Chess, a general overview & some reflection
Chess is one of the best known, most popular and most prestigious games worldwide. The year 2020 moreover saw a surge in its popularity (especially online) because of both the Netflix series the Queen's Gambit and the worldwide quarantine measures to battle the Covid19 pandemic. Chess in its current form (called 'western' / 'international' to distinguish it from related games and 'classical' to distinguish it from variants) emerged in the south of Europe during the second half of the 15th century after having evolved from similar, much older games of Indian and Persian origin (from the beginning of the 7th century). Its name derives from the Persian "Shâh (māt)" meaning "the King (is dead)". It is suggested that those older games in their turn evolved from even older ones from China like xiangqi.
Aspects of art are found in chess composition; and chess in its turn influenced western culture and art, and has connections with other fields such as mathematics, computer science, and psychology. The main reason of its influence is the astounding complexity that arises out of a relatively simple board and playing pieces, and the challenges this yields. Estimates of the number of different games that are possible are as high as 10^123; that's much, much more than the amount of atoms in the universe!
Chess is played on an 8×8 board with alternate dark and light squares. The two players traditionally are called black and white although the colours of their pieces can deviate (somewhat). Each has 16 pieces (8 pawns, 2 rooks, 2 bishops, 2 knights, a queen and a king) that can be moved and captured after which they disappear from the board. Each piece moves differently (see image, only knights can hop over other pieces and pawns capture diagonally instead of straight ahead), consequently each has a different strength / value (respectively 1, 5, 3, 3, 9, 4 in the attack, approximately). Since the objective is to capture the opponent's king (more accurately 'checkmate' him i.e. threaten to capture which the opponent can't counter anymore) the king cannot really have a value comparable to the others. Once during the game the king and a rook can perform a special move together called 'castling' in order to move the king to a safer place (i.e. the rook moves next to the king and the king hops over; both cannot have moved before, the squares in between must be empty and the king cannot be in check or hop over an attacked square). The pawns have special moves too: an initial double step ahead, 'en passent' capture (must directly follow a double step of an opponent's pawn, it is captured as if it had done a single step) and 'promotion' when they arrive at the back rank (to a knight / bishop / rook but generally to a queen, then also called 'queening' otherwise 'underpromotion').
Quite some normal moves also have special names because of the effect they have: a 'battery,' multiple pieces attacking in the same line; a 'fork,' a piece, generally a knight or pawn that attacks two (more valuable pieces) at the same time so one is lost, unless either can be moved with 'tempo' (an attack that forces the opponent to respond); 'overloading,' giving a piece two tasks that it cannot perform at the same time; 'undermining' also known as 'removing the defender,' if there's none left the piece is 'en prise' (ready to be taken) also called 'hanging'; 'interference,' blocking moves that obstruct a line of attack or disrupt a line of defense;
if the interfering piece is adding to the attack it instead makes the defense into a 'windmill' that works like an X-ray; a 'deflection,' forcing a piece to move thus revealing another valuable piece; while a 'decoy' is luring a piece to a certain place; a 'pin', an attacked piece that can't be moved because that would expose a more valuable piece behind; a 'skewer,' like a pin but with the more valuable piece in front; a 'sacrifice,' actually giving up a piece for some positional advantage, the piece intent on giving itself up is a 'desperado'; a 'zwisschenzug,' literally "move in between" with tempo, like a check, instead of a recapture in order to gain inititive; a 'discovery,' an attack (mostly a check) by moving a piece away that can then also attack something else; a 'double check,' a double attack on the king and so the king has to move, no block or capture is possible.
All these belong to what is called 'tactics,' attempts to gain (material) advantages in the short term. Gaining a disadvantage on the other hand is called an 'inaccuracy' / 'blunder' depending on the size of the disadvantage. If instead the disadvantage tempts the opponent into making a losing move it would be called a 'trap.'
