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The First Scientific Theory of Chess

After receiving a request from a reader, I originally intended to write on the subject of chess strategy, but after some preparation and gathering of materials, I realized that a discussion of strategy alone would be akin to paddling a canoe in a turbulent ocean.  It demands grounding on the safe beach of a theory of chess.

Almost all chess writers – titled chess masters included – use the term ‘theory’ as a layman understands the term.  That is, by ‘theory’ they refer to the collective beliefs, maxims, and generalizations that exist among their peers at the present time.  For example, one often reads that a particular move conforms to ‘opening theory’ as is periodically published in such daunting tomes as Modern Chess Openings or The Encyclopaedia of Chess Openings.  In the middle game, ‘theory’ refers to general principles of play, such as that rooks belong on open files; and in the end game ‘theory’ is either similar advice, albeit informed by the experience of high-level play, or particular classes of positions with known outcomes if play continues with perfect and advance knowledge of the result.

However, I would like to employ the term ‘theory’ in its scientifically accepted sense.  In that regard a theory of chess would take the form of an explanation of observed phenomena or data, the most important of which relate to how or whether games are won.  That explanation may compete with other theories also set forth to explain the same data. 

The history of science is replete with fascinating narratives of one theory supplanting another because it is discovered to more accurately or more succinctly account for the observations of interest.  There are also other criteria that are important for a theory to be useful, such as that it have a predictive capability or that it be falsifiable.

To cite just one non-chess example, the germ theory of disease has, at least among educated people, replaced the alternative theory that disease is caused by evil spirits. 

Behavior follows theory.  Among a minority of the world’s inhabitants disease prevention and cure involves ritual incantations and other activities aimed at ridding the body of the spirits that do or threaten to inhabit it.  For most of us, however, disease control involves behavior centered around environmental and personal sanitation, the handling of food, or the administration of medicines and vaccines.  These radically different behaviors follow directly from the two incompatible theories of disease that one subscribes to.

What is the theory – or theories – of chess that compete for our belief systems?  Until we answer this question we cannot intelligently discuss strategies, i.e. behaviors for playing the game.

I am certainly no expert on either the history of chess or its theoretical underpinnings, and I invite readers who disagree with what follows, or who have ‘pieces to fill the holes’, so to speak, to do so in the spirit of mutual teaching and learning.  But I have only found one explanatory framework in my research that satisfies what I understand to be a scientific theory of chess, and that theory is more than a century old.

Steinitz, the Father of Chess Theory

In 1886 at the age of 49, Wilhelm Steinitz defeated Johann Zukertort in a match of 20 games to become the world’s first official chess champion, a title which he held until 1894.  In 1889, three years after claiming the championship and a hundred twenty years before the present time, Steinitz published a book called Modern Chess Instructor, Part I in which he brilliantly put forth the first scientific theory of chess.

In the sixth chapter that begins on page xxxi, Steinitz wrote his humble but profound theory: “…it is now conceded by all experts that by proper play on both sides the legitimate issue of a game ought to be a draw…”   As if to underscore its importance by repetition, he wrote on the very next page that “The principal thesis of the modern school may be briefly summarized thus: … by best play on both sides a draw ought to be the legitimate result.”

Why is this claim to be properly understood as a scientific theory of chess rather than a personal prejudice?  I will address this question when I post part 2 of this blog in a few days.

Comments


  • 4 years ago

    SpaceOddity

    I have a number of comments to your blog that I decided to write my own on the subject.  It is called, "Why there cannot be a 'scientific' theory of chess".  I hope it adds clarity to some of the issues raised here and in your other blog.  I have a PhD in Philosophy which, surprisingly, is actually useful in life on rare moments, though I'm using the term 'useful' quite gratuitously.  In any case, here is the link.

    http://blog.chess.com/SpaceOddity/why-there-cannot-be-a-scientific-theory-of-chess


  • 4 years ago

    Interrobang

    Zetes, of course it's appropriate for us to understand how we as individuals approach gameplay psychologically, etc., but this has no bearing on the game itself.  If we restrict our treatment to the game itself, analyzing only the properties the rules and of the games and positions they give rise to, the social context in which the game is played by humans is irrelevant.  It occurs to me, though, that there have been facets of the game's history that have been influenced by human social considerations, like modifications of the original rules of piece movement and such.  That might be interesting to explore.  Just the same, though, I feel that an analytical treatment of the game as we now know it would only become colored by our imperfect understanding of its principles if we let ourselves address the social facets of gameplay.

