(2018-08-07) The old games of Chaturanga and Shatranj.
Apart from Go, all ancien board games can all be classified as single-track race games. Mancala is purely strategic (if you're allowed to count the stones in each pit) but all the others involve an element of pure luck. Here are the three most notable examples:
The Mesopotamian Royal Game of Ur. One of the best designs of all time. It's played with twosets of seven pieces (at most) racing on a special board of 20 squares (two symmetrical 14-square tracks sharing an 8-square middle lane). The game traditionally uses 4 tetrahedral dice with two marked corners. The outcome of a throw is the total number of marked corners landing at the top; it's 0,1,2,3,4 (respectively with 1,4,6,4,1 chances in 16). The exact rules were found on a late-period clay tablet from the British Museum deciphered by Irving Finkel. [Play online]
The Egyptian game of senet (the game of passing). Two sets of 5 pieces, racing mostly forward on a single 30-square track (laid out on a 3 by 10 board). This simple game has been resurrected using the rules reconstructed by the twogame historians Timothy Kendall and R.C. Bell (1917-2002).
By contrast, the early forms of chess didn't involve chance at all andmade full use of the two dimensions of the game board.
The earliest recognizable form of chess was called chaturanga (or catur for short). It appeared in India, in the seventh century AD and is first mentioned inthe Harshacharita (biography ofHarsha, c.590-647) by Banabhatta.
Shortly thereafter, the game appeared in Persia under a new name (shatranj or chatang) and slightly revised rules. It was possible to win in shatranj by capturing all piecesbesides the King (but it was a draw if the opponent could do the same on the next move).
The strongest shatranj player on record was Al-Suli (AD 880-946) the author of a famous shatranj problem known as Al-suli's Diamond, which was solved in the 1980sby Yuri Averbakh (1922-2022). White wins by capturing the black ferz which can only move diagonally one square ata time) without losing his own on the next ply... in 19 moves!
The starting positions in those games were similar to that of chess (up to a switch of the king and the minister/general/queen). However, the pieces had different names, shapes and properties (somewhat shrouded in uncertainty) as tabulated below.
Pawns capture diagonally. All other pieces capture the same way they move.
At first, the games were played on an uncheckered boardof 64 squares The familiar alternating light and dark colorsof modern chessboards first appeared in Europe around 1090.
Fantasy
Legend has it that Chaturanga was invented for Iadava, King ofTelangana, who was mourning the loss of his son Adjamir. The Prince had died heroically to secure victory in a decisivebattle at Decsina against the conqueror Varangul.
A young brahmin, called Lahur Sessa, walked 30 days from the village of Manir to the Andhra royal palaceand presented Iadava with the new game he had designed. The king was so pleasedthat he asked the young man to name any reward he wished. The lad made a simple request related to the 64 squares on the board: He asked for one grain of wheat on the first square, two on the second, four on the third and twice as many grains on every square as on itspredecessor. The King thought that this was a modest price topay, until he was advised that the number of grains so named was humongous:
Incidentally, that factorization contains the five known Fermat primes and a famous factorization ofEuler(1732): 232+1 = 641 . 6700417.)
Nice tale, isn't it? Unfortunately, that's all it is. In someversions, the young inventor is made vizir for life. In other versions, he is executed.
By convention, the chessboard must be oriented so that the closest corner to the right of either player is a light square (light rhymes with right). This was first specified in print by Pedro Damiano (1480-1544) in 1512. The practice of shading dark squares in printed chess diagrams was introduced by the scientist Girolamo Cardano (1501-1576).
Three modern moves have no equivalent in ancient chess:
On its first move, a pawn may travel two squares forward (if both the destination and the passed-over square are free).
En passant capture by a pawn is allowed immediately after one such move (it takes place at the passed-over square). It's customaryto stress such a move with the annotation "e.p." (postfixed) which is entirely optionalsince a diagonal pawn move into an empty square can only occur by virtue of an en passant capture. The option is only open on the very next move, which incidentallydoesn't void the classical way to gain a tempo by putting the king in check. (A tempo is gained anyway because preventing check is at the cost of an immediate capture. This is illustrated by #48875 or#62178, where the tempo so gained allows a rook capture (winning the game) whether the opponent accepts the pawn check or prevents it using en passant. The rule was primarily invented to prevent the newly-minted two-square pawn movesto allow too many "passed pawns" (pawns with no opposing pawns on their way to promotion). Only pawns can capture en passant (other pieces controllingthe square jumped over by a pawn can't capture it en passant, although it would have been perfectly logical to allow that).
Castling (French roque; 14th or 15th century, in Europe) If all squares between the king and a rook are free, thena legal move consists in moving the rook next to the king and having theking jump over it, provided the following conditions are met:
The king and the rook have never moved before.
No square in the path of the king is under attack.
Two more additions have transformed traditional chess into the game which is mostcommonly played today, especially online:
Thechess clock. Originally introduced merelyto avoid tournament games that could be so long that they would routinely be adjourned from one day to the next, the clockhas become such a dominant part of modern games that people routinely winlots of games merely by outpacing their opponents. With some silly local rules, a player who doesn't have enough material tomate may be declared the winner. Arguably, a perversion of chess.
TheElo rating system. It has outgrown its originalpurpose to organize tournaments for all categories of players (you're banned from lower grades when you become too strong). Improving one's rating may become the most important goalto achieve. ; At all strength levels from utmost beginnerto World champion (World champion Magnus Carlsenonce stated that his top priority was to achieve an Elo of 2900 rather thanretain his World title).
Chess used to be played until the king was actually captured. This meant that a player who didn't move out of check (or even moved into check) would lose by having the king capturedon the next turn, unless the opponent blundered the game away.
To avoid such endings, it's now illegal to move into check or not to move out of check. To better enforce that law, whoever puts a king in check must announce it. In several languages, the plural form of such announcements morphed into the nameof the game itself (chess is a corrupted form of checks in English; the game is called échecs in French).