A 'strategy' would be the longer term equivalent of a tactic. A 'gambit' is a good example of a strategic sacrifice right at the beginning. That's the first of three fases of a chess game called the 'opening.' Dozens of chess openings are named and many more variants exist (a chess encyclopedia some time ago already listed 1327 ones?!). There are quiet openings mainly aimed at positional play (i.e. a closed game e.g. the 'Reti') and very agressive openings (yielding open games e.g. the 'Latvian gambit') where material is exchanged quickly. The end of popular openings is called the 'tania,' a sort of take off point for the (real) game. A theoretical novelty on the other hand is called an 'innovation.'
In the opening it's all about development of the pieces, trying to control the center of the board, getting your king to safety and achieving a solid pawn structure. NB If at some point of the game a player is able to get a strongly positioned knight in enemy territory (from a well advanced pawn called an 'outpost') that knight is called an 'octopus' (because it attacks 8 squares at the same time). When the rooks are 'connected' (on the same rank or file with no pieces in between, mostly after about 20 moves) the opening / development is generally considered finished.
Then the 'middle game' starts where the greatest complexity is and so most attention is given to. Generally in this fase a player tries to gain a decisive advantage by means of a 'combination.' This is a series of moves with a blend of different tactics and is called the "heart of chess;" famous combinations get named. In this fase the game is also 'simplified' by the exchange of pieces. When a rook is exchanged for a knight or bishop you are said to have lost 'the exchange.'
When most pieces are off the board we have arrived at the 'endgame' where the game will be decided. In this last fase the king gets a more active role, pawns become more important and 'zugzwang' can occur: you are forced to move although that gains you a disadvantage. A pawn with no more opponent ones on its file (column) or neighbouring files is called a 'passed pawn' since it cannot easily be stopped from promotion.
As mentioned the goal of the game is to checkmate the opponent's king. Other possible endings are to 'resign' when the situation is hopeless, to 'get flagged' (you loose because your time ran out; but only if it is still theoretically possible to get checkmated otherwise it's a draw), a 'stalemate' (when no legal move is possible while not in check; a draw), a draw by agreement, by insufficient material, by a 3-fold repetition of the same position (this needs a claim from one of the players) or by having had 50 moves without a capture or pawn movement (idem dito). The last can happen when the player with less material has a 'fortress,' a position that cannot (easily) be penetrated.
Special examples of checkmate are the 'smothering mate' (delivered by a knight to a king that is blocked by its own pieces), the 'Fool's mate' for black in two moves (1.f3 e5 2.g4 Qh4#, the shortest possible game) & the 'Scholar's mate' for white in four moves (seven 'ply' = half moves; 1.e4 2.Qh5/Qf3 3.Bc4 4.Qxf7#). NB this way to note games is called the 'Short Form Algebraic Notation': a single letter is used for the piece that is moved (or even none for pawns) and only the arrival square is noted (in case of confusion also the starting file or row), x before the arrival square is capture, + after it indicates check and finally # checkmate; castling b.t.w. is noted by 0-0-0 (queen side; 0-0 for king side). In 'Figurine Algebraic Notation' figures replace piece letters for it to be language independent.
To have an objective way to rate a player's strength, the Hungarian-American physics professor Arpad Elo came up with the now generally used rating system that carries his name (so 'Elo' is not a short as is often thought; b.t.w. he compared his system to "measuring the position of a cork bobbing up and down on the surface of agitated water with a yard stick tied to a rope and which is swaying in the wind"). The amount of points one loses or wins is based on the strength difference with the opponent (and the importance of the game); the total amount of points always remains the same. A 400 point difference equals a factor of 10 in strength (ratio of wins/losses). A rating of 1500 Elo equals that of an average club player.
FIDE (the international chess federation) awards various life time titles (since 1950) of which a certain Elo rating achieved is (one of) the requirement(s): Candidate Master (2200) / Fide Master (2300) / International Master (2400) / Grand Master (2500). NB players with ratings above 2700 Elo are unofficially called 'super grandmasters'; up till now there have been 123 of them, with as newest addition the Dutchman Jorden van Foreest who recently won the prestigious Tata Steel Masters. Just 13 players ever achieved a rating of over 2800 (the top four being Carlsen, Kasparov, Caruana, Aronian). FIDE moreover awards World Champion titles since 1948.
