start between the rooks in Chess960?

So that castling is defined on both sides. Short castling sends the king to g1 with the rook on its right; long castling sends it to c1 with the rook on its left. If both rooks stood on the same side of the king, one of those moves would have no rook to use. The requirement also fixes the last step of the count: three squares hold R, K, R in three possible orders, and exactly one qualifies.

Q: Are all 960 Chess960 positions balanced?

Every position is symmetric between the two sides, since Black mirrors White, but the positions differ from each other. 360 of the 960 begin with every pawn defended by a piece, as standard chess does. In 162, castling is legal as the very first move. Four positions leave three pawns undefended at move one, position 59, NNRQBKRB, among them.

By Carl Brodsky

Chess960 shuffles the eight back-rank pieces under three constraints. Bishops on opposite colours, king between the rooks, Black mirrors White. The constraints leave exactly 960 arrangements, which is where the name comes from. The count is short enough to do in full, so here it is in full.

How do you count to 960?

Place the pieces in an order that keeps each step independent of the last.

Light-square bishop. On White's back rank the light squares are b1, d1, f1 and h1. Four choices.
Dark-square bishop. The dark squares are a1, c1, e1 and g1. Four choices, and they cannot collide with the first bishop, because the two lists have no square in common.
Queen. Six squares are still empty. Six choices.
Two knights. Five squares are still empty and the knights are interchangeable, so what you are counting is a pair of squares out of five: C(5,2) = (5 × 4) / 2 = 10.
King and rooks. Three squares are still empty and there is exactly one legal way to fill them.

Multiply: 4 × 4 = 16, then 16 × 6 = 96, then 96 × 10 = 960, then 960 × 1 = 960.

Why is the last step forced?

This is the step most explanations skip, and it is the only one that does any work.

Three squares are left and three pieces have to go on them: a rook, the king, a rook. Left to right, the orders are KRR, RKR and RRK. There are three of them, not six, because the two rooks are identical and swapping them changes nothing. Of those three, exactly one puts the king between the rooks. So the last step contributes a factor of one.

That constraint exists for castling. Chess960 castling asks the king to travel to g1 with its right-hand rook or to c1 with its left-hand rook. If both rooks stood on the same side of the king, one of those two moves would have no rook to use and no definition. Requiring a rook on either side keeps both castling moves available in every one of the 960 positions. The castling rules work through what that looks like on the board.

The same number, counted from the other end

Start with every arrangement and throw the illegal ones away.

Eight pieces on eight squares gives 8! = 40,320 orderings. The two rooks are interchangeable, so are the two knights, so are the two bishops. Divide by 2 × 2 × 2 = 8, and 40,320 / 8 = 5,040 distinct back ranks. That is the full shuffle, with no constraints at all.

Now apply the bishop rule. There are C(8,2) = 28 ways to choose the two bishop squares, and 4 × 4 = 16 of those put one bishop on each colour. So 5,040 × 16 / 28 = 2,880 arrangements survive.

Now apply the king rule. Whatever else is placed, the last three squares hold R, K, R in one of three orders, and one order qualifies. So 2,880 / 3 = 960.

Two routes, one answer. If you want to see the third route, step the position generator through all 960 and count.

What is a Chess960 position number?

Every legal arrangement has a number from 0 to 959, from the numbering Reinhard Scharnagl set out. It is the same numbering on Lichess, on chess.com and in FIDE material, so a position number means the same position everywhere. Position 518 is ordinary chess.

The numbering is the count above run backwards, and you can do it by hand. Take 518.

Divide by 4: 518 = 4 × 129 + 2. The remainder 2 selects the third light square from b1, d1, f1, h1, so the light bishop goes to f1.
Divide 129 by 4: 129 = 4 × 32 + 1. The remainder 1 selects the second dark square from a1, c1, e1, g1, so the dark bishop goes to c1.
Divide 32 by 6: 32 = 6 × 5 + 2. The remainder 2 selects the third empty square from a1, b1, d1, e1, g1, h1, so the queen goes to d1.
What is left is 5, which selects row 5 of the ten knight-rook-king patterns. Counting from zero, they run NNRKR, NRNKR, NRKNR, NRKRN, RNNKR, RNKNR, and row 5 is RNKNR. Lay it on the five empty squares a1, b1, e1, g1, h1: rook a1, knight b1, king e1, knight g1, rook h1.

Read the rank: RNBQKBNR. Standard chess. Set the generator to 518 and check it against a board, because a generator that fails this check is producing something other than Chess960.

Are all 960 positions reasonable?

They are all playable. They are not all alike, and the differences are measurable rather than a matter of taste.

18 first moves · NQBRKBRN

21 first moves · BQNNRKRB

The arrangements are not equally open. Position 310 gives White eighteen legal first moves, position 3 gives twenty-one, and the standard array sits between them at twenty. Knights on the rim reach fewer squares.

360 of the 960 begin with every pawn defended by a piece, as standard chess does. In the remaining 600, at least one pawn on the second rank is defended by nothing at all. Four positions leave three pawns hanging. Position 59 is NNRQBKRB, and a2, b2 and h2 all start undefended.

In 162 positions castling is legal as the very first move, which changes the opening completely. Position 3, BQNNRKRB, has the king on f1 and a rook on g1, and 1.O-O simply swaps them.

108 positions put rooks in both corners as standard chess does. 240 put a queen in a corner. The king starts on d1 or e1 in 408 positions and on b1 or g1 in 216.

No position is its own mirror image. Reflecting a legal back rank left to right gives another legal back rank, but a symmetric arrangement of eight pieces would need the king on two squares at once, and it only has one. So the 960 fall into 480 mirror pairs with nothing left over. Standard chess is paired with position 534, RNBKQBNR, which is standard chess with the king and queen swapped.

Why did Fischer stop at 960?

He wanted to remove opening preparation, not to change chess. Each constraint protects something the theory does not own.

Opposite-coloured bishops keep the bishop pair covering both colour complexes, so every endgame you have learned still applies. The king between the rooks keeps castling available on both wings, so the middlegame still has a king-safety problem to solve rather than none. Black mirroring White keeps the first move as the only asymmetry.

Drop the constraints and you get the full 5,040. Among them are positions with two light-squared bishops, positions where one side cannot castle at all, and positions that would need their own theory to tell you whether they are broken. That trades one body of memorised knowledge for a larger one. The 960 all behave the same way ordinary chess behaves, and none of them can be prepared for.

The full rules, castling included, are on the Chess960 rules page. Once the position stops being the hard part, the tactics start: the puzzle trainer and the books drill patterns on back ranks you have never seen before.