Update

chess.md

@@ -21,7 +21,7 @@ Many however see [go](go.md) as yet a more [beautiful](beauty.md) game: a more m
 
 Chess as a game is not and cannot be [copyrighted](copyright.md), 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 [capital worshippers](capitalism.md) 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 and [IQ](iq.md)/intelligence**: there is a debate about how much of a weight general vs specialized intelligence, IQ, memory and pure practice have in becoming good at chess. It's not clear at all, everyone's opinion differs. A popular formula states that *highest achievable Elo = 1000 + 10 * IQ*, though its accuracy and validity are of course highly questionable. All in all this is probably very similar to language learning: obviously some kind of intelligence/talent is needed to excel, however chess is extremely similar to any other sport in that putting HUGE amounts of time and effort into practice (preferably from young age) is what really makes you good -- without practice even the biggest genius in the world will be easily beaten by a casual chess amateur, and even a relatively dumb man can learn chess very well under the right conditions (just like any dumbass can learn at least one language well); many highest level chess players admit they sucked at math and hated it. As one starts playing chess, he seems to more and more discover that it's really all about studying and practice more than anything else, at least up until the highest master levels where the genius gives a player the tiny nudge needed for the win -- at the grandmaster level intelligence seems to start to matter more. Intelligence is perhaps more of an accelerator of learning, not any hard limit on what can be achieved, however also just having fun and liking chess (which may be just given by upbringing etc.) may have similar accelerating effects on learning. Really the very basics can be learned by literally ANYONE, then it's just about learning TONS of concepts and principles (and automatizing them), be it tactical patterns (forks, pins, double check, discovery checks, sacrifices, smothered mates, ...), good habits, positional principles (pawn structure, king safety, square control, piece activity, ...), opening theory (this alone takes many years and can never end), endgame and mating patterns, time management etcetc.
+**Chess and [IQ](iq.md)/intelligence** (a quite comprehensive summary of the topic is available here: http://www.billwallchess.com/articles/IQ.htm): there is a debate about how much of a weight general vs specialized intelligence, IQ, memory and pure practice have in becoming good at chess. It's not clear at all, everyone's opinion differs. A popular formula (Levitt equation) states that *highest achievable Elo = 1000 + 10 * IQ*, though its accuracy and validity are of course highly questionable. All in all this is probably very similar to language learning: obviously some kind of intelligence/talent is needed to excel, however chess is extremely similar to any other sport in that putting HUGE amounts of time and effort into practice (preferably from young age) is what really makes you good -- without practice even the biggest genius in the world will be easily beaten by a casual chess amateur, and even a relatively dumb man can learn chess very well under the right conditions (just like any dumbass can learn at least one language well); many highest level chess players admit they sucked at math and hated it. As one starts playing chess, he seems to more and more discover that it's really all about studying and practice more than anything else, at least up until the highest master levels where the genius gives a player the tiny nudge needed for the win -- at the grandmaster level intelligence seems to start to matter more. Intelligence is perhaps more of an accelerator of learning, not any hard limit on what can be achieved, however also just having fun and liking chess (which may be just given by upbringing etc.) may have similar accelerating effects on learning. Really the very basics can be learned by literally ANYONE, then it's just about learning TONS of concepts and principles (and automatizing them), be it tactical patterns (forks, pins, double check, discovery checks, sacrifices, smothered mates, ...), good habits, positional principles (pawn structure, king safety, square control, piece activity, ...), opening theory (this alone takes many years and can never end), endgame and mating patterns, time management etcetc.
 
 { NOTE (speculative): I think I've heard some research suggested that it's not so much the spatial/visual part of the brain that's responsible for playing chess but rather the language part, it really seems like learning chess might be more similar to learning a foreign language -- it takes about the same time to become "fluent" at chess and the key to being good at it is starting at young age. I.e. the relationship of chess and intelligence is probably similar to that of language learning and intelligence. ~drummyfish }
 
@@ -46,11 +46,11 @@ A single game of chess is seen as consisting of three stages: **opening** (start
 
 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 Fischer, was of this opinion and has created a chess variant with randomized starting position that prevents such memorization, so called *chess 960*.
 
