Fischer Random Chess

Fischer Random Chess (also called Chess 960, Fischerandom chess, FR chess, or FRC) is a chess variant created by Grandmaster Bobby Fischer (who was world chess champion from 1972 until 1975). It was originally announced on June 19, 1996, in Buenos Aires, Argentina. Fischer's goal was to create a chess variant in which chess creativity and talent would be more important than memorization and analysis of opening moves. His approach was to create a randomized initial chess position, which would thus make memorizing chess opening move sequences far less helpful.

Starting position

The starting position for Fischer random chess must meet the following rules:

• White pawns are placed on their orthodox home squares.
• All remaining white pieces are placed on the first rank.
• The white king is placed somewhere between the two white rooks.
• The white bishops are placed on opposite-colored squares.
• The black pieces are placed equal-and-opposite to the white pieces. For example, if white's king is placed on b1, then black's king is placed on b8.

Note that the king never starts on file a or h, because there has to be room for a rook.

There are many procedures for creating this starting position. Hans L. Bodlaender has proposed the following procedure using one six-sided die to create an initial position; typically this is done just before the game commences:

• Roll the die, and place a white bishop on the black square indicated by the die, counting from the left. Thus 1 indicates the first black square from the left (a1 in algebraic notation), 2 indicates the second black square from the left (c1), 3 indicates the third (e1), and 4 indicates the fourth (g1). Since there are no fifth or sixth positions, re-roll 5 or 6 until another number shows.
• Roll the die, and place a white bishop on the white square indicated (1 indicates b1, 2 indicates d1, and so on). Re-roll 5 or 6.
• Roll the die, and place a queen on the first empty position indicated (always skipping filled positions). Thus, a 1 places the queen on the first (leftmost) empty position, while a 6 places the queen on the sixth (rightmost) empty position.
• Roll the die, and place a knight on the empty position indicated. Re-roll a 6.
• Roll the die, and place a knight on the empty position indicated. Re-roll a 5 or 6.
• Place a white rook on the 1st empty square of the first rank, the white king on the 2nd empty square of the first rank, and the remaining white rook on the 3rd empty square of the first rank.
• Place all white and black pawns on their usual squares, and place Black's pieces to exactly mirror White's (so Black should have on a8 exactly the same type of piece that White has on a1).

This procedure generates any of the 960 possible initial positions of Fischer Random Chess with an equal chance; on average, this particular procedure uses 6.7 die rolls - an optimal procedure would use on average somewhere between 4 and 4.45 die rolls. Note that one of these initial positions is the standard chess position, at which point a standard chess game begins.

It is also possible to use this procedure to see why there are exactly 960 possible initial positions. Each bishop can take one of 4 positions, the Queen one of 6, and the two knights can have 5 or 4 possible positions, respectively. This means that there are 4×4×6×5×4 = 1920 possible positions if the two knights were different in some way. However, the two knights are indistinguishable during play; if they were swapped, there would be no difference. This means that the number of distinguishable positions is half of 1920, or 1920/2 = 960 possible distinguishable positions.

Castling

Rules for castling

Once the starting position is set up, the rules for play are the same as standard chess. In particular, pieces and pawns have their normal moves, and each player's objective is to checkmate their opponent's king.

Fischer random chess allows each player to castle once per game, a move by potentially both the king and rook in a single move. However, a few interpretations of standard chess games rules are needed for castling, because the standard rules presume initial locations of the rook and king that are often untrue in Fischer Random Chess games.

After castling, the rook and king's final positions are exactly the same positions as they would be in standard chess. Thus, after a-side castling (notated as O-O-O and known as queen-side castling in orthodox chess), the King is on c (c1 for White and c8 for Black) and the Rook is on d (d1 for White and d8 for Black). After h-side castling (notated as O-O and known as king-side castling in orthodox chess), the King is on g and the Rook is on f. It is recommended that a player state "I am about to castle" before castling, to eliminate potential misunderstanding.

