Fischer Random Chess
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Fischer Random Chess (also called Chess960, 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.
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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 would be no 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.
Rules
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 the opponent's king.
Rules for castling
Fischer random chess allows each player to castle once per game, moving both the king and a 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, also known in some places as c-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 a-side Rook is on d (d1 for White and d8 for Black). After h-side castling, also known in some places as g-castling, (notated as O-O and known as king-side castling in orthodox chess), the King is on g and the h-side 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:
- Unmoved: The king and the castling rook must not have moved before in the game, including castling.
- 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.
- 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 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 the meantime there has been an adjustment setting of the WNCA that when performing a castling move it is irrelevant in which sequence involved pieces were touched. All pieces involved in a move may be touched arbitrarily. When castling those pieces are the King and Rook, and in capturing moves they are the capturing and the captured piece. Especially with players new to Fischer Random Chess it might make sense also to announce a castling to avoid misunderstandings. When a chess clock will be used, pressing the button could be taken as a sign that a castling move has been 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. Recommended gestures are: the King is moving to his at least two steps distant castling target square or else upon the involved Rook, to avoid by this a possible confusion with normal King's moves.
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. 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. A game of traditional Chess could easily be recognized via the missing SetUp and FEN tags.
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, X-FEN, has been devised by Reinhard Scharnagl to remove this ambiguity. In X-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 substituting (uppercase when white) the related "K", "k", "Q", or "q". In other words, in X-FEN notation, castling potentials belong to the outermost rooks by default. This means that the maximum length of the castling value unchanged is 4 characters, though positions needing that change are extremely improbable. Note that X-FEN is upwardly compatible, that is, a program supporting X-FEN will automatically use the normal FEN codes for a traditional chess starting position without requiring any special programming. As a benefit all 18 pseudo FRC positions (positions with traditional placements of Rooks and King) still remain uniquely encoded.
Starting position IDs in Fischer Random Chess / Chess960
Some people have wanted each possible starting position to have a unique standard numeric identifier (id). Reinhard Scharnagl recommends in his Chess960 Enumbering Scheme 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.
Using repeated multiplication or division
| KRN code | Position |
|---|---|
| 0 | N N R K R |
| 1 | N R N K R |
| 2 | N R K N R |
| 3 | N R K R N |
| 4 | R N N K R |
| 5 | R N K N R |
| 6 | R N K R N |
| 7 | R K N N R |
| 8 | R K N R N |
| 9 | R K R N N |
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 for RNKNR) = 518
The sample position shown above, BNRBNKRQ, is id
id = (1 because the light square Bishop is on file d) +
4 × (0 because the dark square Bishop is on file a) +
16 × (5 because the Queen is on file h, skipping both bishops) +
96 × (1, the KRN code for NRNKR) = 1+0+16*5+96 = 177
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.
Fritz9
Fritz9, a program due to get a lot of publicity, generates numbers from positions in a somewhat different way. The Bishops are treated as above. Next, attention is given to the Knights (rather than to the Queen). There are 15 ways that 2 Knights can be arranged in 6 squares (skipping over Bishops).
NN codes
0 NN**** 3 N***N* 6 *N*N** 9 **NN** 12 ***NN* 1 N*N*** 4 N****N 7 *N**N* 10 **N*N* 13 ***N*N 2 N**N** 5 *NN*** 8 *N***N 11 **N**N 14 ****NN
Here the * could be Q, K, or R. Then the Queen is left with 4 possibilities: 0,1,2,3 (skipping over Bishops and Knights).
id = (light square Bishop) + 4*(dark square Bishop) + 16*(NN code) + 240*Queen + 1.
The 1 is added so that the id will vary between 1 and 960 instead of 0 and 959.
The last two numbers that are needed in this calculation become easier to see if the NQ-skeleton for the position is written down. To do this, omit the Bishops, and replace "K" and "R" by a common character, say, "-". So, for the standard starting position, the NQ-skeleton is -NQ-N-. The Queen's position number is the number of hyphens to the left of "Q" (1 in this case). Imagining that the "Q" is a "-" makes the NN code apparent (7 in this case). For the standard starting position, the light square Bishop is at position 2, and the dark square Bishop is at position 1. This gives
id = 2 + 4*1 + 16*7 + 240*1 + 1 = 359
Upon entry to Chess960, Fritz9 prompts the user to enter a position id or to "Draw Lots". This limited choice means that the calculation above is needed if the user wants to play against Fritz9 and choose the locations of the pieces on the back rank.