One interesting consequence of that modern rule is the possibility of stalemate (French: pat) whichis a situation when a player is not in check but has no legal move available. This is now declared a draw. In some endgames, the goal of the dominating playerthus becomes to force checkmate while avoiding a stalemate situation.
Some obsolete rules considered a stalemate a win for whoever was called to play from such a situation. This was the case in England until 1800.
The German term Zugzwang (capitalized if German spelling is to be respected) denotes a configuration whichis less favorable if you have to move first than if you don't, especially in endgamesituations very near to a checkmate or stalemate. (In combinatorial games theory the term is sometimes used to denote a losing situation for whoever has to move first.)
The oldest extantgame of modern chess was played in 1475 in Valencia between Don Franci de Castellvi (White) and Narciso Vinyoles (Black). The game illustrates a famous poem entitled Scachs d'Amor (Chess Game of Love) written in Catalan (more precisely Valencian) by Castellvi (Venus), Vinyoles (Mars) and Mossèn Bernat de Fenollar (Mercury).
Caissa (Scacchia)
Caissa (pronounced ky-eé-sah) isa nymph of Greek mythologywho became known as the patron godess of chess after a celebrated poem writtenin 1763 by the young William Jones(1746-1794) and entitled CAISSA or The Game at Chess; a Poem.
The poem of Jones was itself inspired by a 658-line poem in Latin called Scacchia Ludus (The Game of Chess) due to Marco Girolamo Vida(c.1485-1566) who wrote it around 1513, as Chess in its modern form was gaining popularity in Europe. It was first published anonymously in 1525 before appearing officiallyunder Vida's name in 1527.
In many languages, the name of the game of chess is related to the nameof the nymph Cassia (herself called Scacchia in Vida's Latin poem).
(2018-09-11) Various ways the actual chess playing surface is provided.
The generic term of chessboard (or just board) is used for all of these, but it need not be an actual rigid board. It can also be inlaid into a dedicated table or, for best portability, a mat can be used which can be rolled up (or folded, if made out of silicone).
In the US, the most common size for tournaments features 2.25'' squares (57 mm). In metric countries, it's nominally 55 mm.
The playing surface itself is thus 18'' (46 cm). Typically about 20'' with the borders which oftenfeature two sets of rank numbers and file letters (to accomodate both players).
Smaller boards are 2'' (51 mm) or 50 mm. Larger ones are 60 mm. (about 2 3/8 ) rarely 2.5'' (63.5 mm). Anything outside that range is unsuitable for competition (especially for quick bullet games).
Among many others Wholesale Chess offers 60 mm mahogany-and-maple boards for $80 or $90 (with notation). The playing surface on those boards is exactly 19''. They measure 21½'' with the borders.
I love the look and feel of a borderless regulation board (2¼'' = 57 mm) which spans only 18½''. (If borders with notation are ever needed, such a board can be placedon top of an ordinary tournament mat.) The best-bang-for-the-buck I found is the inlaid mahogany and maple Zeluschessboard ($55) which comes double-boxed for shipping (Amazon even puts that double box in an oversized shipping box of their own.)
Such high-quality borderless chessboards can also be used in a customized tableor a one-of-a-kind frame (the playing surface can be mounted recessed, flushor raised, according to taste). That's a cost-effective way to bypass the time-consuming process offinishing a good playing surface by hand. If you make your own frame, considerproviding some substantial rounding or overhang on the outside edges to makethe assembly easy to pick up (most commercial products don't).
Arguably, the board need not match the colors of the pieces. Playability is hindered when ebonized pieces are camouflaged on black squares.
(2018-09-07) Recommended sizes.
When the game of chess is discussed abstractly, we talked about pawns and pieces. The word chessmen is normally used only forthe physical objects made from wood, metal, stone, clay or plastic.
In modern tournament play, only minor variants of the Staunton chessmen are used. The official tournament guideline states that the base diameter of the king should be no more than 75%of the side of a squares on the chessboard. Four pawns should barely fit into a square (base diameter being 50% the side of a square).
My own plastic tournament set, for use with a standard 2¼'' mat, is the common 3.75'' Staunton design above.
With the slim Zagreb '59 design, a tall king (3.9'') can fit nicely on a standard 2¼'' board. I bought the new weighted boxwood set shown below off of eBay directly from India (for $68.64, including expedited shipping from Amritsar toLos Angeles). It arrived in less than 4 days.
The above picture shows 2'' squares, which are a bit too small forthe Zagreb pieces whose precise measurements are listed below:
Zagreb '59 Measurements (3.9'' nominal)
Mass
Height
Base
King
57 g
3.87''
98.3 mm
1.69''
42.8 mm
K
Queen
53 g
3.50''
88.9 mm
1.59''
40.5 mm
Q
Bishop
39 g
3.08''
78.2 mm
1.42''
36.0 mm
B
Knight
46 g
2.78''
70.5 mm
1.45''
37.0 mm
N
Rook
38 g
2.23''
56.7 mm
1.43''
36.3 mm
R
Pawn
17 g
1.99''
50.5 mm
1.20''
30.4 mm
P
Matching Square Size
2.25''
57.2 mm
S
The ideal square size for a given set of pieces depends only on the bases, not the heights. Two good rules of thumb are floating around. The first one is simple but the second one is more robust andmore general (it applies to all round designs, even outside the Staunton family):
The king base should be about 75% of the side of the field square.
If a king and a queen are diagonally adjacent, the distance between them should be greater than the bishop's base.
The first rule corresponds to the rough formula K = 0.75 S. The second one says that the diagonal of the square must begreater than the bishop's base plus half the sum of the king and queen bases. Namely:
S 2 > B + (K+Q) / 2
For the above dimensions of the Zagreb pieces, those two formulas give:
S = 2.25'' or 57.2 mm S > 2.16'' or 54.9 mm
This does indicate that a regulation chessboard (55 or 57 mm) is nearly ideal for the above zagreb pieces (while a 2'' board is definitely too tight).