The first world champion is considered to be Wilhelm Steinitz from Prague in 1886. Earlier, in the midth 19th century the German Adolf Anderssen was hailed as the leading chess master; he had a brilliant, energetic attacking style typical for the time. Shortly afterwards the extraordinary American chess prodigy Paul Morphy won from all during his short chess career (1857-1863) by infusing his attacks with sound strategy.
The German mathematician Emanuel Lasker took over Steinitz' title and kept it for an astonishing 27 years. Then José Raúl Capablanca from Cuba, known for his skill in endgames, won the world championship title from Lasker in 1921 (and was undefeated in tournament play from 1916 to 1924). His successor (in 1927) was the Russian-Frenchman Alexander Alekhine, a strong attacking player who died as the world champion in 1946. Alekhine briefly lost the title to the Dutchman Max Euwe in 1935 and regained it two years later.
A (politically heavily supported) era of Soviet dominance began in the chess world after the death of Alekhine. A great example is the 23-year-old Latvian prodigy Mikhail Tal becoming world champion in 1960, the youngest ever; as one of the most creative players ever he was called 'the magician from Riga.'
The American Bobby Fischer achieved the only interruption in the Soviet dominance for the rest of the century by convincingly defeating Boris Spassky for the world championship in the 'Match of the Century' in 1972 (anyhow being the first non-Soviet challenger since World War II). In 1975 no agreement was reached on championship conditions with FIDE and Anatoli Karpov obtained the title by default. Karpov dominated the 1970s and early 1980s with a string of tournament successes.
Then in 1985 Garry Kasparov from Baku, Azerbaijan won the rematch against Karpov that was needed since the match the year before had ended undecided. Kasparov subsequently became the dominant figure of world chess until his retirement from competition in 2005.
The reigning world champion is Norwegian Magnus Carlsen who won the title from Indian Viswanathan Anand in 2013. He is set to defend it for the fourth time later this year.
In 2014 Carlsen also set the all time Elo rating record of 2882. Noteworthy is that the current best computers (chess engines) already have ratings over 3600 Elo (so are roughly 100x better than the best human!). NB It has been argued that Elo ratings cannot be used to compare players from various eras since the average top ratings have been increasing for quite some time (at least partly related to more players participating, then also the top of the distribution increases). Therefore in 2017 a Markovian model was proposed in which the best chess engine analysed all the games of the best year of each world champion ever and ranked them according to the accuracy of their play. The resulting top 5 was: Carlsen (2013), Kramnik (1999), Fischer (1971), Kasparov (2001) & Anand (2008). From this list a relative recent increase in chess level can be inferred as well (at least partly related to chess technology helping top players to improve). An alternative way of comparison is by a popular vote of experts; then generally Fisher comes out on top for his talent and Kasparov for his completeness & duration of his dominance.
One of the goals of early computer scientists was to create a chess-playing machine. Chess-playing computer programs (later known as chess engines) began to appear in the 1960s and became better and more widespread in the following decades. However, the overall standard of computer chess was low until the 1990s. Two resources available by then helped to improve it greatly: endgame tablebases & chess (game) databases (besides of course improved programming and Moore's Law, the ever & continuous exponential increase in calculating power).
The first endgame tablebases, which provided perfect play for relatively simple endgames such as king and rook versus king and bishop, appeared in the late 1970s. This set a precedent to the complete six- and seven-piece tablebases that became available in 2005 and 2012, respectively, and which revealed some surprisingly new decisive outcomes.
The first commercial chess database, a collection of chess games searchable by move and position, was introduced by the German company ChessBase in 1987. Databases containing millions of chess games have since had a profound effect on opening theory and other areas of chess research (including players preparing for important matches) .