Almost all of the arithmetic can be eliminated by using the tables below. The columns of the NQ-skeleton table correspond to the Queen's position (the number of hyphens to the left of the "Q"), and, within each column, the ordering is alphabetic with "-" last. Thus any NQ-skeleton can be located quickly, and its number takes care of all the Knight, Queen arithmetic and the final + 1. The Bishop's table takes care of the Bishop's arithmetic. So, for the standard starting position, id = 353 + 6 = 359.
NQ-skeleton Table
1 NNQ--- 241 NN-Q-- 481 NN--Q- 721 NN---Q 17 NQN--- 257 N-NQ-- 497 N-N-Q- 737 N-N--Q 33 NQ-N-- 273 N-QN-- 513 N--NQ- 753 N--N-Q 49 NQ--N- 289 N-Q-N- 529 N--QN- 769 N---NQ 65 NQ---N 305 N-Q--N 545 N--Q-N 785 N---QN 81 QNN--- 321 -NNQ-- 561 -NN-Q- 801 -NN--Q 97 QN-N-- 337 -NQN-- 577 -N-NQ- 817 -N-N-Q 113 QN--N- 353 -NQ-N- 593 -N-QN- 833 -N--NQ 129 QN---N 369 -NQ--N 609 -N-Q-N 849 -N--QN 145 Q-NN-- 385 -QNN-- 625 --NNQ- 865 --NN-Q 161 Q-N-N- 401 -QN-N- 641 --NQN- 881 --N-NQ 177 Q-N--N 417 -QN--N 657 --NQ-N 897 --N-QN 193 Q--NN- 433 -Q-NN- 673 --QNN- 913 ---NNQ 209 Q--N-N 449 -Q-N-N 689 --QN-N 929 ---NQN 225 Q---NN 465 -Q--NN 705 --Q-NN 945 ---QNN
Bishop's Table
0 BB------ 4 -BB----- 8 -B--B--- 12 -B----B- 1 B--B---- 5 --BB---- 9 ---BB--- 13 ---B--B- 2 B----B-- 6 --B--B-- 10 ----BB-- 14 -----BB- 3 B------B 7 --B----B 11 ----B--B 15 ------BB
The reverse problem, given an id to find the position, can be solved in several ways. Fritz9 does this instantly, but, if for some reason, a manual method is desired, there are two possibilities. The repeated division process of the section above can be adapted to this setting (subtract 1, then do divisions by 4, by 4, and by 15), or the tables can be used. In the NQ-skeleton Table, find the largest number, call it N, that is less than or equal to the id. Then id - N gives the Bishop's positions; the NQ-skeleton at N takes care of the Queen and Knights, and the Rooks and King fill in the remaining spaces.
Lookup using two tables
The Chess960 Enumbering Scheme could be shown in the form of a simple two tables representation. This mapping of starting arrays and numbers stems from Reinhard Scharnagl and is now worldwide used for Chess960. The enumeration has been published first in the internet an then 2004 in his (German language) book "Fischer-Random-Schach (FRC / Chess960) - Die revolutionäre Zukunft des Schachspiels (inkl. Computerschach)",.
How to use the two Tables
This both tables will serve for a quick mapping of an arbitrary Chess960 starting position (short: SP) at White's base row to a drawn number between 1 and 960 (rsp. 0 and 959). First search for the same or the nearest smaller number from the King's Table. Then determine the difference (0 to 15) to the drawn number and select that matching Bishops' positioning from the Bishop's Table. According to this first place both Bishops at the first base row, then the six pieces in the sequence of the found row of the King's Table upon the six free places left over. Finally the black pieces will be placed symmertically to White's base row.
Example: look at the SP-518. In the King's Table we will find No. 512 "RNQKNR". For the remainder 6 we will find "--B--B--" in the Bishop's Table at No. 6. Altogether by that for the SP-518 = 512+6 this will result in the well known white starting array "RNBQKBNR" from traditional Chess.
The tables can also be used in the reverse direction. Given a starting position 8 letter array, SP, extract from it the 5 letter subarray involving the letters K,R,N. Then search for this subarray among the ten entries in the King's Table whose numbers are marked with a #. It will appear in the first 5 columns followed by a "Q". This is essentially the same as the KRN search which is the last step in the "repeated multiplaction " method above. Then look upward (at most 5 numbers) until an entry is found with the "Q" in the same relative place as in SP. Call this number N. Locate, in the Bishop's Table that number, call it M, whose Bishops position matches that in SP. Then ID = N + M.