However, castling may only occur under the following conditions, which are extensions of the standard rules for castling:

1. Unmoved: The king and the castling rook must not have moved before in the game, including castling.
2. Unattacked: No square between the king's initial and final squares (including the initial and final squares) may be under attack by any opposing piece.
3. Vacant: All the squares between the king's initial and final squares (including the final square), and all of the squares between the rook's initial and final squares (including the final square), must be vacant except for the king and castling rook. An equivalent way of stating this is that the smallest back rank interval containing the king, the castling rook, and their destination squares contains no pieces other than the king and castling rook.

These rules have the following consequences:

• If the initial position happens to be the standard chess initial position, these castling rules have exactly the same effect as the standard chess castling rules.
• All the squares between the king and castling rook must be vacant.
• Castling cannot capture any pieces.
• The king and castling rook cannot "jump" over any pieces other than each other.
• A player may castle at most once in a game.
• If a player moves his king or both of his initial rooks without castling, he may not castle during the rest of the game.
• In some starting positions, some squares can stay filled during castling that would have to be vacant in standard chess. For example, after a-side castling (O-O-O), it's possible for to have a, b, and/or e still filled, and after h-side castling (O-O), it's possible to have e and/or h filled.
• In some starting positions, the king or rook (but not both) do not move during castling.
• The king may not be in check before or after castling.
• The king cannot move through check.

How to castle

When castling on a physical board with a human player, it is recommended that the king be moved outside the playing surface next to his final position, the rook then be moved from its starting to ending position, and then the king be placed on his final square. This is always unambiguous, and is a simple rule to follow.

Eric van Reem suggests that there are other acceptable ways to castle:

• If only the rook needs to move (jumping over the king), you can simply move only the rook.
• If only the king needs to move (jumping over the castling rook), you can simply move the king.
• One can pick up both the king and rook (in either order), then place them on their final squares (this is called "transposition" castling).
• One can move the king to its final square and move the rook to its final square as two separate moves, in either order (this is called "double-move" castling). Obviously, if the rook is on the square the king will occupy, the player needs to move the rook first, and if the king is on the square the rook will occupy, the player needs to move the king first.

In contrast, Reinhard Scharnagl strongly recommends that, since castling is fundamentally a king's move, the king should always move first.

Generally, when playing with human player on a physical board, it's wise to announce "I'm going to castle" before castling. If one is playing a timed game, once the player done castling, he or she should press the appropriate button on his or her chess clock to show his or her move has completed.

When castling using a computer interface, programs should have separate a-side (O-O-O) and h-side (O-O) castling actions (e.g., as a button or menu item). Ideally, programs should also be able to detect a king or rook move that cannot be anything other than a castling move and consider that a castling move.

When using an electronic board, to castle one should remove the king, remove the castling rook, place the castling rook on its new position, and then place the king on its new position. This will create an unambiguous move for electronic boards, which often only have sensors that can detect the presence or absence of an object on each square (and cannot tell what object is on the square). Ideally, electronic boards should detect a king or rook move that can only be a castling move as well, but users should not count on this.

Castling rule ambiguities

Many published castling rules are unfortunately ambiguous. For example, the rules first published by Eric van Reem and chessvariants.org, as literally stated, did not specifically state that there must be vacant squares between the king and his destination except for the participating rook. As a result, those rules appeared to some to allow the king to "leap" over other pieces.

In 2003 David A. Wheeler contacted many active in Fischer Random Chess to determine the exact castling rules, including Eric van Reem, Hans-Walter Schmitt, and R. Scharnagl. All agreed that there must be vacant squares between the king and his destination except for the participating rook, clarifying the castling rules.

Playing Fischer Random Chess

Examining openings for Fischer Random Chess is in its infancy, but opening fundamentals still apply. These include: protect the King, control the center squares (directly or indirectly), and develop your pieces rapidly starting with the less valuable pieces. Some starting positions have unprotected pawns that may need to be dealt with quickly.

Some have argued that two games should be played with each initial position, with players alternating as white and black, since some initial positions may turn out to give white a much bigger advantage than standard chess. However, there is no evidence that any position gives either side a significant advantage.