By the 1990s, chess engines consistently defeated amateurs, and in 1997 IBM's supercomputer Deep Blue defeated World Champion Garry Kasparov in a six-game match, starting the era of chess computer dominance. By 2009 even chess software running on mobile phones achieved super-human levels of chess. In the 2010s top chess engines became accessible for free on a number of PC and mobile platforms, and free engine analysis became a commonplace feature on internet chess servers. These have existed since 1992 when the University of Utah (USA) developed their Internet Chess Server.
In 2017 Google's AlphaZero ─ a neural network also capable of playing shogi and go ─ convincingly beat the then best conventional chess engine: Stockfish from Norway. Consequently, an international team began developing Leela Chess Zero, the public equivalent of AlphaZero; within a few years it had beaten Stockfish a few times in the Top Chess Engine Championship.
Chess engines, especially neural networks, have deeply influenced the development of chess theory, introducing novelties themselves and helping top chess players prepare their own ones. The 'fawn pawn,' a quickly advanced pawn in front of the (castled) king, is a good example of a novelty by neural nets. B.t.w. it seems to me that in general increased chess levels favour a more careful playing style (relying more on memory) over a more daring one exploring the unknown (relying more on intuition).
In 2020 Stockfish got it's own neural network elements, called Neural Net Updated Efficiently, which significantly increased its strength and immediately made it the undisputed champion once again. Stockfish already has an Elo rating of over 3640, while Leela performs at a level of around 3620. NB be aware that these numbers depend relatively strongly on circumstances (hardware, time control, test games used) and that a real comparison with human ratings is no longer possible.
I have tried to figure out what the historical development of computer chess has been regarding Elo rating. From the limited (useful & seemingly trustworthy) data that I could find online, a consistent, essentially linear increase follows: for over 50 years computer chess has been gaining about 40 Elo points per year (so every 10 years it has become about 10x as strong; see figure); it even seems that for Stockfish the increase rate the last few years has been almost the double of that?!
So it seems that chess engines are well on their way to play chess games perfectly (if that is possible at all, see later discussion). Anyhow a statician and chessmaster has argued that this would be the case at a (human) level of 3600 Elo?!
The highest possible summit of the art of chess has been reached in sparkling historical games like Anderssen's Immortal Game and his Evergreen Game.
"The Immortal Game" he played against Lionel Kieseritzky in 1851 and featured bold sacrifices: both rooks and a bishop, then his queen, and finally checkmating his opponent with his three remaining minor pieces in only 23 moves. The "Evergreen Game" featured Anderssen vs Dufresne in 1852, which he won in 24 moves, mating with 'a combination second to none in the literature of the game.'
Most top chess players have their 'personal Immortal Game,' the 50th game of the match La Bourdonnais – McDonnell in 1834 is described as "the first great immortal game of chess;" McDonnell won by sacrificing his queen for two minor pieces. Paul "Morphy's disputed Immortal" was played (with black) vs Bird in 1858, and won in 29 moves; the dispute (still!) is about what would have been the best line of play. The same year Morphy played his famous "Opera Game" against the Duke of Brunswick / Count Isouard in which he quickly developed and won by sacrificing much material, mating already on the 17th move with his last two pieces.
There's also an "Immortal Draw," played in 1872 between Carl Hamppe and Philipp Meitner, and involving a queen sacrifice. The first world champion, "Steinitz," played his "Immortal" against Von Bardeleben in 1895, and won in 25 moves. His successor Lasker played his "Immortal Rooks" game (with black) against Pillsbury in 1896 and won in 30 moves.
In 1907 "Rubinstein" won his "Immortal" with black against Rotlewi in 25 moves with one of the most famous combinations ever played. In 1912 Lasker (again) played his "Immortal King Walk" vs G.A. Thomas, and won in just 18 moves. In the same year "Capablanca" played his "Immortal" vs J. Baca Arus, winning in 25 moves; as well as Marshall his "Immortal Queen Sacrifice" (with black) against S. Levitsky, a win in 23 moves; many consider it the most amazing move ever played. An "Opera of Sacrifices" was played by H. Wagner vs W. Schoenmann in 1919, a white win in 25 moves.
