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Chess

Chess is an old two-player board game, perhaps most famous and popular among all board games in history. It is a complete information game that simulates a battle of two armies on a 8x8 board with different battle pieces. Chess has a world-wide competitive community and is considered an intellectual sport but is also a topic of active research (as the estimated number of chess games is bigger than googol, it is unlikely to ever be solved) and programming (many chess engines, AIs and frontends are being actively developed).

{ There is a nice black and white indie movie called Computer Chess about chess programmers of the 1980s, it's pretty good, very oldschool, starring real programmers and chess players, check it out. ~drummyfish }

Drummyfish has created a suckless/LRS chess library smallchesslib which includes a simple engine called smolchess.

At LRS we consider chess to be one of the best games for the following reasons:

Chess as a game is not and cannot be copyrighted, but can chess games (moves played in a match) be copyrighted? Thankfully there is a pretty strong consensus and precedence that say this is not the case, even though capitalists try to play the intellectual property card from time to time (e.g. 2016 tournament organizers tried to stop chess websites from broadcasting the match moves under "trade secret protection", unsuccessfully).

Chess In General

Chess evolved from ancient board games in India in about 6th century. Nowadays the game is internationally governed by FIDE which has taken the on role of an authority that defines the official rules: FIDE rules are considered to be the standard chess rules. FIDE also organizes tournaments, promotes the game and keeps a list of registered players whose performance it rates with so called Elo system –⁠ based on the performance it also grants titles such as Grandmaster (GM, strongest), Internation Master (IM, second strongest) or Candidate Master (CM).

A single game of chess is seen as consisting of three stages: opening (starting, theoretical "book" moves, developing pieces), middlegame (seen as the pure core of the game) and endgame (ending in which only relatively few pieces remain on the board). There is no clear border between these stages and they are sometimes defined differently, however each stage plays a bit differently and may require different skills and strategies; for example in the endgame king becomes an active piece while in the opening and middlegame he tries to stay hidden and safe.

The study of chess openings is called opening theory or just theory. Playing the opening stage is special by being based on memorization of this theory, i.e. hundreds or even thousands of existing opening lines that have been studied and analyzed by computers, rather than by performing mental calculation (logical "thinking ahead" present in middlegame and endgame). Some see this as weakness of chess that makes players spend extreme energy on pure memorization. One of the best and most famous players, Bobby Fisher, was of this opinion and has created a chess variant with randomized starting position that prevents such memorization, so called chess 960.

Elo rating is a mathematical system of numerically rating the performance of players (it is used in many sports, not just chess). Given two players with Elo rating it is possible to compute the probability of the game's outcome (e.g. white has 70% chance of winning etc.). The FIDE set the parameters so that the rating is roughly this: < 1000: beginner, 1000-2000: intermediate, 2000-3000: master. More advanced systems have also been created, namely the Glicko system.

The rules of chess are quite simple (easy to learn, hard to master) and can be found anywhere on the Internet. In short, the game is played on a 8x8 board by two players: one with white pieces, one with black. Each piece has a way of moving and capturing (eliminating) enemy pieces, for example bishops move diagonally while pawns move one square forward and take diagonally. The goal is to checkmate the opponent's king, i.e. make the king attacked by a piece while giving him no way to escape this attack. There are also lesser known rules that noobs often miss and ignore, e.g. so called en-passant or the 50 move rule that declares a draw if there has been no significant move for 50 moves.

At the competitive level clock (so called time control) is used to give each player a limited time for making moves: with unlimited move time games would be painfully long and more a test of patience than skill. Clock can also nicely help balance unequal opponent by giving the stronger player less time to move. Based on the amount of time to move there exist several formats, most notably correspondence (slowest, days for a move), classical (slow, hours per game), rapid (faster, tens of minutes per game), blitz (fast, a few seconds per move) and bullet (fastest, units of seconds per move).

Currently the best player in the world is pretty clearly Magnus Carlsen from Norway with Elo rating 2800+.

During covid chess has experienced a small boom among normies and YouTube chess channels have gained considerable popularity. This gave rise to memes such as the bong cloud opening popularized by a top player and streamer Hikaru Nakamura; the bong cloud is an intentionally shitty opening that's supposed to taunt the opponent (it's been even played in serious tournaments lol).