Recording games and positions

Since the initial position is usually not the orthodox chess initial position, recorded games must also record the initial position. Games recorded using the Portable Game Notation (PGN) can record the initial position using Forsyth-Edwards Notation (FEN), as the value of the "FEN" tag. Castling is marked as O-O or O-O-O, just as in standard chess. Note that not all chess programs can handle castling correctly in Fischer Random Chess games (except if the initial position is the standard chess initial position). To correctly record a Fischer Random Chess game in PGN, an additional "Variant" tag must be used to identify the rules; the rule named "Fischerandom" is accepted by many chess programs as identifying Fischer Random Chess. Be careful to use "Variant" and not "Variation", which has a different meaning. This means that in a PGN-recorded game, one of the PGN tags (after the initial 7 tags) would look like this:

[Variant "Fischerandom"]

R. Scharnagl does not agree with that. It simply is reflecting the inability of the Winboard protocol to handle FEN positions correctly. There is no need for distinguishing its so called variants "normal", "nocastle" and "fischerandom", because the different or skipped castling rights could be completely encoded in an appropriate FEN string. It would be a bad solution to inflate a PGN file with superfluous tags only to cover weaknesses of some protocols. An engine, aware to play FRC, will play always FRC. Loaded with a Shuffle Chess FEN string it would play correctly with that just like it would handle a traditional chess starting array without error.

FEN is capable of expressing all possible starting positions of Fischer Random Chess. However, unmodified FEN cannot express all possible positions of a Fischer Random Chess game. In a game, a rook may move into the back row on the same side of the king as the other rook, or pawn(s) may be underpromoted into rook(s) and moved into the back row. If a rook is unmoved and can still castle, yet there is more than one rook on that side, FEN notation as traditionally interpreted is ambiguous. This is because FEN records that castling is possible on that side, but not which rook is still allowed to castle.

A modification of FEN, FRC-FEN, has been devised by R. Scharnagl to remove this ambiguity. In FRC-FEN, the castling markings "KQkq" have their expected meanings: "Q" and "q" means a-side castling is still legal (for white and black respectively), and "K" and "k" means h-side castling is still legal (for white and black respectively). However, if there is more than one rook on the baseline on the same side of the king, and the rook that can castle is not the outermost rook on that side, then the column letter of the rook that can castle is appended right after the related "K", "k", "Q", or "q". In other words, in FRC-FEN notation, castling potentials belong to the outermost rooks by default. This means that the maximum length of the castling value is 8 characters instead of 4 (KkQq plus 4 disambiguation characters), though positions needing that many characters are extremely improbable. As long as there have not been underpromotions into rooks the limit of 4 will always hold. Note that FRC-FEN is upwardly compatible, that is, a program supporting FRC-FEN will automatically use the normal FEN codes for a traditional chess starting position without requiring any special programming.

Starting position IDs

Some people have wanted each possible starting position to have a unique standard numeric identifier (id). R. Scharnagl recommends the following method for defining each position id, where each position has a different id ranging from 0 to 959. Position 0 also could be regarded as position 960. All positions are listed in detail in his book.

To create a starting position given an id:

• Divide the id by 4, producing a truncated integer and a remainder. The remainder locates the light-square Bishop: 0 means file b, 1 means file d, 2 means file f, and 3 means file h.
• Take the previous truncated integer and divide by 4, producing another integer and a remainder. This remainder locates the dark-square Bishop: 0 means file a, 1 means file c, 2 means file e, and 3 means file g.
• Take the previous truncated integer and divide by 6, producing another integer and a remainder. This remainder locates the queen, and identifies the number of the vacant square it occupies (counting from the left, where 0 is the leftmost square and 5 is the rightmost square).
• The previous truncated integer now has a value from 0 to 9 inclusive. Its value, called the KRN code (pronounced "kern"), indicates the positions of the king, rooks, and knights among the remaining 5 squares.