The most famous back-rank-mate combination in chess literature stems from the 23-move game Adams vs Torre from 1920 (likely composed), involving six consecutive offers of the queen(?!); it consequently goes by the name "Immortal Queen Offers."
"Alekhine's Immortal" (with black) vs Bogoljubov from 1922 (won in 53 moves) is a candidate for greatest game ever: involving manoeuvres encompassing the entire chessboard, fascinating combinations, brilliant sacrifices of queens and rooks, two remarkable promotions and a third in the offing before white capitulated.
"The Immortal Zugzwang Game" was played in 1923 by Sämisch vs Nimzovich, and won by black in 25 moves. "The Immortal Combination" was another win by Alekhine with black, now against Reti in 1925, in 40 moves. In the "Polish Immortal" from 1929 with Glucksberg vs Najdorf, black sacrificed all four minor pieces for victory.
"Lilienthal's Immortal" was in 1935 against Capablanca, who thus lost this time, in 26 moves. In the same year "The Pearl of Zandvoort" gained Euwe the world championship against Alekhine (thus losing this time). The "Ukraine Immortal" of Korchmar vs E. Poliak from 1937 was a white win in 23 moves. The "Dutch Evergreen" featured C. de Ronde vs H. Kamstra in 1938 and was won in 50 moves.
The "Uruguayan Immortal" from the national championship there in 1943 seeing Molinari vs Roux Cabral, had black sacrifice the exchange twice, followed by sacrifices of two minor pieces; then on move 33 all three of his remaining pieces were en prise—and his opponent couldn't stop checkmate anymore.
1953 offered the great game Geller – Euwe ("Euwe's Immortal"?): Euwe seemed to be swept off the board by Geller's attack when a counterattack with an amazing sacrifice on move 22 won him the game in only four more moves.
The "Game of the Century" was from 1956 featuring D. Byrne vs Fischer. On move 11 white lost a tempo by moving the same piece twice and Fischer pounced with accurate sacrificial play (with the queen as last) gaining him a material advantage and forced checkmate in 41 moves.
The "Immortal Losing Game" from 1957 between Bogdan Sliwa and David Bronstein saw black having a lost game but setting some elegant traps in attempting to snatch victory from the jaws of defeat yet losing in 29 moves.
In 1960 the "Blue Bird Game" featured Spassky against Bronstein, playing the 'King's Gambit' and winning with a sacrificial attack in 23 moves. "Nezhmetdinov's Immortal Queen Sacrifice" vs O. Chernikov is from 1962, a win in 33 moves.
"Fischer's Immortal" (with black again) vs R. Byrne from 1963 was won in just 21 moves executing a deep sacrificial attack. Many players present thought Fischer's position was hopeless and were surprised to hear Byrne had resigned. "Tal's most famous Immortal" was from 1965 against Larsen, a win in 37 moves.
"Spassky's Immortal" from 1970 (this time with black) against Larsen, was a win in just 17 moves. The famous "Tomb Game" from 1971 of Harper vs Zuk saw black exploit two pins to drive white's pieces into a corner in a position where his only legal move helped Zuk to checkmate him. In the 6th game of the world championship in 1972 of Fischer (once again) vs Spassky, white's opening surprise led to a win which even Spassky joined to applaud.
"Karpov's Immortal" was against Unzicker in 1974, a win in 44 moves. The "Supreme Creative Achievement" was by Kasparov (with black) vs Karpov (thus this time losing) in the 16th game of their match in 1985; he employed a daring gambit, obtained a dominating position for his knight stifling Karpov's forces and finished off with a mating attack in 40 moves.
Two years later, in the last game of their new match with Kasparov trailing by a point, he surprisingly began quietly in Karpov's own style; when his opponent ran low on time, Kasparov sacrificed a pawn for an attack, Karpov failed to find the best defence and was finally forced to resign, thus Kasparov retaining the championship.
In 1991, Yusupov (with black; "Yusupov's Immortal") in the 9th game of his match against Ivanchuk sacrifices the house in his quest for the attack and breaks through after white's inaccuracies; voted as the best game of 1966–96.