-**[Elo](elo.md) rating** is a mathematical system of numerically rating the performance of players (it is used in many sports, not just chess); Elo basically assigns players a rating number that says how skilled the player is. 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 (currently best humans rate close to 3000). More advanced systems have also been created, namely the Glicko system, however these are often quite [bloated](bloat.md) and complicated, so Elo stays the most commonly used rating system. **Alternative ways** of determining player skills also exist, for example so called accuracy, which says how closely one played to the perfect play according to some strong engine such as stockfish. The advantage here is that to rate a player we don't need too much data like with Elo (which needs to see many games of the player against other already rated players) -- it may be enough to let the player play a few games against a computer to determine his skill. A disadvantage however lies in how exactly to compute accuracy because that gets a little complicated by other factors, for example many times finding the best move is trivial (like retaking a queen in an exchange) while in others gets much more difficult, or the fact that humans often DON'T want to play the mathematically best move but rather a bit weaker, more comfortable one, so even grandmasters often choose a weaker move even though they know the theoretically best move. Another idea may be to use a standard set of puzzles, basically like an [IQ](iq.md) test. Yet another idea is for example to compute so called [Erdos number](erdos_number.md), i.e. the minimum length of a chain of victories from the world's best player, i.e. for example rating player A with number 3 says he defeated someone who defeated someone who defeated the world's best. A guy called tom7 devised a method for measuring performance of weak chess engines by basically mixing stockfish (the strongest chess engine) with a random move bot in certain ratios -- i.e. making an engine that with certain probability (given by the mixture ratio) plays either a move by stockfish or a random move -- and then determining the mixture ratio at which this monstrosity becomes indistinguishable from the tested engine (i.e. we can say "the tested engine is a mixture of stockfish and random moves in this ratio"). Along these lines we may similarly try to compute how much of a different kind of handicap -- let's say material or time -- we have to give to the strong engine for it to become on par with the tested entity (i.e. the ratio of wins and losses is about 1).
+**[Elo](elo.md) rating** is a mathematical system of numerically rating the performance of players (it is used in many sports, not just chess); Elo basically assigns players a rating number that says how skilled the player is. 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 (currently best humans rate close to 3000). More advanced systems have also been created, namely the Glicko system, however these are often quite [bloated](bloat.md) and complicated, so Elo stays the most commonly used rating system. **Alternative ways** of determining player skills also exist, for example so called accuracy, which says how closely one played to the perfect play according to some strong engine such as stockfish. The advantage here is that to rate a player we don't need too much data like with Elo (which needs to see many games of the player against other already rated players) -- it may be enough to let the player play a few games against a computer to determine his skill. A disadvantage however lies in how exactly to compute accuracy because that gets a little complicated by other factors, for example many times finding the best move is trivial (like retaking a queen in an exchange) while in others gets much more difficult, or the fact that humans often DON'T want to play the mathematically best move but rather a bit weaker, more comfortable one, so even grandmasters often choose a weaker move even though they know the theoretically best move. Another idea may be to use a standard set of puzzles, basically like an [IQ](iq.md) test. Yet another idea is for example to compute so called [Erdos number](erdos_number.md), i.e. the minimum length of a chain of victories from the world's best player, i.e. for example rating player A with number 3 says he defeated someone who defeated someone who defeated the world's best. A guy called tom7 devised a method for measuring performance of weak chess engines by basically mixing stockfish (the strongest chess engine) with a random move bot in certain ratios -- i.e. making an engine that with certain probability (given by the mixture ratio) plays either a move by stockfish or a random move -- and then determining the mixture ratio at which this monstrosity becomes indistinguishable from the tested engine (i.e. we can say "the tested engine is a mixture of stockfish and random moves in this ratio"). Along these lines we may similarly try to compute how much of a different kind of handicap -- let's say material or time (or, with humans, amount of alcohol) -- we have to give to the strong engine for it to become on par with the tested entity (i.e. the ratio of wins and losses is about 1).
 
 The rules of chess are quite simple ([easy to learn, hard to master](easy_to_learn_hard_to_master.md)) and can be found anywhere on the Internet. In short, the game is played on a 8x8 board by two players: one with **[white](white.md)** men, one with **[black](black.md)** (LOL IT'S [RACIST](racism.md) :D). Each man has a way of moving and capturing (eliminating) enemy men, 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 man 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).
+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). There is also a category called cyborg or centaur chess in which computer assistance is allowed (which would normally be seen as [cheating](cheating.md)) -- this category usually greatly overlaps with correspondence chess.
 
 Currently the best player in the world -- and probably best player of all time -- is pretty clearly Magnus Carlsen (born 1990), a [white](white.md) man from Norway with Elo rating 2800+. He just keeps beating all the other top players effortlessly, he was winning the world championship over and over before giving up the title out of boredom.
 
@@ -58,11 +58,11 @@ During [covid](covid.md) chess has experienced a small boom among normies and [Y
 
 **White is generally seen as having a slight advantage over black** (just like in [real life](irl.md) lol). It is because he always has the first move -- statistics also seems to support this as white on average wins a little more often. 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 for the white (with imperfect play, i.e. that white plays easier, tolerates slightly less accurate play), though most experts think chess is a draw with perfect play (pro players can usually quite safely play for a draw and secure it if they don't intend to win; world championships mostly consist of drawn games as really one player has to make a mistake to allow the other one to win). Minority of experts think white has theoretical forced win. Probably only very tiny minority of people think white doesn't have any advantage. Some people argue black has some advantages over white, as it's true that sometimes the obligation to make a move may be a disadvantage. Probably no one thinks black has a forced win, though that's not disproved yet so maybe someone actually believes it.
 