Let's do the same computation for the tournament plastic set I use:
Classical Staunton Measurements (3.75'' nominal)
Mass
Height
Base
King
68 g
3.70''
93.9 mm
1.79''
45.4 mm
K
Queen
62 g
3.12''
79.2 mm
1.71''
43.5 mm
Q
Bishop
37 g
2.78''
70.6 mm
1.43''
36.3 mm
B
Knight
41 g
2.40''
61.0 mm
1.38''
35.1 mm
N
Rook
46 g
2.21''
56.1 mm
1.50''
38.1 mm
R
Pawn
22 g
2.07''
52.6 mm
1.26''
32.0 mm
P
American Regulation Square
2.25''
57.2 mm
S
The aforementioned guideline formulas would give:
S = 2.39'' or 60.6 mm S > 2.25'' or 57.2 mm
Thus, those pieces can be played on regulation US mats (57.2 mm). An oversized 60 mm board would be fine too.
Our next example involves the French style which was dominant throughout Europe beforethe Staunton pattern displaced it for serious play. It's best called Régence. Drop the accent if you must, but avoid the Regency misnomer, since this chess style was actually named after what was the undisputed nevralgic center ofChess in the eighteenth century: Le café de la Régence in Paris, France (best left untranslated).
Incidentally, Howard Staunton (1810-1874) crowned himself World champion in 1843, when he won his return match against the most prominent Régence player of the time, Pierre Saint-Amant (1800-1872).
Traditionally, Boxwood was used for white pieces and ebony for black pieces. Both kinds of wood are denser than water with very fine grain which makesthem exceptionally well suited for turning and fine carving.
Because of recent restrictions on the harvest of ebony, boxwood is increasingly used for black pieces as well usingwhat's call ebonization, whichcan be done several different ways.
Black color is obtained when ferric acetate reacts with wood tannin. This reaction uses the same basic principleas iron-gall ink (upon which Western civilization was arguably founded).
This is a mordant which blackens wood by reacting with the tannin in it.
(2018-10-31)
The bag I recommend to carry full-sizedpieces,a rolled-upmat, a clock,scoresheets and pens is from the USCF ($25).
(2018-08-07) Some controversial aspects of timed games.
Time limitations on chess games are of relatively recent origins. Chess clocks have been used in competition since the London International Tournament of April 1883. In official FIDE tournaments, the chess clock always sits to the rignt of whoeverplays with the black pieces.
Time controls were born out of necessity to make the organization of tournaments possible. The possibility of losing on time was originally justa way to enforce those time limits without altering the nature of the game.
Bonus and Delay :
Those are the two simplest ways to force fast play on low time withoutmaking it humanly impossible to execute decent moves. In practice, these two methods are never used together (although they're not incompatible).
Bronstein delay is also called simple delay or US delay. The player's alloted time doesn't start to be debited until a certainpreset delay has ellapsed. A player who plays every move faster than thispreset delay will never run out of time.
Fischer increment is a preset bonus time which is added at the beginning of every turn. The unused portion of those bonuses can accumulate so thata future move which requires more consideration can be played less recklessly.
Currently, almost all classical chess tournaments endorsedby the Worldwide Chess Federation are played in90 minutes (per player) for the first 40 moves and 20 minutesfor each side for the rest of the game, with a 30-second Fischer increment per move (starting with the very first move). That gives each player 110 minutes to complete the first 40 moves. (That's code 04 on the Wholesale Chess Advanced Digital Game Timer.)
For the World Championship (and the qualifying Candidate Tournament) the time limits are 100 minutes for the first 40 moves, 50 minutesfor the next 20 moves and 15 minutes for the rest of the game. Again with a 30-second Fischer increment starting at the first move. (That's code 05 on the Wholesale Chess Advanced Digital Game Timer.)
Japanese Byo-Yomi:
This is a more complicated time-control used for mostly for shogi and go butdigital chess clocks often allow it.
Gentleman's Rules:
It's a monstrosity to grant a win in chess to a player who doesn't even have enoughpieces to mate (although it's sometimes done in automated online play). In that case, a player is awarded a draw if the other runs out of time.
The game is an instant draw if neither player has enough to mate.
Furthermore, a good Gentleman's Agreement in a timed game is to resign with a bare king if the other side has at least:
A queen.
A rook.
Two bishops.
A bishop and a knight.
It would be nice if chess-playing software enforced this automatically.
In over-the-board play, someone who grabs a piece which has at least one legal movemust play that piece (the old-school touch-move rule). A legal move is final when the player lets go of the piece. I argue that no penalty should be incurred when an illegal move is correctedbefore the clock is punched (but punching the clock after an illegal move forfeits the game).
(2022-02-07) By far, the most common way is the algebraic one. Others still exist.
(2018-08-13) (Philipp Stamma, 1737) Only one notation survives to record chess games, with minor variants.
Each square is identified by a lowercase letter from "a" to "h" according toits file and a numeral from "1" to "8" according to its rank. Squares are either light or dark. The corner squares to the right of either player (h1 and a8) are light. In the starting position, the white queen is on d1 (a light square) andthe black queen is on d8 (a dark square). You may want to remember that queens start on their own colors.
Each type of piece (besides the pawns) is identified by a single capitalletter: K, Q, B, N, R (at each move, White moves first and Black second). When a piece is not specified, a pawn move is understood (the abbreviation P is deprecated).
In case of ambiguity (when the landing square is accessible to two like pieces) give the lowercase letter identifying the file (column) where the piece is moving from after the name of the piece. If that doesn't lift the ambiguity, give the number of the rank instead.
Long and short castling are respectively denoted O-O-O and O-O.
When a pawn is promoted, the piece it becomes is indicated after anequal sign (formerly, a slash was used). For example: 67. c8=Q
No special notation is used (or needed) for en passant capture.
A move which puts the king in check is followed by a plus sign (+).
Checkmate is indicated by a pound sign # (++ is deprecated).