The KRN code values are as follows, showing the order from white's perspective from left to right (where K is king, R is rook, and N is knight):

Conversely, given a board position, its id can be computed as follows:

id = (light square Bishop location, where file b is 0) +
     4 × (dark square Bishop location, file a is 0) +
     16 × (Queen location, counting leftmost as 0 and skipping Bishops) +
     96 × (KRN code)

The standard chess position is position id 518. This can be shown by computing it:

id = (2 because the light square Bishop is on file f) +
     4 × (1 because the dark square Bishop is on file c) +
     16 × (2 because the Queen is on file d, skipping bishop on c) +
     96 × (5, the KRN code) = 518

Computer software can use this algorithm to quickly create any of the standard positions, by simply selecting a random number from 0 to 959 and using that as the position id. Note that some random number generators are poor (e.g., they are predictable and/or do not have an equal distribution of possible values), so implementors should make sure they use a good random number generator.

Other ways to create initial positions

There are several other methods that can create initial positions.

Coin-tossing method

Edward Northam has developed the following approach for creating initial positions using only two distinguishable coins.

First, two coins (small and large) are used to randomly generate numbers with equal probability. He suggests doing this by declaring that 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).

Any other technique that randomly generates numbers from 1 to 4 (or at least 1-2) will work as well, such as as the selection of a closed hand that may hold a white or black Pawn.

As with a die, the coin tosses can build a starting position one piece at a time. Before each toss there will be at most 4 vacant squares available to the piece at hand, and they can be numbered counting from the a-side (as with the die procedure described above). Place the white pieces on white's back rank as follows:

1. Place a Bishop on one of the 4 light squares.
2. Place a Bishop on one of the 4 dark squares.
3. Place the King. There 6 vacant squares, but only the middle 4 are available to the King, since there must be room for a Rook on each side of the King.
4. Place a Rook on the a-side of the King.
5. Place a Rook on the h-side of the King.
6. Place the Queen on one of the 3 vacant squares that remain.
7. Place Knights on the two squares that are left.

The average number of tosses needed to complete the process is 6. If a die and coins are at hand, no tosses need be repeated. The coins are used unless a number 1,2,3 is needed. Then the die is rolled, and 4,5,6 is counted as 1,2,3.

Both the die and coins methods can be speeded up by introducing parallelism. Several dice of different colors can be rolled, so long as there is a prior agreement about the ordering of the colors (which color is counted as the first roll, the second etc.). Using US coins, if each player tosses a penny, nickel, dime, and quarter (penny goes with nickel, dime goes with quarter), this single action gives four outcomes. Again, there must be a prior agreement about the order of these outcomes. Two such actions will place all of the pieces more than 97% of the time.

The ultimate parallelism of this type would have each player toss four different coins and a die. If a die is used only when 1,2,3 is needed, this single action will place all eight pieces. Again, there must be a prior agreement about the ordering of these outcomes.

Drawing methods

David J. Coffin suggests the following procedure, which has the advantage of not requiring computers, dice, or lookup tables:

1. Place the eight white pieces in a bag. Draw them one by one and place them on squares a1, b1, ... h1.
2. If the bishops are on the same color, look at the following pairs: a1-b1, c1-d1, and e1-f1. Swap the leftmost pair that contains a bishop.
3. If the king is not between his rooks, swap the king with the closer rook.

However, while all positions can be generated this way, not all positions have the same probability to be generated. Mathematical analysis shows that positions with the bishops on a pair a1-b1, c1-d1, e1-f1, or g1-h1 actually have half the probability to be generated than the other positions.

R. Scharnagl also has a method for correcting same color Bishop positions when the pieces are drawn from a bag. He acknowledges that it does not produce all positions with equal probability, but makes the point that the this is not necessary to achieve the main objective of Fischer Random Chess. See the external reference.

One mathematically correct way of proceeding when the Bishops start on squares of the same color would have a randomly selected Bishop move to a randomly selected square of the opposite color. This idea is due to David Wheeler. A choice involving a white Pawn and a black Pawn could be used to select the a-side or h-side Bishop, which would be removed from the board. Then the black pieces could be put in the bag and mixed up. One would be drawn out, and the numbering of the square of opposite color could, for example, be given by R=1, N=2, B=3, K,Q=4.

Many other algorithms for creating initial positions have been created, but in many cases they have the same problem: not all positions will be selected with equal likelihood.