  • 4 years ago

    Zetes

    Fascinating stuff. Is a game an abstract or a social phenomena can we understand a game independant of the language world(Witgenstein game...?) in purely thoretical terms. A game of chess is not played by machines but by humans in environemental contexts political and historical contexts. Does it possibly follow that a theory of agame might then have to take intoaccount the nature of its players and their context. Perhaps  a purely scientific acoount of chees is possible butthis may onlybe of partial relavence a s chess is a shared set of rules in a social context.  To what extent does a theory of chess have to take acoountof this social context.

     

    How can a theory of chess help us play better if it does not as I contend Kotov does in think like a grandmaster point our perception not just at the board pieces and rules governing their movementbut also at the practical psychological issues facing an otb player.

     

    You guys fascinate me this is wonderfull to read. A bit holy grailish..wow

  • 4 years ago

    MetalK

    Enthymene - I appreciate your points and I do not care if my points are attacked.  But claiming (not you) that I am ignorant, failed to learn, and my knowledge is woefully lacking are all personal attacks, have no basis, and are completely unnecessary.

  • 4 years ago

    Interrobang

    Enthymene: More fascinating points!  Yes, what can we say about the path of a perfect game?  Material seems to be a sufficiently accessible consideration to start with, but I'm not sure I could say anything non-trivial about that, especially if Steinitz was right and the initial position is drawn.  Draws can happen in many ways, and with many different combinations of pieces scattered across the board.  The set of all drawn positions is indeed finite, as is the set of all won positions (in case Steinitz was wrong), and so, therefore, must be the subset of all such positions that could arise from perfect play; but I wonder if we can characterize them all through such a narrow criterion as material content.  (Pawns are an issue in and of themselves, as they carry the threat of promotion - in some sense at least, chess pieces don't always entirely leave play either!)

    On that note, I tried to define my idea of a best move carefully to allow for the possibility of there being more than one.  Since there are only three possible states for the game to be in, and since you can't improve the state of the game by moving, a move is "best" if the situation won't be any worse after you make it either.  So in any given position, there could be any number of moves that preserve the current state of the game; as far as I'm concerned here, all such moves are equally "best", and all games in which both players play only such moves are equally "perfect".

    Rumsim: The accolade is certainly appreciated, but unexpected.  The definitions' circularity didn't strike me as problematic when I wrote it because every game must eventually either result in a win or a draw; at any rate, however, I can certainly sacrifice logical precision to state the point even more plainly (and without so much of a programmer's mindset):

    "A position is called 'won' if the player with the move can win the game in spite of his opponent's best efforts, 'lost' if every move results in a position that is 'won' for his opponent, or 'drawn' if it is neither won nor lost."  In this scheme, a "best" move for a player is one that cannot worsen the evaluation of the position on his next turn.

    Anyway, thank you.  Clearly I have to brush up on my John von Neumann.  And my Kolmogorov complexity.  =)

  • 4 years ago

    enthymene

    I was referring more to the elementary results in Kolmogorov Complexity which can be derived for an arbitrary description language with an arbitrary overhead.

    So, the issue is whether there is a won position for white at the beginning of the game.

    I wonder what we can say about the specific path through the space of possible positions that results from best play.  Assuming that perfect play produces a drawn game, what pieces are guaranteed to be on the board?  We've got the kings to start with, but we already know from endgame tablebases that certain positions, like King and Rook versus King, for a trivial example, are won positions for one side.

    Or alternatively, assuming that perfect play is a win for White, what combinations of pieces are we guaranteed not to see?  What specific positions?

    Might be some interesting clues to when a game is or is not proceeding down the lines of the perfect game.

    Actually, do we know that there is exactly one game that results from perfect play?  Might either player at some point have a choice between two equally good moves?

    I've got schoolwork to do, so I'm going to contemplate that instead, for the time being.

  • 4 years ago

    rumsim

    Interrobang,

    Because of yours "it seems to me ..." i suppose you came alone to your findings.

    Congratulations! You are close to the John von Neumann basics of the Theory of Games.