In the computer era, it's important to always record moves in the tersest way (so plain text searches can fetch them). However, in handwritten or printedscores, it's nice to name the captured piece for the sake of readability. For example, the key move in Legal's mate could be written :
5. Nxe5 BxQd1
Likewise, one of six abbreviated annotations of one or two characters, can be given after any move, except a checkmateor a forced move.
Brilliant (!!).
Excellent (!).
Debatable (!?).
Dubious or inaccurate (?!).
Mistake (?).
Blunder (??).
This is in addition to the automatically affixed qualifiers not subject to any judgement call:
Check (+). Marks a move that would allow capture of the king on the next turn.
Double-check (++). In check by two different pieces, the king has to move.
Forced (,). Only legal move. (Optional but helpful symbol, replacing the tombstone.)
Checkmate (#). The king is in check and can't get out of it. Game over.
Single-line (,,). Obvious or sample choice (the other possibilities needn't be discussed). This may also mark an irrelevant waiting move or one of several moves which vacate the same square in a discovery attack. A double-comma indicates two or more options. More than two commas must indicate the exact number of those options.
Unfortunatey, the names of the pieces and their abbreviations are differentin different languages (in addition, following Maurice Beaucaire, the French used to replace "c" and "e" by "ç" and "é" for in square coordinates, to help distinguish the two). For international communication, graphical hieroglyphs for the pieces are often used in print, although I find them harder to read (if your eyes are on the wrong side of the half-century mark).
English
K
Q
R
B
N
(P)
French
R
D
T
F
C
(P)
German, Dutch, Swedish
K
D
T
L
S
(B)
Italian, Spanish
R
D
T
A
C
(P)
Portuguese
R
D
T
B
C
(P)
Czech
K
D
V
S
J
( )
Reversible (long) notation :
Formerly, both the origin and destination were always recorded. This convention is now fairly rare. It's known as long or reversible because it makes it easy to move back from a positiongiven in a diagram (especially since the names of captured pieces are alwaysgiven with the destination square). For example:
1. e2-e4 e7-e5
(2018-08-13) An advanced player's repertoire consists in familiarity with many lines.
White has 20 possible first moves (2 per pawn and 2 for each knight) corresponding to the 20 headings below, listed in order of popularity. Because the Sicilian Defense (1. 1. e4 c4) is so strong, the second-most-popular opening move for White (1. d4) can be considered strongerthan the most popular one (1. e4) whose continuations take up more space in thislist than all the other variations combined.
This structured list introduces the names of some notorious openings discussed among players. The Oxford Companion to Chess goes well beyond this, with 1327 named opening lines.
A given situation can often be obtained by executing the same moves in different orders. In that case, the resulting variations are said to be transposed from each other. For example, the Nf3 variation of the Scandinavian defense transposes to a Zukertort opening:
1. e5 d5 2. Nf3 --> 1. Nf3 d5 2. e5
(2021-12-20) A position commonly reached from severalopening lines.
Reaching the same position through the same half-moves played in different ordersis of course a common thing, called transposition in chess jargon. After the second move, this is the rule rather than the exception. For cultural and historical reasons, the Ragozin position is normallystudied only under the name of Ragozin defense as a variation of the Queen's Gambit Declined corresponding to the first of thelines enumerated below, to which other transpositions usually refer to;
A chess diagram merely describes the positions of the various pieces on the chessboard. whereas a chess position also includes information about castling and en passant privileges. (The terms configuration or situation are used here to covereither concept indifferently.)
A complete position consists of a chess position and a ply number (odd only when it's White's turn to play). Transposition tables in chess-playing software typicallycontain only positions with ply-parity (indicating whose term it is to play) although complete ply information would be needed to properly dealwith draws by repetition and apply the 50-move rule (and/or the new automatic 75-move rule, officially introduced in 2014).
In the case of the above enumeration, the ply number is given a priori, so the mere position fully determines the complete position.
Les pions sont l'âme des échecs. André Danican Philidor (1726-1795)
Enumerating one-sided pawn configurations :
Pawns can occupy only 6 ranks (the first and last one are ruled out). If they were only alloed to go straight, there wouldonly be C(8,p) 6p configurations of p pawns (0≤p≤8). This adds up to 78 = 5764801 possible configurations. That number is thus a lower bound to the total number of configurations. (One quick way to obtain this resulatis to consider that there are 7 possibities for each file; either no pawn or a singlepawn in one of the 6 allowed ranks).
On the other hand, we can obtain an upper bound by allowing the p pawns distinct positions anywhere in the 48 squares where they can be. That's C(48,8) = 377348994.
Thus, the correct number is between 5 and 378 millions.
Actually, the p pawns may have been involved only ina total of c captures (c≤0≤15-p). Some leftward,some rightward. Our first lower bound is actually the exact count when c = 0.
Upper bounds to the number of possible chess diagrams
To find a fairly tight upper bound, we start by the exact number of ways to place the twokings so that they're not next to each other. Then, we'll place all possible remaining pieces on the other 62 square. This does leave some impossible postions (for example,when both kings are in check) but relatively few. Also, there arediagrams which are notoriously unreachable for nontrivial reasons. Most notorious;y the two-knight checkmate. (what could the previous move have been?)
A white king on one of the 4 corners rules out 4 squares for the black king.
A white king on the rest of the border (24 squares) rules out 6 squares for the black king.
A white king on one on the 36 inners squares disallows 9 squares for the other king.
All told, the number of ways to place the two kings on non-adjacent squares is:
4 × (64-4) + 34 × (64-6) + 36 × (64-9) = 3612
That's a 10.4% improvement on the number of ways to place thetwo kings on twi different squares d (64 × 63 = 4032).
(2021-12-18) This code includes the name of the moving piece.
The encoding scheme described below is able to specify any legal move (and a number of illegal ones) for a given player in a known diagram, sssuming only that there are fewer than four pieces of each type.