Example: Given SP = "RNBQKBNR" extract "RNKNR" and locate this at No. 560 in the King's Table. Look upward and find "RNQKNR" at No. 512. The Bishop's position in SP is found at No. 6 in the Bishop's Table. So ID = 512 + 6 = 518.
King's Table
| Max. | Positioning Sequence of the other Pieces | ||||||||||||||||||||||
| 0 | Q | N | N | R | K | R | 336 | N | R | K | Q | R | N | 672 | Q | R | K | N | N | R | |||
| 16 | N | Q | N | R | K | R | 352 | N | R | K | R | Q | N | 688 | R | Q | K | N | N | R | |||
| 32 | N | N | Q | R | K | R | #368 | N | R | K | R | N | Q | 704 | R | K | Q | N | N | R | |||
| 48 | N | N | R | Q | K | R | 384 | Q | R | N | N | K | R | 720 | R | K | N | Q | N | R | |||
| 64 | N | N | R | K | Q | R | 400 | R | Q | N | N | K | R | 736 | R | K | N | N | Q | R | |||
| #80 | N | N | R | K | R | Q | 416 | R | N | Q | N | K | R | #752 | R | K | N | N | R | Q | |||
| 96 | Q | N | R | N | K | R | 432 | R | N | N | Q | K | R | 768 | Q | R | K | N | R | N | |||
| 112 | N | Q | R | N | K | R | 448 | R | N | N | K | Q | R | 784 | R | Q | K | N | R | N | |||
| 128 | N | R | Q | N | K | R | #464 | R | N | N | K | R | Q | 800 | R | K | Q | N | R | N | |||
| 144 | N | R | N | Q | K | R | 480 | Q | R | N | K | N | R | 816 | R | K | N | Q | R | N | |||
| 160 | N | R | N | K | Q | R | 496 | R | Q | N | K | N | R | 832 | R | K | N | R | Q | N | |||
| #176 | N | R | N | K | R | Q | 512 | R | N | Q | K | N | R | #848 | R | K | N | R | N | Q | |||
| 192 | Q | N | R | K | N | R | 528 | R | N | K | Q | N | R | 864 | Q | R | K | R | N | N | |||
| 208 | N | Q | R | K | N | R | 544 | R | N | K | N | Q | R | 880 | R | Q | K | R | N | N | |||
| 224 | N | R | Q | K | N | R | #560 | R | N | K | N | R | Q | 896 | R | K | Q | R | N | N | |||
| 240 | N | R | K | Q | N | R | 576 | Q | R | N | K | R | N | 912 | R | K | R | Q | N | N | |||
| 256 | N | R | K | N | Q | R | 592 | R | Q | N | K | R | N | 928 | R | K | R | N | Q | N | |||
| #272 | N | R | K | N | R | Q | 608 | R | N | Q | K | R | N | #944 | R | K | R | N | N | Q | |||
| 288 | Q | N | R | K | R | N | 624 | R | N | K | Q | R | N | 960 | Q | N | N | R | K | R | |||
| 304 | N | Q | R | K | R | N | 640 | R | N | K | R | Q | N | R. Scharnagl | |||||||||
| 320 | N | R | Q | K | R | N | #656 | R | N | K | R | N | Q | ||||||||||
Bishop's Table
| Remainder | Bishops' Positioning | |||||||
| a | b | c | d | e | f | g | h | |
| 0 | B | B | - | - | - | - | - | - |
| 1 | B | - | - | B | - | - | - | - |
| 2 | B | - | - | - | - | B | - | - |
| 3 | B | - | - | - | - | - | - | B |
| 4 | - | B | B | - | - | - | - | - |
| 5 | - | - | B | B | - | - | - | - |
| 6 | - | - | B | - | - | B | - | - |
| 7 | - | - | B | - | - | - | - | B |
| 8 | - | B | - | - | B | - | - | - |
| 9 | - | - | - | B | B | - | - | - |
| 10 | - | - | - | - | B | B | - | - |
| 11 | - | - | - | - | B | - | - | B |
| 12 | - | B | - | - | - | - | B | - |
| 13 | - | - | - | B | - | - | B | - |
| 14 | - | - | - | - | - | B | B | - |
| 15 | - | - | - | - | - | - | B | B |
Other ways to create initial positions
There are several other methods that can create initial positions. Keep in mind that some of these, as noted, do not produce all legal arrangements of pieces with equal probability, and in that sense are less than random.