The "Immortal King Walk" was of Short vs Timman in 1991, a win in 34 moves. In 1992, Tal, in his final tournament before his death at age 55, produced one last masterpiece (against Lautier). Further, the "Immortal Sacrificing Game" was of Serper vs I Nikolaidis in 1993, a win in 48 moves.
"Kamsky's Immortal" was against Kramnik in 1994, a win in 41 moves. "Kramnik's Immortal" (again with black) was against Kasparov (thus this time losing) in 1996, a win in 35 moves.
The "Immortal Bishop sacrifice" of Shirov (with black) vs Topalov from 1998 he won in 53 moves.
"Kasparov's Immortal" (once again) vs Topalov (thus losing again) was in 1999, a win in 44 moves featuring a rook sacrifice with a sacrificial combination lasting over 15 moves and one of the most commented chess games ever. "Topalov's Immortal" (now winning with with black) vs Kharlov was in 2004, a game of 53 moves.
The "Modern Immortal Draw" of Kramnik (again) vs Anand was from 2004, a game of 25 moves.
"Carlsen's Immortal" stems from 2004 against S. Ernst, a win in 29 moves. The "Last Brilliancy from the Beast" saw Kasparov (once again, with black) winning against Adams in 2005 in 26 moves. The game of Anand vs Topalov (once again) from 2005 was called "23rd Century Chess," a draw in 60 moves. "Anand's Immortal" (now with black) vs Karjakin was in 2006, a win in 37 moves.
"Topalov's Exchange Sacrifices" let him win (again) in 44 moves now against Aronian in 2006.
Finally in 2015 the "21st-century Immortal" was by Wei Yi vs Bruzon, where this chess prodigy with a rook sacrifice forced a king walk and after several quiet moves more black had to throw the towel.
Finally, some reflection on what it would mean to play chess perfectly and/or to solve the game of chess. For this the 'Lichtenberg figure' above (of electric discharges on insulating surfaces, named after the German physicist Lichtenberg who began to study them in 1777) will be illustrative of all chess games/positions. The start of the game is in the middle, every move is one step outward, in many possible directions by virtue of the complication of chess. The light pathways are where the position is balanced, the dark 'abysses' where either player has a decisive advantage which is what each player is trying to achieve but in opposite directions. As a result most part of most games follow the light pathways although those constitute only a small minority of the total area thanks to chess being a very hard game (it's very easy to lose!). In the following reasoning this representation will be helpful.
Chess can be seen as a mathematical problem. Then there are two main types of solutions: a 'weak' one that for each position (or at least the starting position, we could call that 'superweak') resolves one way or another whether it is a win/loss/draw (with best play, of course); second a 'strong' one that gives a sequence of moves (or an algorithm) to actually achieve that outcome.
I will now argue that only the superweak solution effectively differs from the other ones, that that one is clear and that for the other ones one can both say that we have them already ánd that we will never have them, depending on how one looks at it. [NB possibly excepting a Quantum Computer that is really able to map ALL possible chess positions?!]
First the superweak solution: from the ratio of wins of white/black and the percentage of draws as a function of Elo rating we can decide what the outcome of chess would be in case of perfect play. From the little, seemingly reliable, data that I could find online, it follows that with increasing rating not just the percentage of draws increases, but also the winratio white/black and all seems to be approximately linear. Around 2000 Elo each outcome has equal chance, so 1/3; around 3500 Elo (so a currently good chess engine) black cannot win anymore and there are 3x as many draws as wins for white. Extrapolating this downwards yields no draws around 1000 Elo (seems reasonable), and upwards that somewhere above 4000 Elo only draws remain. Looking at the performance of the current top chess engines either this extrapolation is too conservative or engine ratings are pretty deflated since one needs a pretty biased position nowadays to get a decisive result at all. In conclusion, perfectly played chess is a draw and that result has already been reached!