Each side always has only one king and never more than eight pawns. Each piece other than the rook ansd pawn is identified by a numebr from 1 to 3among its twins as they occur on the board reading line by line from top to bottom and rightto left. It does take some thinking to pack all the information requiredin a single byte in such a way that it can be decoded without ambiguity. There is not enough room to allow for more than 3 pieaces of each kind. The leftovers in the decoding process are used to encode special moves likecastling, resigning and offering a draw as well as an exception hanling mechanismto allow escape to a second byte of code whan abolutely necessary inthe aforementioned pathological cases with many pieces of the same type (an 10-bit code is then used whose top two bits are embedded in the leading byte).
Different single-byte half-move codes :
B7
B6
B5
B4
B3
B2
B1
B0
Second-byte extension
Queen
1
1-3
b/r
D
1 to 7
10-bit codes are only used when there are 4 or more like pieces.
King
1
1
K-Move
000
10-bit
1
0
1
E9
E8
000
E7
E6
E5
E4
E3
E2
E1
E0
Pawn
1
00
Move
0-7
Under- promotion
Piece
Move
Rook
0
1-3
1
D
1 to 7
Usual promotion to a queen is just denotedby an ordinary (nonzero) move to the lastrank in a single byte. A zero move just indicates the presence ofan extra byte containing the actual(nonzero) code and the code for the pieceyou're under-promoting to.
The only other use of a zero-code moveis to denote a two-square jump as theinitial move of a pawn.
Distance traveled along a direction (D) for long-range pieces is a nonzero number (1-7)understood modulo 8 (thus possibly as a negative number when the positive interpretationfalls off the board. Thus, for the horizontal motion of a rook, the following codeapplies where only one occurence of the two possible meaning of a 1-7 code is valid,as the other is off the board.
Horizontal rook-move shows how only one value of a 1-7 displacement is valid.
001
010
011
100
101
110
111
001
010
011
100
101
110
111
Example, when on file "c":
a
b
c
d
e
f
g
h
Vertical rook-move shows how only one value of a 1-7 displacement is valid.
001
010
011
100
101
110
111
001
010
011
100
101
110
111
Example, when on file "3":
1
2
3
4
5
6
7
8
Likewise, there are two kinds of bishop moves:
Ascending (D=0): Vertical and horizontal displacements are equal.
Descending (D=1): Those two displacements are opposite.
.The board is always shown as White normally sees it: White pawns only move upward, black pawns go downwards. There are three ordinary (nonzero) types of pawn moves. All one square forwardpossibly diagonally (to the left or to the right) in case ofcapture. The zero move is either a two-square jump from the starting rank or an under-promotion (a pawn being promoted to any piece other than the usual queen). In that case, the next byte contains two bits specifying the true (nonzero)pawn move and two bits encoding the desired piece (rook, bishop or knight). That's to say nine possibilitiesencoded in four bits (and four unused bits).
Extra byte is almost never called for :
The special extended "10-bit code" contains 2 bits of data in the leading byteand 8 bits from the following byte. Four of those bits are used to specify which of the 16 piecesis to be moved (each player has at most 16 pieces on the board). The other 6 bits specify the desired relative displacement modulo 64. As this can't be zero, the extra byte is never zero and we can besure that a zero byte cannot occur in an encoded sequence of chess half-moves, except as an endmarker. This makes it trivial to skip an entire sequence of moves to accessthe rest of the data.
Can we do better ?
Yes, very much so. From any chess position (including diagram, turn, castling and en passant information) we can use a fixed procedure to generate all the possible legal moves and simplyspecify the index within that list of the move to be played. Even better, we don't need to specify a fixed number of bits for each half-movebut simply encode the whole sequence of moves as a (large) number N. from a given position, we may generate the p possiblemoves. The index in that list of the first move to play is N mod p and the code for the rest of the sequence is (N-m)/p. An so onuntil the code for the remaining sequence is 0 (no more moves to play).
Acknowledgment :
(2022-01-14) A more practical approach is more flexible, with improved generality.
Different single-byte half-move codes :
B7
B6
B5
B4
B3
B2
B1
B0
Second-byte extension
Queen
1
1-3
b/r
D
1 to 7
10-bit codes are only used when there are 4 or more like pieces.
King
1
1
K-Move
000
10-bit
1
0
1
E9
E8
000
E7
E6
E5
E4
E3
E2
E1
E0
Pawn
1
00
Move
0-7
Low Queening
Piece
Move
Rook
0
1-3
1
D
1 to 7
Usual promotion to a queen is just denotedby an ordinary (nonzero) move to the lastrank in a single byte. A zero move just indicates the presence ofan extra byte containing the actual(nonzero) code and the code for the pieceyou're under-promoting to.
The only other use of a zero-code moveis to denote a two-square jump as theinitial move of a pawn.
(2018-08-15) A tiny collection of chess proverbs and famous quotes.
Whoever answers before pondering the questionis foolish and confused. Proverbs 18:13
If you see a good move, try to find a better one. (Damiano, 1512)
The threat is more powerful than the execution.
Knight on the rim is dim.
A pawn on the seventh is worth two on the fifth.
A pawn on the seventh is worth a rook.
Brilliancy can only occur if the opponent makes a mistake. (Rubinstein)
(2021-12-14) Foolproof recipes devised to solve some standard endgame situations.
(2007-07-01) Tabulating all positions is an efficient way to solve an endgame perfectly.
If the total number of game positions is small enough,then each of them can be allotted a small computer record in an explicit table. The entire game can then be solved efficiently by analyzing thattable top-down (first completing the records corresponding to final positions, like checkmates). For the game ofchess, this is practical only in endgame situations,when only very few pieces remain on the board.
A database is a set of stored key/value pairs, where onlya small portions of the possible keys exist (for example, not all possiblesurnames exist in a database of people whose names are used as "keys"). By contrast, a tablebase includes (almost) all keys. The key itself need not be stored in a tablebase; it's merely usedto compute the unique numerical address where the information corresponding tothat key is located. In game tablebases, the game position is the "key" used to access thevalue recorded in the tablebase.
Perfect play is defined as achieving victory as fast aspossible, or delaying defeat as much as possible. A full analysis of thegame is normally possible only by recording the length of a perfect game foreach tabulated position (the position is a first-player win when that lengthis odd, it's a first-player loss otherwise (the issue of ties is discussed below).