-**Blindfold play**: it's quite impressive that very good players can play completely blindfold, without any actual chessboard, and some can even play many games simultaneously this way. This is indeed not easy to do and playing blindfold naturally decreases one's strength a bit (it seems this is more of a case on lower level of play though). It is however not the case that only an exceptional genius could play this way, probably anyone can learn it, it's just a matter of training. Probably all masters (above FIDE ELO 2000) can play blindfold. They say the ability comes naturally just by playing countless games. How to learn playing blindfold then? Just play a lot of chess, it will come naturally -- this is the advice probably most often given. However if you specifically wish to learn blindfold play, you may focus on it, e.g. by training blindfold against very weak computer. Some software chess boards offer a mode in which one can see the position and color of all men but not which type they are -- this may perhaps be a good start.
+**Blindfold play**: it's quite impressive that very good players can play completely blindfold, without any actual chessboard, and some can even play many games simultaneously this way. This is indeed not easy to do and playing blindfold naturally decreases one's strength a bit (it seems this is more of a case on lower level of play though). It is however not the case that only an exceptional genius could play this way, probably anyone can learn it, it's just a matter of training (it's a matter of developing an efficient mental representation of the board rather than actually exactly remembering the whole board -- in psychology called *chunking*). Probably all masters (above FIDE ELO 2000) can play blindfold. They say the ability comes naturally just by playing countless games. How to learn playing blindfold then? Just play a lot of chess, it will come naturally -- this is the advice probably most often given. However if you specifically wish to learn blindfold play, you may focus on it, e.g. by training blindfold against very weak computer. Some software chess boards offer a mode in which one can see the position and color of all men but not which type they are -- this may perhaps be a good start. It may possibly also be done very gradually -- for example start by covering just part of the board and every week cover yet more squares; eventually you'll have them all covered.
 
 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.
 
-Fun fact: there seem to be **almost no black people in [chess](chess.md)** :D the strongest one seems to be Pontus Carlsson which rates number 1618 in the world; even [women](woman.md) seem to be much better at chess than black people. But how about black women? [LMAO](lmao.md), it seems like there haven't even been any black female masters :'D The web is BLURRY on these facts, but there seems to be a huge excitement about one black female, called Rochelle Ballantyne, who at nearly 30 years old has been sweating for a decade to reach the lowest master rank (the one which the nasty oppressive white boys get at like 10 years old) and MAYBE SHE'LL DO IT, she seems to have with all her effort and support of the whole Earth overcome the 2000 rating, something that thousands of amateurs on the net just causally do every day without even trying too much. But of course, it's cause of the white male oppression =3 lel { anti-disclaimer :D Let's be reminded [we](lrs.md) love all people, no matter skin color or gender. We are simply stating facts about nature, which don't always respect political correctness. ~drummyfish }
+Fun fact: there seem to be **almost no black people in [chess](chess.md)** :D the strongest one seems to be Pontus Carlsson which rates number 1618 in the world; even [women](woman.md) seem to be much better at chess than black people. [This](http://www.billwallchess.com/articles/Black%20chess%20players.htm) website says that as of 2015 there were only 3 black grandmasters in the whole world. But how about black women? [LMAO](lmao.md), it seems like there haven't even been any black female masters :'D The web is BLURRY on these facts, but there seems to be a huge excitement about one black female, called Rochelle Ballantyne, who at nearly 30 years old has been sweating for a decade to reach the lowest master rank (the one which the nasty oppressive white boys get at like 10 years old) and MAYBE SHE'LL DO IT, she seems to have with all her effort and support of the whole Earth overcome the 2000 rating, something that thousands of amateurs on the net just causally do every day without even trying too much. But of course, it's cause of the white male oppression =3 lel { anti-disclaimer :D Let's be reminded [we](lrs.md) love all people, no matter skin color or gender. We are simply stating facts about nature, which don't always respect political correctness. ~drummyfish } EDIT: We seem to have missed Tuduetso Sabure who became a WOMAN grandmaster (i.e. NOT a regular grandmaster) in 2005, however her peak rating is merely 2075, which is quite low, seems very sus.
 
 ## Chess And Computers
 
@@ -134,7 +134,7 @@ Chess stats are pretty [interesting](interesting.md). Thanks a lot e.g. to Liche
 
 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. EDIT: now it seems there is one in 584 moves. Please note this: there most likely exist much longer forced mates, these are just the KNOWN ones. Consider e.g. that if black blunders a queen in the opening, the game is very likely a theoretical win for white since then, i.e. a forced mate, and with perfect play black can probably resist for very long. However such situations are too complex to explore fully.
+**Shortest possible checkmate** is by black on ply number 4 (so called *fool's mate*); in fact there are 8 different games that can end like this. As of 2022 the **longest known forced checkmate** is in 549 moves -- it has been discovered when computing the Lomonosov Tablebases. EDIT: now it seems there is one in 584 moves. Please note this: there most likely exist much longer forced mates, these are just the KNOWN ones. Consider e.g. that if black blunders a queen in the opening, the game is very likely a theoretical win for white since then, i.e. a forced mate, and with perfect play black can probably resist for very long. However such situations are too complex to explore fully.
 
 Average game of chess lasts 40 (full) moves (80 plies). **Average [branching factor](branching_factor.md)** (number of possible moves at a time) is around 33. **Maximum number of possible moves in a position** seems to be 218 (FEN: `R6R/3Q4/1Q4Q1/4Q3/2Q4Q/Q4Q2/pp1Q4/kBNN1KB1 w - - 0 1`).