White is generally seen as having a slight advantage because he always has the first move. This doesn't play such as big role in beginner and intermediate games but starts to become apparent in master games. How big the advantages is is a matter of ongoing debate, most people are of the opinion there exists a slight advantage, some people think chess is a win for white with perfect play while others believe chess is a draw with perfect play. Probably only very tiny minority of people think white doesn't have any advantage.

On perfect play: as stated, chess is unlikely to be ever solved so it is unknown if chess is a theoretical forced draw or forced win for white (or even win for black), however many simplified endgames and some simpler chess variants have already been solved. Even if chess was ever solved, it is important to realize one thing: perfect play may be unsuitable for humans and so even if chess was ever solved, it might have no significant effect on the game played by humans. Imagine the following: we have a chess position in which we are deciding between move A and move B. We know that playing A leads to a very good position in which white has great advantage and easy play (many obvious good moves), however if black plays perfectly he can secure a draw here. We also know that if we play B and then play perfectly for the next 100 moves, we will win with mathematical certainty, but if we make just one incorrect move during those 100 moves, we will get to a decisively losing position. While computer will play move B here because it is sure it can play perfectly, it is probably better to play A for human because human is very likely to make mistakes (even a master). For this reason humans may willingly choose to play mathematically worse moves -- it is because a slightly worse move may lead to a safer and more comfortable play for a human.

Chess And Computers

{This is an absolutely amazing video about weird chess algorithms :) ~drummyfish}

Chess are a big topic in computer science and programming, computers not only help people play chess, train their skills, analyze positions and perform research of games, but they also allow mathematical analysis of chess and provide a platform for things such as artificial intelligence.

There is a great online Wiki focused on programming chess engines: https://www.chessprogramming.org.

Chess software is usually separated to libraries, chess engines and frontends (or boards). Chess engine is typically a CLI program capable of playing chess but also doing other things such as evaluating arbitrary position, hinting best moves, saving and loading games etc. Frontends on the other hand are GUI programs that help people interact with the underlying engine.

For communication between different engines and frontends there exist standards such as XBoard (engine protocol), UCI (another engine protocol), FEN (way of encoding a position as a string), PGN (way of encoding games as strings) etc.

Computers have already surpassed the best humans in their playing strength (we can't exactly compute an engine's Elo as it depends on hardware used, but generally the strongest would rate high above 3000 FIDE). As of 2021 the strongest chess engine is considered to be the FOSS engine Stockfish, with other strong engines being e.g. Leela Chess Zero (also FOSS) or AlphaZero (proprietary, by Google). GNU Chess is a pretty strong free software engine by GNU. There are world championships for chess engines such as the Top Chess Engine Championship or World Computer Chess Championship. CCRL is a list of chess engines along with their Elo ratings. Despite the immense strength of modern engines, there are still very specific situation in which humans beat the computer (shown e.g. in this video).

The first chess computer that beat the world champion (at the time Gary Kasparov) was famously Deep Blue in 1997. Alan Turing himself has written a chess playing algorithm but at his time there were no computers to run it, so he executed it by hand -- nowadays the algorithm has been implemented on computers (there are bots playing this algorithm e.g. on lichess).

For online chess there exist many servers such as https://chess.com or https://chess24.com, but for us the most important is https://lichess.org which is gratis and uses FOSS (it also allows users to run bots under special accounts which is an amazing way of testing engines against people and other engines). These servers rate players with Elo/Glicko, allow them to play with each other or against computer, solve puzzles, analyze games, play chess variants, explore opening databases etc.

Playing strength is not the only possible measure of chess engine quality, of course -- for example there are people who try to make the smallest chess programs (see countercomplex and golfing). As of 2022 the leading programmer of smallest chess programs seems to be Óscar Toledo G. (https://nanochess.org/chess.html). Unfortunately his programs are proprietary, even though their source code is public. The programs include Toledo Atomchess (392 x86 instructions), Toledo Nanochess (world's smallest C chess program, 1257 non-blank C characters) and Toledo Javascript chess (world's smallest Javascript chess program). He won the IOCCC. Another small chess program is micro-Max by H. G. Muller (https://home.hccnet.nl/h.g.muller/max-src2.html, 1433 C characters, Toledo claims it is weaker than his program).