Unfortunately a weak solution cannot be arrived at in the same way, i.e. one for all positions, first because there are simply too many of them and second because there is not enough data for specific positions to give proper statistics.
Therefore we have to turn to a strong solution through an algorithm as already mentioned. The alternative, an actual sequence of moves for any position is (generally) not possible since there are simply too many alternatives that one can't all cover, even in principle.
First let's have a look at how complex chess actually is, so putting some (rough) numbers on the Lichtenberg figure earlier.
In the beginning of this post it was mentioned that the estimated amount of games that are (theoretically) possible is 10^123. However, since the only restriction on the length of a game is the fifty move rule (requiring a capture or pawn movement every fifty moves) and so games could take thousands of moves, some maximum length must have been assumed. In practice most games take between 20 and 50 moves to finish (see e.g. the list of all time best games), and probably around move 40 it's generally already clear what the outcome will be (assuming there will be no more blunders otherwise anything would be possible). Although chess engine games generally seem to be quite longer than 40 moves, by then practically always the game has already been decided effectively.
In most positions between 20 and 30 different moves are theoretically possible; most of these will either be not good or decide the game (and so do not increase the complexity, at least in practice). So the good, non decisive moves per position, on average, could well reduce to 10. This reasoning thus results in a sequence of 40 moves (so 80 ply, the total moves of both!) with 10 possibilities each, so an estimated total number of games in practice of 10^80, i.e. hugely less than the theoretical estimate before.
Yet this number is still far greater than the estimated amount of legal positions in chess (10^43; note also that a 40 move game has 80 different positions). Thus eliminating blunders and stopping (effectively) decided games must also have eliminated many of the revisiting of identical positions in different games (the reason why the amount of possible games can be so much higher than that of possible positions).
For computer chess the relevant complexity is actually that of positions not of games. Moreover, it should be realised that quite some of the legal positions belong to decided games (or cannot legally be reached). And those actually constitute the majority since an undecided game means that the position is sufficiently balanced (and has enough pieces still on the board) and a balance is quite a restriction. We can estimate how much from the total value of all pieces (excluding the necessary king and possible promotions): this is 39 for one player and 78 for both, also being the maximum possible difference between them. A value difference somewhat greater than 1 (pawn equivalent) is generally decisive and so undecided positions are about one percent of the the total number! [NB other factors enter into the strength evaluation of a position too like piece development and their coordination (amongst themselves, like a good pawn structure, ánd against the opponent, providing good defense/attack options) but those can either enhance or counteract the material difference (e.g. in a 'gambit'; less pieces can even have a better development more easily but a better coordination more difficultly?!) and so they effectively cancel out.]
In conclusion, there about 10^41 undecided chess positions that chess engines would need to take into consideration!?
And so to keep chess tractable one has to make (pretty severe) assumptions on which moves/positions are possible (which then are analysed/evaluated) and which not (which then are discarded).
For any 'normal' position or 'normal' continuation from an 'exceptional' position this works wonderfully (miraculously???) well as top chess engines are showing (so in this way we could say that chess IS strongly solved).
However, Jonathan Schrantz (USA, rating 1974 Elo) has made it his goal to invent 'crazy gambits' and beat Stockfish with them (see his YouTube channel)?! Yes, he does need days of preparations using chess engine evaluation, and the online available Stockfish he uses is not the strongest one possible, yet it should still have superhuman strength. One could call these situations 'artifacts' (that might be eliminated one by one but not in principle yet are not very interesting since they are not inherent to chess only to chess engines) but as positions become more complicated (like very 'unequal' balances that 'hang on a thread') then 'exceptional' positions/continuations might really well be good options and, because of the inherent assumptions underlying all chess engines, we can never be sure (so in this way we could say that chess will NEVER be strongly solved).
Yet, chess engine development will ever continue to push the boundaries of complicated positions (crazy gambits?!) and exceptional continuations (new 'lines') that can be considered to show what and how the outcome of them is. Some of them (but less and less since they ever get more complicated) can actually be expected to be usable by (top) human players and so push the limits of human chess as well... {:-)
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