A computer database which gives the number of half-moves to the end of aperfectly played game is called a Nalimov table. It's easy to play perfectly by looking up such a table: Play into the smallest even position if you can, otherwise play into the largestodd position. A special label must be assigned to ties which isadequately defined as an odd number larger than any other... (for example 255, if Nalimov records consist of a single byte).
There is no notion of "perfect play" for a game which ends in a tie. Such a game is merely considered equivalent to a game which goes on foreverbecause neither player can force a victory. Yet, it's possible to refine Nalimov values to distinguish betweena tie "by the book" (which tells that an undecided game is over)having the highest odd value and other ties which have odd values just belowthat (but above any other odd values corresponding to truefirst-player wins).
Eugene Nalimov was born in Novosibirsk in 1965. He joined Microsoft as a programmer in 1997, he later joined the Seattle-based Context Relevant startup (called Versive since 2017). Nalimov started writing tablebases generators for chess endgames in 1998. He was honored for that work by ChessBase at their 2002 convention, in Maastricht.
Example: The Knight and Bishop Endgame
The basic table base (TB) only needs to consider the positions where the bishopis on one of the 16 topmost white squares. Ignoring obvious illegalpositions (e.g., several pieces on the same square or adjacent kings) the otherpieces can be on one of 64 squares and it can be the turn of eitherBlack or White. All told, the size of the TB,at one byte per position, is fairly small:
2 . 16 . 64 . 64 . 64 = 8 MB
Each of those bytes just contains the number of moves to mate.
Well beyond what humans can compute :
Ignoring the 50-move rule, starting from this positionWhite can mate Black in 94 moves. The only winning move is Ke3!!
Kde-e3 !! Kh2-g3
Against another reply, White can mate in at most 10 moves (instead of 93).
(2021-21-31) Color matching required to mate a cornered king with a knight.
In the folloing diagram, when the white knight is on a numbered square opposite to the colorof the cornered black king it can mate it in the number of moves so indicated. Mate can only be delivered from a last move from the only square numbered "1" (c1)to the unique square numberd "0" (b3). When on c1, the knight puts the king in check, so the only black move available is to advance the pawn to a2, cornering theking which is checkmated when the knight moves to b3. If Black were to choose to advance the pawn before being forced to do so that way, the white knight would be on a dark odd-numbered square and could deliver mateby moving directly to b3.
Otherwise, the strategy is simply for the knight to move from a numbered squareto a numbered square with a lower number. Moving to another numbered squaresimply delays the mate. The knight can ultimately deliver checkmateif and only if it moves from the same solor as that of the black king. If the knight is on the wrong color, there can never be a checkmate even if Black cooperates. If the knight isn't on a numbered square, Black will have an opportunity to force stalemate by advancing thepawn when a2 is free and the knight is too far to check.
8
7
4
4
6
4
4
4
5
5
3
4
4
4
6
3
4
3
0
2
4
2
5
2
1
6
1
6
a
b
c
d
e
f
g
h
The above is the basis for some chess puzzles composed before the first publication of Bonus Socius compilation (around 1266). The changes in the rules of chess since thattime didn't affect kings, rooks, knights and pawns (except on their first moves).
Also, the single line given below (which leads to a different mating position) can be used when the pawn is as high as a4. No such thing exists for a5 or above, because that would entail a possibilty for the pawn to capture the knight or for the black kingto escape to b4.
If N starts from a6, c6, d5 or d3 (shown left).
Mate in 3
Nb4! a3Kc1 a2Nc2#
Checkmating Chases :
The above is perhaps the ultimate example of a chase ending in checkmate which the winner can onlylengthen and the loser only shorten. Few chases has this feature and it's difficultto define precisely what a chase is but you know one when you see one. Here are examples from real archived games:
#2FdzU (1847) . 27...Qh2+? would be a mistake instead of 27...Bh2+!
(2010-01-28) Evaluating quiescent positions is an art form.
Relative values of chess pieces according to various authors :
P
N
B
B'
R
Q
André Danican Philidor, 1777
1.00
3.00
3.50
4.00
5.50
10.00
Peter Pratt, 1799
1.00
3.00
3.00
3.00
5.00
10.00
Larry Evans 1958
1.00
3.50
3.50
4.00
5.00
10.00
Maurice Beaucaire, 1967
1.10
3.00
3.00
3.50
5.00
10.00
Bobby Fisher, 1972
1.00
3.00
3.25
3.75
5.00
9.00
Garry Kasparov, 1986
1.00
3.00
3.15
3.65
4.50
9.00
Hans Berliner, 1999
1.00
3.20
3.30
3.80
5.10
8.80
Larry Kaufman, 1999
1.00
3.25
3.25
3.75
5.00
9.75
With the only possible exception of the earliest one (Pratt) all the above authorshave pointed out that a pair of bishops is worth more than twice the value of a lone bishop. When pressed to quantify that bonus, they reluctantly say it's about half a pawn (50 centipawns). In the above table we added that bonus (0.5 by default) to the value of the second bishop, denoted B', which is mathematically equivalent.
A knight and a bishop are better than a rook and a pawn. Three minor pieces are better than a queen.
Endgame evaluations :
A radical method would be to consider the ability to mate of certain combinations of pieces against others, measured by the maximum number of moves needed to resolve the situation to a mate (as obtained from Endgame tablebases):
(2010-01-28) Minimize your opponent's gain, maximize your own.
(2010-01-28) In a minimax search, some alternatives need not be explored at all.
(2010-01-28) How to avoid exploring the same position more than once.
There are 8 variations which result in a position similar tothe one depicted at right, where White is checkmated. They differ by the order White moves his two pawns and also by twopossible choices for moving the central pawns of each player (one square or two squares).
The locution fool's mate is sometimes used as a generic termto denote any very early checkmate, especially the following one:
This mate is often attempted among newcomers. The French call it le coup du berger which translatesliterally as Shepherd's mate, as do the names of that checkmatein several other languages, includingSpanish,German,Dutch andPortuguese.