    The only thing you missed is that strictly speaking your definition of "won", "drawn" and "lost" is still not scientific. In order to make sense for your definition of "won" you need to already have made sense for your definition of "lost". But also, In order to make sense for your definition of "lost" you need to already have made sense for your definition of "won".

    As a consequence:

    In order to make sense for your definition of "won" you need to already have made sense for your definition of "won".

    If you find a way to correct this then I will admit that you rediscovered the John von Neumann basics of the Theory of Games.

    Whish you Good Luck!

    Two questions to the company:

    1. Do you thing that Steinitz had in mind the scheme presented here by Interrobang?

    2. Do you thing that Steinitz was closer to John von Neumann then Interrobang?
    ================================================================================
    Interrobang
    Taipei Taiwan  
    It seems to me that, in terms of information theory, there is an objective measure that can, at least in theory (ouch, sorry), be applied.  Since the outcome of every game is either a win, a draw, or a loss for one's choice of player, independent of any kind of material or positional consideration that might factor into the players' move choices, it makes sense to me to view the idea of perfect or unimprovable play in that light.
    Long version:
    We call a position "won" for the player with the move if there is at least one move (a "best" move) that will either checkmate his opponent or give rise to a position that is "lost" for his opponent.  A position is "drawn" for the player with the move if it is not won but there is at least one move that will either draw the game or give rise to a position that is "drawn" for his opponent.  And a "lost" position for the player with the move is one in which every move results in a position that is "won" for his opponent (in the game theoretical sense, all moves are equivalent in a lost position).
    ================================================================================

  • 4 years ago

    Interrobang

    It seems to me that, in terms of information theory, there is an objective measure that can, at least in theory (ouch, sorry), be applied.  Since the outcome of every game is either a win, a draw, or a loss for one's choice of player, independent of any kind of material or positional consideration that might factor into the players' move choices, it makes sense to me to view the idea of perfect or unimprovable play in that light.

    Long version:

    We call a position "won" for the player with the move if there is at least one move (a "best" move) that will either checkmate his opponent or give rise to a position that is "lost" for his opponent.  A position is "drawn" for the player with the move if it is not won but there is at least one move that will either draw the game or give rise to a position that is "drawn" for his opponent.  And a "lost" position for the player with the move is one in which every move results in a position that is "won" for his opponent (in the game theoretical sense, all moves are equivalent in a lost position).

    Now, the "best" move in a won or drawn position will, by definition, never change the outcome of the game.  That is, if the position was originally drawn, the best move will preserve the draw, whereas a blunder might allow the opponent to win.  Similarly, a position that is won for the player with the move will still be won after the player makes the best move, but not necessarily otherwise.  So if both players always play best moves, the outcome of the game will not change.

    In the endgame, this is very obvious - so obvious that we take it for granted in our presentation of endgame studies: "White to play and win" means "Find the only move for White from this position that does not result in a draw or a win for Black"; the game is won for White, but only the best move will keep it that way.  But since chess is deterministic and therefore solvable (though not by us, for now), we can just treat the entire game tree as a gargantuan endgame study.  It's still true that the best move will not change the game's outcome.  Steinitz's musings simply address the identity of the game's outcome before even the first best move is made.

    Short version:

    Logically, in any position, exactly one of these three statements is true:

    1. the side to move can force a win;
    2. the side to move can't force a win, but the side without the move can; or
    3. neither side can force a win.

    The question is simply in which of these states the game begins.

  • 4 years ago

    enthymene

    Interrobang, my claim about the fundamental assumptions of science isn't very profound.  It basically boils down to a) there are rules, and b) we can learn them.

    Rejecting either, though, seems to mean rejecting the scientific method, or refuting the object of the method, namely the existence of "Laws of Nature."

    I'm sure, however, from deep historical precedent, that I can be wrong.

    Anyway, Steinitz' argument assumes perfect or correct play from both sides, which I think I'll have to soften to "unimprovable" play.  That is, in each situation each player makes the best possible move.  I don't know how you'd objectively evaluate the quality of an individual move apart from those to come and those before, but perhaps, as in Information Theory, we don't have to.

    Thinking about it that way, the issue is whether there is some structural quality in chess that eventually causes White to lose the advantage, since the statistical evidence seems to say that White starts with one.  I can't see where that turning point lies.  But arguments from ignorance are unconvincing for a reason.