{ Nanochess is actually pretty strong, in my testing it easily beat smallchesslib Q_Q ~drummyfish }

Stats

Chess stats are pretty interesting.

Number of possible games is not known exactly, Shannon estimated it at 10^120 (lower bound, known as Shannon number). Number of possible games by plies played is 20 after 1, 400 after 2, 8902 after 3, 197281 after 4, 4865609 after 5, and 2015099950053364471960 after 15.

Similarly the number of possibly reachable positions (position for which so called proof game exists) is not known exactly, it is estimated to at least 10^40 and 10^50 at most. Numbers of possible positions by plies is 20 after 1, 400 after 2, 5362 after 3, 72078 after 4, 822518 after 5, and 726155461002 after 11.

Shortest possible checkmate is by black on ply number 4 (so called fool's mate). As of 2022 the longest known forced checkmate is in 549 moves -- it has been discovered when computing the Lomonosov Tablebases.

Average game of chess lasts 40 moves. Average branching factor (number of possible moves at a time) is around 33.

White wins about 38% of games, black wins about 34%, the remaining 28% are draws.

What is the longest possible game? It depends on the exact rules and details we set, for example if a 50 move rule applies, a player MAY claim a draw but also doesn't have to -- but if neither player ever claims a draw, a game can be played infinitely -- so we have to address details such as this. Nevertheless the longest possible chess game upon certain rules has been computed by Tom7 at 17697 half moves in a paper for SIGBOVIK 2020.

What's the most typical game? We can try to construct such a game from a game database by always picking the most common move in given position. Using the lichess database at the time of writing, we get the following incomplete game (the remainder of the game is split between four games, 2 won by white, 1 by black, 1 drawn):

1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4 exd4 6. cxd4 Bb4+ 7. Nc3 Nxe4 8. O-O Bxc3 9. d5 Bf6 10. Re1 Ne7 11. Rxe4 d6 12. Bg5 Bxg5 13. Nxg5 h6 14. Qe2 hxg5 15. Re1 Be6 16. dxe6 f6 17. Re3 c6 18. Rh3 Rxh3 19. gxh3 g6 20. Qf3 Qa5 21. Rd1 Qf5 22. Qb3 O-O-O 23. Qa3 Qc5 24. Qb3 d5 25. Bf1

You can try to derive your own stats, there are huge free game databases such as the Lichess CC0 database of billions of games from their server.

Variants

Besides similar games such as shogi there are many variants of chess, i.e. slight modifications of rules, foremost worth mentioning is for example chess 960. The following is a list of some variants:

Programming Chess

Programming chess is a fun and enriching experience and is therefore recommended as a good exercise. There is nothing more satisfying than writing a custom chess engine and then watching it play on its own.

The core of chess programming is writing the AI, everything else, i.e. implementing the rules, communication protocols etc., is pretty straightforward (but still a good programming exercise). Nevertheless one has to pay a great attention to eliminating as many bugs as possible; really, the importance of writing automatic tests can't be stressed enough as debugging the AI will be hard enough and can become unmanageable with small bugs creeping in.

The AI itself works in almost all cases on the same principle: firstly we implement so called static evaluation function -- a function that takes a chess position and outputs its evaluation number which say how good the position is for white vs black (positive number favoring white, negative black). This function considers a number of factors such as total material of both players, pawn structure, king safety, piece mobility and so on (in new engines this function is often a learned neural network, but it may very well be written by hand). Secondly we implement a search algorithm -- typically some modification of minimax algorithm -- that recursively searches the game tree and looks for a move that will lead to the best result, i.e. to position for which the evaluation function gives the best value. This basic principle, especially the search part, gets very complex as there are many possible weaknesses and optimizations.