The fool's mate and scholar's mate may well be as old as chess itself but they were apparently not mentioned in print beforethe seventeenth century,as they found their rightful place in the early classificationproposed by one Arthur Saul in "Famous Games of Chesse-play" (1614).
Counting the number of 4-move games ending in a scholar's mate can be an interesting exercise: The game may end with Qf3xf7# (e.g., after the infamousNapoléonopening) or Qh5xf7# (as above). In either case, White can play in 4 different ways (opening with either e3 or e4, then moving either the bishop or the queen). Each sequence makes different "compatible" moves available to Black. If the black queen moves, she must move back. To allow the mating move,the white queen's path must be clear and f7 must be unprotected...
(2021-12-11) The challenge may be to prove one can checkmate in N moves or less.
Checkmate is the situation when the king is in check and cannot get out of it. That would mean that it couldn't avoid capture on the next move if the games was allowed to go on. Under modern rules, a checkmate ends the game.
The only recorded outcome in competitive chess is win, lose or draw. However, in the world of chess puzzles, best play is always meantto force chackmate in as few moves as possible against an opponent doing his best to delay it.
Here, White just queened with check. Clearly Black should have resigned a long time ago. The challenge for White is to arrive at a checkmate on his third move or earlier. The problem is to find the winning move (there's only one).
Mate in 3
1. Bd8+ Kc6 2. Qf6+ KxN 3. Qb6#
1. Bd8+ Kc6 2. Qf6+ Kb5 3. Qb6#
1. Bb8+ Kc8? 2. Bb6#
The third variation ended earlier because Black didn't play well.
An ancient mate-in-2 puzzle
There's only one solution: Rg7!! (It's much easier to mate in 3...)
This appears in the Bonus Socius manuscript (c. 1266).
However, the following analyzed game illustrates a bold counterattack which isfar from elementary (to avoid it, White could play 5. Bxf7+ gaining a pawn). If White ever loses a tempo with Nxh8 then the game ishopelessly lost when Black plays perfectly! I'm using this as an example of how a written analysis can be presented: We show the strongest move of the winning side (Black here) for every possible reply of the opponent, except when the move to be refuted (Nxh8) is played.
The paradoxical consequence of the following refutation of Nxh8 is that the threat on the rook is only apparent. At least for extremely sharp play...
Conveniently, the quoted 1967 game doesn't last very long becauseof the mistakes of White (starting with 6. Kxf2). The opponent of Traxler in 1890 didn't take the bait, which opensup an interesting 17-move game. Both actual games are shown in bold, within the combined decision tree.
The term Traxler counterattack is normally used to describe this opening (especially when the Bishop's sacrifice is accepted, as in Traxler's original game 6. Kxf2). However, in the United States, it's also called the Wilkes-Barre Variation (especially when 6. Ke2 or 6. Kf1 is played) because it was analyzed by John Menovsky (1873-1947) and other members of the Wilkes-Barre Chess Club (first established in 1887 and restarted in 1907). Menovsky published the work in 1934 and 1935 and subsequentlydiscussed the problem with Kenneth F. Williams (1907-1993) who would eventually publish a 58-page pamphlet on the topic in 1979, with only few flaws.
Even with the best reply 6. Kf1 White lost all the games on record:
1947: James L Harkins vs. Eugene Levin (20 moves).
Arguably, the most famost miniatures of all timewas played informally on 21 June 1851, during a recess of the firstinternational chess ournament, between Adolf Anderssen (1818-1879) and Lionel Kieseritzky (1806-1853). Anderssen, playing White, sacrificed his queen, two rooks and a bishop to delivera brilliant mate with the three remaining minor pieces (without capturing a single black piece).
(2010-01-29) Toying with chess positions which can't arise in actual games.
The American columnist Sam Loyd(1841-1911) devised many clever puzzles based on the rules of chesswhich have no relevance to actual play.
Lone black king on h4 (against 16 white pieces). Mate in 3 moves. The same problem for other positions for the black king is less easy to analyze. Tabulated below are the number of moves needed to mate, according to Fritz 8. In this context, e4 is almost always the strongest move;often the only strongest move,as indicated by the exclamation mark (!)... d4 is second best.
Full White Starting Lineup against Lone Black King
(2022-03-17) of Chess (Maja'sbotte). Pull-and-fork (attraction sacrifice). A startling 3-move combination.
This appears in about 2% or 3% of Chess Tempo tactical puzzles.
A sacrificial piece moves next to the king (usually grabbing something in the process, but not always). As the king takes the bait, it's then forked with the true target. The king may be forced to takes the bait but it may not be. In the latter case, when the rest of the botte would result in an exchange of equal pieces, the opponent choice is irrelevant to the puzzle, which may thus be truncated at that point (as illustrated by #73015808. #48729, #51993 or #55364,taken from a game resigned after the botte started with 2.Rxe7) Examples (in order of ratings, at the time of writing):
Finally, #163607 is a borderline case of a passive botte, if we may call it that, where the rook to be sacrificed is already in place, calling for a Swischenzug capture of a bishop.
Not covered here are pulls of pieces besides the king or the target (e.g., a pawn getting the queen which grabbed the knight in #163052) or the rarer push-and-fork trick illustrated by #62490 or the nice #123150068 (where both possible replies to 1,Rg8+ allow the fork 2.NXC5+ which wins the rook).
(2010-01-28) Well-known deadly traps in the opening game.
Ruy López, Berlin defense; The "fishing pole" black trap (1,2,3,4)
(2018-08-09) Rating player skills in a zero-sum game.
One key aspect of the Elo rating system is that the rating only changeas the outcome of a game but the sum of the ratings always stays the same. Whatever one gains, the other loses.
