Update

chess.md

@@ -32,15 +32,15 @@ During [covid](covid.md) chess has experienced a small boom among normies and [Y
 
 {[This](https://www.youtube.com/watch?v=DpXy041BIlA) is an absolutely amazing video about weird chess algorithms :) ~drummyfish}
 
-Chess have a very strong relationship with computers, computers help people play chess, train their skills but also analyze positions, perform research about chess, create and search game databases and find new play styles. The game also provides a nice framework for machine learning.
+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](ai.md).
 
 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](cli.md) 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](gui.md) 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.
+For communication between different engines and frontends there exist standards such as XBoard (engine [protocol](protocol.md)), 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](foss.md) engine [Stockfish](stockfish.md), with other strong engines being e.g. Leela Chess Zero (also FOSS) or AlphaZero ([proprietary](proprietary.md), by [Google](google.md)). [GNU Chess](gnu_chess.md) is a reasonably strong [free software](free_software.md) engine by [GNU](gnu.md). There are world championships for chess engines such as the *Top Chess Engine Championship* or *World Computer Chess Championship*. [CCRL](https://ccrl.chessdom.com/ccrl/4040/) 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](https://www.youtube.com/watch?v=R9IZWgArWUE) video).
+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](foss.md) engine [Stockfish](stockfish.md), with other strong engines being e.g. Leela Chess Zero (also FOSS) or AlphaZero ([proprietary](proprietary.md), by [Google](google.md)). [GNU Chess](gnu_chess.md) is a pretty strong [free software](free_software.md) engine by [GNU](gnu.md). There are world championships for chess engines such as the *Top Chess Engine Championship* or *World Computer Chess Championship*. [CCRL](https://ccrl.chessdom.com/ccrl/4040/) 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](https://www.youtube.com/watch?v=R9IZWgArWUE) video).
 
 The first chess computer that beat the world champion (at the time Gary Kasparov) was famously [Deep Blue](deep_blue.md) in 1997. [Alan Turing](turing.md) 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).
 
@@ -48,7 +48,7 @@ For online chess there exist many servers such as https://chess.com or https://c
 
 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](countercomplex.md) and [golfing](golf.md)). 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](proprietary.md), even though their source code is public. The programs include Toledo Atomchess (392 [x86](x86.md) instructions), Toledo Nanochess (world's smallest [C](c.md) chess program, 1257 non-blank C characters) and Toledo Javascript chess (world's smallest [Javascript](javascript.md) chess program). He won the [IOCCC](ioccc.md). 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](smallchesslib.md) :') ~drummyfish }
+{ Nanochess is actually pretty strong, in my testing it easily beat [smallchesslib](smallchesslib.md) Q_Q ~drummyfish }
 
 ## Variants
 
@@ -74,7 +74,7 @@ Programming chess is a [fun](fun.md) and enriching experience and is therefore r
 
 The core of chess programming is writing the [AI](ai.md), 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](neural_network.md), but it may very well be written by hand). Secondly we implement a **search** 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.
+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](neural_network.md), but it may very well be written by hand). Secondly we implement a **search** algorithm -- typically some modification of [minimax](minimax.md) 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).