Exhaustively searching the tree to great depths is not possible due to astronomical numbers of possible move combinations, so the engine has to limit the depth quite greatly. Normally it will search all moves to a small depth (e.g. 2 or 3 half moves or plys) and then extend the search for interesting moves such as exchanges or checks. Maybe the greatest danger of searching algorithms is so called horizon effect which has to be addressed somehow (e.g. by detecting quiet positions, so called quiescence). If not addressed, the horizon effect will make an engine misevaluate certain moves by stopping the evaluation at certain depth even if the played out situation would continue and lead to a vastly different result (imagine e.g. a queen taking a pawn which is guarded by another pawn; if the engine stops evaluating after the pawn take, it will think it's a won pawn, when in fact it's a lost queen). There are also many techniques for reducing the number of searched tree nodes and speeding up the search, for example pruning methods such as alpha-beta (which subsequently works best with correctly ordering moves to search), or transposition tables (remembering already evaluated position so that they don't have to be evaluated again when encountered by a different path in the tree).

Many other aspects come into the AI design such as opening books (databases of best opening moves), endgame tablebases (databases of winning moves in simple endgames), heuristics in search, clock management, pondering (thinking on opponent's move), learning from played games etc. For details see the above linked chess programming wiki.

Rules

The exact rules of chess and their scope may depend on situation, this is just a sum up of rules generally used nowadays.

The start setup of a chessboard is following (lowercase letters are for black pieces, uppercase for white pieces, on a board with colored squares A1 is black):

        _______________
    /8 |r n b q k b n r|
 r | 7 |p p p p p p p p|
 a | 6 |. . . . . . . .|
 n | 5 |. . . . . . . .|
 k | 4 |. . . . . . . .|
 s | 3 |. . . . . . . .|
   | 2 |P P P P P P P P|
    \1 |R N B Q K B N R|
        """""""""""""""
        A B C D E F G H
        \_____________/
             files

Players take turns in making moves, white always starts. A move consists of moving one (or in special cases two) of own pieces from one square to another, possibly capturing (removing from the board) one opponent's piece -- except for a special en passant move capturing always happens by moving one piece to the square occupied by the opposite color piece (which gets removed). Of course no piece can move to a square occupied by another piece of the same color. A move can NOT be skipped. A player wins by giving a checkmate to the opponent (making his king unable to escape attack) or if the opponent resigns. If a player is to move but has no valid moves, the game is a draw, so called stalemate. If neither player has enough pieces to give a checkmate, the game is a draw, so called dead position. There are additional situation in which game can be drawn (threefold repetition of position, 50 move rule). Players can also agree to a draw. A player may also be declared a loser if he cheated, if he lost on time in a game with clock etc.

The individual pieces and their movement rules are:

Check: If the player's king is attacked, i.e. it is immediately possible for an enemy piece to capture the king, the player is said to be in check. A player in check has to make such a move as to not be in check after that move.

A player cannot make a move that would leave him in check!

Castling: If a player hasn't castled yet and his king hasn't been moved yet and his kingside (queenside) rook hasn't been moved yet and there are no pieced between the king and the kingside (queenside) and the king isn't and wouldn't be in check on his square or any square he will pass through or land on during castling, short (long) castling can be performed. In short (long) castling the king moves two squares towards the kingside (queenside) rook and the rook jumps over the king to the square immediately on the other side of the king.

Promotion: If a pawn reaches the 1st or 8th rank, it is promoted, i.e. it has to be switched for either queen, rook, bishop or knight of the same color.

Checkmate: If a player is in check but cannot make any move to get out of it, he is checkmated and lost.

En passant: If a pawn moves 2 squares forward (from the start position), in the immediate next move the opponent can take it with a pawn in the same way as if it only moved 1 square forward (the only case in which a piece captures a piece by landing on an empty square).

Threefold repetition is a rule allowing a player to claim a draw if the same position (piece positions, player's turn, castling rights, en passant state) occurs three times (not necessarily consecutively). The 50 move rule allows a player to claim a draw if no pawn has moved and no piece has been captured in last 50 moves (both players making their move counts as a single move here).

LRS Chess

Chess is only mildly bloated but what if we try to unbloat it completely? Here we propose the LRS version of chess. The rule changes against normal chess are:

See Also


All content available under CC0 1.0 (public domain). Send comments and corrections to drummyfish at disroot dot org.