An often overlooked consequence of this, is that the average rating of a fixedpool of players never changes. That average may only vary as new players enter the pool or old playersleave it as they retire or die. To prevent the average rating from varying over time. the regulator (e.g., FIDE in the case of Chess) should estimate as accurately as possible the average of departing playersand attribute that average as the starting rating of new players. Otherwise, the average rating changes over time not becauseplayers are getting better or worse but simply becausethe regulations for the starting ratingd of newcomers drive it lower or higher. Nothing else.
On chess.com when you sign up, they ask you if you area beginner, intermediate, advanced or expert and just ask you an initial ratingof 1200, 1400. 1600 or 1800 accordingly. The initial puzzle rating of everybody is 1000.
On Lichess, the initial puzzle rating of everyone is 1500.
In the case of Chess. we can also hudge the ski;; from games of recordand adjust the entry regulation to make the rating match the absolute skill soobtained.
Comparing ratings from different eras :
Actual Elo evaluations allow the average of top players to drift substantiallyover time and the individual ratings are subject to considerable uncertainty.
The skills of individual players throughout history is best estimated byanalyzing a significant sample of the individual moves they actually playedin the midgame without significant time constraints.
One weakness of this approach is that the current chess engines outplay the best human players using an artificial style which isa poor predictor of typical human opposition on a move-by-move basis. Yet, the results so obtained are equally flawed throughouthistory and give an objective evaluation of actual skills whichstrongly correlates with performance in actual matches between humans.
Computerization also allows private estimates of the Elo rating of playerswho don't participate in regular chess tournaments with FIDE-rated players.
(2018-08-17) Traditional ways to even out games between players of different strengths.
In a game at odds of pawn and 2 (P and 2) the stronger player plays the black pieces without the f7 pawnand White plays two initial moves.
With rook odds, White plays without the a1 rook. The "a" pawn is placed on a3.
(2018-08-09) FIDE titles for over-the-board regular chess play.
Historically, the title of Chess Grandmaster was first formally conferred by Tsar Nicolas II upon the five finalists of the Saint-Petersburg tournament of 1914. Namely: José Raúl Capablanca, Emmanuel Lasker, Siegbert Tarrasch Alexandre Alekhine, and Frank James Marshall.
When the title was instated by FIDE in 1950, it was bestowed upon an initial list of 27outstanding players still alive. Complex rules are now in place, using tournament norms and a minimum Elo rating for the award of thistop chess distinction and a few lesser titles, as summarized in the following table:
Elo rating can be achieved anytime before tournament requirements, if any.
Between 1977 and 2003, FIDE awarded 31 Honorary Grandmaster titles to chess players withoutstanding records, including Jonathan Penrose (brother of Roger Penrose) in 1993. The courtesy couldn't be extended to Rashid Nezhmetdinov (1912-1974) who was already dead by then. Since 2007, no formal distinction is made between these and other Grandmasters.
The Grandmaster distinction was awarded shortly after his death to Karoly Honfi (1930-1996) by the FIDE Congress of September 1996, inYerevan.
(2018-09-09) Including global chess sites hosting online play in the Computer Era.
The first chess club was organized in Italy in 1550.
In the Renaissance, the leading chess players listed belowwere rarely challenged over-the-board in anything resembling a modern tournament. The reputation of a chess player was often based on the success of the books he wrote. The list below starts with Vicent, who is credited forinventing modern chess, by increasing the powerof the bishop and the queen (replacing the lowly fierca of shatranj). The earliest game of modern chess ever recorded,in the form of a poem, was Scachs d'amor (1475) at a time when castling and en passant capture wereprobably not yet standard. The first treatise was written by Vicent in 1493.
Last column indicates main residence during peak years.
For a whole century after the death of Greco, The Calabrese (Le Calabrais) the historical record doesn't single out any dominant player, with the possible exception of Salvio from 1634 to 1640 who may have regained thecrown he had held before Greco. Meanwhile, the nevralgic centerof World-class chess migrated from Naples to Paris...
Diderot and Rousseaureported that thethe undisputed World center of chess in the mid-eighteenth century was the Caféde la Régence in Paris. Around 1730, François Antoine de Légal, sire de Kermeur emerged as the most respected player there. (He spelled his own name Legall.)
Legall's only extant recorded game is the fabulous 7-move checkmate below, known far and wide as Legall's mate.
Legall played this in1750, against Saint-Brié (Black) at rook odds (no rook on a1; a-pawn moved to a3).
Légal mentored the young Philidor who dethroned him in 1755 and famouslyheld on to the crown for 40 years, till his own death in 1795. Philidor left Paris during the French Revolution and took on residenceat Parsloe's Coffee House on St. James Street (that chess club was active from 1772 to 1825). He was soon joined there by Verdoni, the strongest player in Europeafter Philidor (according to Philidor himself). Arguably, Verdoni was the strongest chess player in the Worldbetween Philidor's death (1795) and his own (1804).
The London Chess Club was organized on the 6th of April 1807. Chronologically, it was the third club created in London (after Slaughter's in 1715 and Parsloe's in 1772). None of those had yet gained enough momentum to compete with the Café de la Régence. So, after the passing of Philidor and Verdoni, the crown went back to France. The three leading players between 1804 and the arrival of Deschapelles (1815)were Bernard, Carlier and Léger (in no particular order).
Tabulated below are the successive purported modern World champions rootedin that era, with a few challengers of note (shaded rows).
Last column indicates main residence during championship years.
In the above table, yellow highlighting is for the 17 people who have been undisputed World champions at somepoint after the Steinitz era. Two of them (Kasparov and Kramnik) held the PCA/Braingames title at the dates during the period (1993-2006) when that title what distinct from the FIDE title. Dates in black correspond to the World title recognized by FIDE. The two titles were reunited in 2006 when Kramnik held them both. He was then heralded as the 14th modern World Chess Champion.
(2020-05-16) Some of the most brilliant moces ever played.
Chess Jargon
Woodpusher : Clueless chess player.
Flag an opponent : Win on time (old clocks raised a flag on timeout).
Types of Moves :
Waiting move : A neutral move played to get out of zugzwang.
Safing a piece : Moving an attacked piece to a safe square.