Eight cards method

This method makes use of eight home made cards, perhaps about the size of ordinary business cards. The cards should be marked, respectively, with the names of the eight pieces, R,N,B,Q,K,B,N,R, and, additionally, should be marked, respectively, with the eight labels a-1, a-2, a-3, a-4, h-1, h-2, h-3, h-4.

After the cards are shuffled and dealt in a row, the white pieces should be placed on the back rank as designated by the piece labels. If the Bishops are on squares of the same color, the cards should be put face down, mixed up, and one selected at random. The second label designates whether the a-side or h-side Bishop is to be moved, and which square of the opposite color it moves to. It trades places with the piece that is there. The idea behind this, a randomly selected Bishop moves to a randomly selected square of the opposite color, is due to David Wheeler.

After the Bishops are on squares of different colors, attention is given to the King and Rooks. If the King is not between the Rooks, it must trade places with the nearest Rook.

Platonic solid dice

If one has polyhedral dice shaped like each of the Platonic solids, one never needs to reroll any dice.

• Roll the dice.
• Place a white bishop on the square indicated by the octahedron (d8).
• Place the other white bishop on the square of opposite colour indicated by the tetrahedron (d4).
• Place the white queen on the square indicated by the cube (d6).
• Take the number of the icosahedron (d20). Multiply by 2, then add 8. For example, 19 -> 46. Divide the second digit by 2 and add 1. For example, 46 -> 44. Place a white knight on the square indicated by the second digit, then place the other white knight on the square indicated by the first digit. An alternative would be to label the 20 faces of the icosahedron with the 20 pairs of digits where the first digit varies from 1 through 4, and the second digit varies from 1 through 5. A second alternative would be to use the icosahedron (d20) (dividing by 4 to get numbers 1-5) to determine where the first knight goes and dodecahedron (d12) (Dividing by 3 to get numbers 1-4) to determine where the second knight goes. This uses all 5 Platonic solids and saves you a lot of math.
• Ignore the dodecahedron (d12) and place the white rooks and the white king between the rooks. Alternatively, use the dodecahedron to decide who plays white, so as to randomize in the absence of other reasons (one player uses white if the dodecahedron comes up odd, the other if it comes up even).
• Place the white pawns and mirror the position for black.

A matched Platonic-solids set of five dice, (from left) tetrahedron (d4), cube (d6), octahedron (d8), dodecahedron (d12) and icosahedron (d20).

Non-random setups

The initial setup need not necessarily be random. The players or a tournament setting may decide on a specific position in advance, for example.

Edward Northam suggests the following approach for allowing players to jointly create a position without randomizing tools. First, the back ranks are cleared of pieces, and the white Bishops, Knights, and Queen are gathered together. Starting with Black, the players, in turn, place one of these pieces on White's back rank, where it must stay. The only restriction is that the Bishops must go on opposite colored squares. There will be a vacant square of the required color for the second Bishop, no matter where the previous pieces have been placed. After all five pieces have been put on the board, the King must be placed on the middle of the three vacant back rank squares that remain. Rooks go on the other two.

This approach to the opening setup has much in common with Pre-Chess, the variant in which White and Black, alternately and independently, fill in their respective back ranks. If Pre-Chess were to be played with the requirement of ending up with a legal Fischer Random Chess opening position, something similar to the above might well be the way to go.

Without some limitation on which pieces go on the board first, it is possible to reach impasse positions, which cannot be completed to legal Fischer Random Chess starting positions. Example: Q.RB..NN If the players want to work with all eight pieces, they must have a prior agreement about how to correct illegal opening positions that may arise. If the Bishops end up on same color squares, a simple action, such as moving the a-side Bishop one square toward the h-file, might be agreeable, since there is no question of preserving randomness. Once the Bishops are on opposite colored squares, if the King is not between the Rooks, it should trade places with the nearest Rook.

History

The first Fischer Random Chess tourney was held in Yugoslavia in the spring of 1996, and was won by Grandmaster Péter Lékó.