Coin-tossing method
This method does not produce all legal starting positions with equal probability. The positions that arise when the King occupies the center two of the four possibilities are two thirds as likely as the others.
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:
- Place a Bishop on one of the 4 light squares.
- Place a Bishop on one of the 4 dark squares.
- 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.
- Place a Rook on the a-side of the King.
- Place a Rook on the h-side of the King.
- Place the Queen on one of the 3 vacant squares that remain.
- 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
These methods all start with a random arrangement of pieces on White's back rank. There are 5040 such arrangements, of which 2880 have the Bishops on opposite colored squares, but only 2160 have the Bishops on same colored squares. Thus, no attempt to correct the latter Bishop positions by linking each of the latter arrangements to one of the former arrangements can produce results with equal probabilities. Usually one fourth of the opposite color Bisop positions will be half as likely as the others. (2880-2160)/2880 = 0.25.
David J. Coffin suggests the following procedure, which has the advantage of not requiring computers, dice, or lookup tables:
- Place the eight white pieces in a bag. Draw them one by one and place them on squares a1, b1, ... h1.
- 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.
- 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 this is not necessary to achieve the main objective of Fischer Random Chess. See the external reference.
One 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, and it produces all opposite color Bishop positions with equal probability. 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.
A much quicker method is to simply gather the 8 pieces into a circle on the table, then squash the circle flat into a line. If the bishops would be on the same colour, gather the pieces and try again. Once the bishops are right, swap the king and rook (as above), and start the game.
Eight cards method
This method produces all legal starting positions with equal probability.
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.
The German version of this article shows that a much simpler deck of cards will suffice. They need only carry the numbers 1 through 8. On the first deal pieces are assigned to the numbers following the starting position in standard chess. ie. 1,8=R, 2,7=N, 3,6=B, 4=Q, 5=K. If a Bishop move is needed, The numbers 1-4 designate that the a-side Bishop is to move, and the numbers 5-8 designate that the h-side Bishop is to move. In the latter case, 4 should be subtracted form the number to get the square of opposite color for the h-side Bishop to move to.
-OR-
This method does not produce all legal starting positions with equal probabilities. The problem is discussed at the top of the "Drawing methods" section.
Using a deck of playing cards, you can select the King, Queen, 2 Jacks, 2 Aces, and 2 Tens. You can seperate these out in seconds, and decide on which minor pieces are represented by which cards (as the King & Queen are obvious.) Shuffle. Cut the deck. Deal. You have to take care as to keep the Bishops on opposite colors, and the King between the Rooks. To deal with a card that would be illegal, just hold that piece to the side until it is legal to place. When a legal square opens, place the held piece. Sometimes, two pieces are held but it is not confusing and quite a speedy and random method.
Platonic solid dice
This method produces all starting positions with equal probability.
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). Subtract one, divide by four, and add one to quotient and remainder. These determine positions of the first and second knight.
- Place the white rooks and the white king between the rooks. If desired, use the dodecahedron to decide who plays white (even numbers for one player, odd for the other).
- Place the white pawns and mirror the position for black.
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. Tournament Directors prefer that all boards in a single round play the same random position, as to maintain order and abbreviate the setup time for each round.
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
A variant of random chess defined by former World Champion Bobby Fischer and introduced formally to the chess public on June 19, 1996, in Buenos Aires, Argentina. Bobby Fischer must have been shocked to see how opening theory had developed since his last game in 1972. It is said that friends from throughout the world sent him masses of analysis, which he ignored during the match against Spassky in 1992. The sheer volume of material probably made Fischer realize, there was no way back... After that experience, Fischer started thinking about an alternative. He also stated when he introduced his variant at a press conference in 1996, that all of the study necessary to play conventional chess made it hard work, and he had gotten into chess in order to avoid work!
Fischer's goal was to eliminate what he considers the complete dominance of openings preparation in chess today, and to replace it with creativity and talent. Since the opening book for each possible opening position would be too difficult to devote to memory (959 "book opening" systems), therefore, each player must create every move originally. From move 1 on both players have to come up with original strategies and can not use well-known thinking patterns. By eliminating memorized book moves, Fischer believes that it will level the playing field; and as an accidental consequence, it makes computer chess programs much weaker, as they depend on the opening book to beat humans.