In 2001, Lékó became the first Fischer Random Chess world champion, defeating GM Michael Adams in an eight game match played as part of the Mainz Chess Classic. There were no qualifying matches (also true of the first orthodox world chess champion titleholders), but both players were in the top five in the January 2001 world rankings for orthodox chess. Lékó was chosen because of the many novelties he has introduced to known chess theories, as well as his previous tourney win; in addition, Lékó has played Fischer Random Chess games with Fischer himself. Adams was chosen because he was the world number one in blitz (rapid) chess and is regarded as an extremely strong player in unfamiliar positions. The match was won by a narrow margin, 4.5 to 3.5.

In 2002 at Mainz, an open Fischer Random tournament was held which attracted 131 players. Peter Svidler won the event. Other interesting events happened in 2002. The website ChessVariants.org selected Fischer Random chess as its "Recognized Variant of the Month" for April 2002. Yugoslavian Grandmaster Svetozar Gligoric published in 2002 the book Shall We Play Fischerandom Chess?, popularizing this variant further.

At the 2003 Mainz Chess Classic, Svidler beat Lékó in an eight game match for the World Championship title by a score of 4.5 - 3.5. The Chess960 open tournament attracted 179 players, including 50 GMs. It was won by Levon Aronian, the 2002 World Junior Champion. He will be invited to challenge Svidler at the 2004 Mainz Chess Classic.

Naming

This particular chess variant has a number of different names. The first names applied to it include "Fischer Random Chess" and "Fischerandom Chess".

Hans-Walter Schmitt (chairman of the Frankfurt Chess Tigers e.V.) is an advocate of this chess variant, and he started a brainstorming process to choose a new name for it. The new name had to obey the following requirements on the parts of some leading grandmasters:

1. It should not use parts of the name of any Grandmaster colleague
2. It should not include negatively biased or "spongy" elements like "random" or "freestyle"
3. It should be understood worldwide.

This effort culminated in the name "Chess960", deriving from the number of different initial positions.

R. Scharnagl, another proponent of this variant, had used the term FullChess instead. But today he uses "FullChess" to address chess variants consistently embedding the traditional chess game, e.g. Chess960 and some new variants based on the extended 10x8 Capablanca piece set. He actually recommends the use of the term "Chess960" instead of Fischer Random Chess.

At this time the terms "Fischer Random Chess" or "Fischerandom chess" are more common. It is not yet clear if these other, newer terms, or yet another one will replace it.

Bridge players would probably suggest it be called "duplicate chess".

External links

• Audio clip of Bobby Fischer describing his Fischer Random Chess. (http://www.wacklepedia.com/bobby_fischer/bobby_fischer_sound_12.htm)
• Fischer Random Chess | Chess Variant Pages (http://www.chessvariants.org/diffsetup.dir/fischer.html)
• FRC: Manual Procedure for Generating Piece Placements | Chess Variant Pages (http://www.chessvariants.org/diffsetup.dir/fischer-random-setup.html)
• Rules Of Chess 960 (FRC) (http://www.frankfurtwest.de/ChessClassic/cc03/e/c960/rules.htm)
• Fischer Random Chess (Chess 960) (http://www.chessbox.de/Compu/fullchess1_e.html) - book by Reinhard Scharnagl
• Fischer Random Chess Description (http://www.dwheeler.com/essays/Fischer_Random_Chess.html)
• "Leko, the first ever kingpin of Fischer Random Chess" (http://www.geocities.com/MIGHTORS1/Leko/Fischerandom6.html)
• Shall We Play Fischerandom Chess? (http://www.chessville.com/reviews/reviews_Fischerandom.htm) - book by Svetozar Gligoric
• Rules Of Fischer Random Chess (in Spanish) | Chess Variant Pages (http://www.chessvariants.org/d.sp/fischer.html)
• Rules Of Fischer Random Chess (in French) (http://www3.sympatico.ca/remi.marois/fischerandom.htm)
• Rules of Fischer Random Chess (http://www.eusa.ed.ac.uk/societies/chess/Chess/Trivia/random.html)
• Fischer Random Chess | Play Against Computer With Arena (http://www.playwitharena.com/) - software.
• Fischer Random Chess | Play at SchemingMind.com (http://www.schemingmind.com)
• Fischer Random Chess | FRC at demand at The Easy Emailchess Club 'E4EC' (http://www.e4ec.org/)

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