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 tournament 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 (Fischer Random Chess) open tournament attracted 179 players, including 50 GMs. It was won by Levon Aronian, the 2002 World Junior Champion. He played Svidler for the title at the 2004 Mainz Chess Classic, losing 4.5-3.5. At the same tournament in 2004, Aronian played two Chess960 games against the Dutch computer chess program The Baron, developed by Richard Pijl. Both games ended in a draw. It was the first ever man against machine match in Chess960. In 2005 The Baron played two Chess960 games against Chess960 World Champion Peter Svidler; Svidler won 1.5-0.5. The chess program Shredder, developed by Stefan Meyer-Kahlen from Düsseldorf, Germany, played two games against Zoltan Almasi from Hungary; Shredder won 2-0. Almasi and Svidler played an eight-game match at the 2005 Mainz Chess Classic. Once again, Svidler defended his title, winning 5-3.
Computer Chess960 (Fischer Random Chess) world championship
During the Chess Classic 2005 in Mainz, initiated by Mark Vogelgesang and Eric van Reem, the first-ever Chess960 computer chess world championship was played.[1] Nineteen programs, including the powerful Shredder, played in this tournament. As a result of this tournament, Spike became the first Chess960 computer world champion.
Naming
This particular chess variant has a number of different names. The first names applied to it include "Fischer Random Chess" and "Fischerandom Chess". However, this has become as unfashionable as Fischer himself. It is his invention, and he put his own name to it.
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:
- It should not use parts of the name of any Grandmaster colleague
- It should not include negatively biased or "spongy" elements like "random" or "freestyle"
- 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.
Similar Chess Variants
There are other chess variants with rules similar to Fischer Random Chess. These include:
- King's Corner chess: like Fischer Random Chess, the placement of the pieces on the 1st and 8th row are randomized, but with the king in the right hand corner. Black's starting position is obtained by rotating white's position 180 degrees around the board's center.
- Randomly opened chess: similar to Fischer Random Chess, except players take turns placing pieces on the board (pawns may go anywhere in the 2nd, 3rd, or 4th ranks, while other pieces may go anywhere)
- Transcendental chess: similar to Fischer Random Chess, but the opening white and black positions do not mirror each other. (Also called Double Fischer Random Chess or Wild Chess)
John Kipling Lewis's "Castling in Chess960: An appeal for simplicity" proposes the same rules for the initial position as Fischer Random Chess, but proposes an alternative set of castling rules. In this variation, the preconditions for castling are the same, but when castling "the King is transferred from its original square two squares towards (or over) the Rook, then that Rook is transferred to the square the King has just crossed (if it is not already there). If the King and Rook are adjacent in a corner and the King can not move two spaces over the Rook, then the King and Rook exchange squares." Note that these rules are different from the Fischer Random Chess rules, since the final position after castling will usually not be the same as the final position of a castling move in traditional chess. Lewis argues that this alternative better conforms to how the castling move was historically developed. Lewis has named this chess varation "Chess480"; this variation follows the rules of Fischer Random Chess with the exception of the castling rules which Lewis has named "Orthodoxed Castling".
External links
Descriptions and commentary
- Audio clip of Bobby Fischer describing his Fischer Random Chess
- Fischer Random Chess Description at ChessVariants.org
- FRC: Manual Procedure for Generating Piece Placements at ChessVariants.org
- Fischer Random Chess Description
- Rules of Fischer Random Chess (UK server)
- "Leko, the first ever kingpin of Fischer Random Chess"
- Shall We Play Fischerandom Chess? - book by Svetozar Gligoric
- Castling in Chess960: An appeal for simplicity by John Kipling Lewis
- Rules of Chess960 (FRC) (German server)
- Reinhard Scharnagl's ChessBox (English/German) and book Fischer-Random-Schach (FRC/Chess960) ISBN 3-8334-1322-0 (German server)
Play via internet
- Play FRC against computer chess engines or against people over the Internet with free Arena software
- Play Fischer Random Chess online
- Play Chess960 via Internet by email or on the web site using Flash
- The Email/Correspondence Chess Club for FRC/Chess960
- Play Correspondence Chess including Chess960 (Fischer Random Chess)
- Play server-based correspondence chess games including FRC
In other languages
- Rules (in Spanish) of Fischer Random Chess
- Rules (in French) of Fischer Random Chess (Canadian server)