    I guess we'll have to wait for Chess to be solved (or nearly so) to get a satisfactory answer.  Barring a rennaissance in computing through quantum computers, though, I suspect that isn't imminent.

    I've also been starting a study of Shogi recently, which boasts a smaller draw percentage (according to Fairbairn, about 2% of all games), no stalemate situations that I know of, and a slight advantage to Black to win, suggesting an inherent first move avantage there too.  Also the 48% win percentage for White, combined with the 2% draw rate, further suggests that White is trying to equalize with Black.  But then, Shogi stays very deep computationally throughout the game because the peices don't really leave play.  All things being equal, captured peices present more possibilities for development than ones on the board, and are a constant threat which alters the character of the game.

    Maybe white's first-move advantage in Chess is enhanced by the loss of material as the game goes on?  I don't understand either game deeply enough to argue it.

    MetalK, we are quite busily appreciating the article.  And while Interrobang might have been a little harsh, he didn't call you names, though he did call your points alternatively, "misguided," and, "mistaken."  He also said you were ignorant of the difference between scientific and unscientific hypotheses.

    I'd like to think I gave you the benefit of the doubt with regard to the relationship between hypothesis, theory, and the outdated concept of a precisely known "law" of nature.

    Standing your ideas up to be attacked is part of science, too.  So attacks on your points, though not yourself, are perfectly fair play.

    Kurt says up-front that he's using the term, "theory," in the lay sense, which isn't completely accurate.

    And yes, scientific hypotheses must be supported by evidence via the scientific method or they, by definition, aren't scientific and can't be scientific theories.

  • 4 years ago

    MetalK

    in some forms of martial arts, letting the opponent attack actually works in ones favor.  in that sense being black should be an advantage.

    As described by the author, he was using "an explanation of observed phenomena or data" as his definition of scientific theory.  which in fact is completely accurate.  just because your understanding and application of scientific theory ALSO includes scientific method, does not mean it HAS to.

    Thank you for the name calling and attacks.  I just wanted people to appreciate the article.

  • 4 years ago

    Interrobang

    They're not incompatible, Mufasah, but one of them doesn't need to use an unobservable phenomenon (evil spirits) to explain the world.

    Genghis: Black most definitely does not win just as often as White (http://www.chessgames.com/perl/explorer, for example).  Winning chances being equal is not what Steinitz meant by "proper play".  He meant that if both players play a perfect game, making no mistakes, that White's first move advantage is not enough to guarantee the win.

    Put another way, if a perfect being played chess against another perfect being, 100% of their games would be drawn.  Assuming Steinitz's assertion is true, the fact that White shows a consistent lead over Black in winning percentage is indicative of two things:

    1. The first move does give White some measure of advantage, and
    2. We're human.

  • 4 years ago

    Genghis_McCann

    “…it is now conceded by all experts that by proper play on both sides the legitimate issue of a game ought to be a draw…” 


    Fascinating. This was written by Steinitz in 1889, when it was impossible to prove or disprove. But the proof is now possible. Through the medium of computers, the results of many millions of games the world over can now be analysed. If Steinitz was correct, the result should be an equal number of wins for white and black. (The theory assumes a "draw", but if the chances for each player are truly equal, the wins for black and white should approximate equality as the numbers increase towards infinity).

    Is this the case?

    What are the statistics on chess.com?

  • 4 years ago

    mufasah123

    What if evil spirits cause the germs to make you sick?  The two theories are not necessarily incompatible.

  • 4 years ago

    Interrobang

    Pawnkeeper, the fact that White is "always one move ahead" doesn't necessarily mean he should win.  What it does mean to me is that the game isn't automatically won for Black.

    But the question is: does having the first move give White enough of an advantage to win even with perfect play by Black, or can Black can still draw in spite of his disadvantage?

  • 4 years ago

    pawnkeeper

    White has the first move and he is always one move ahead so white should win! You think?

  • 4 years ago

    Interrobang

    Oh I hope not.  Those have a tendency to drag on at times.  Anyway, thanks for sharing that.  I'm not entirely sure I agree that acceptance of those propositions is necessarily a prerequisite.  It is certainly an unspoken understanding that the universe appears that way, to an approximation at least, but as I see it, the essence of science is simply:

    1. Make a guess about the universe that you can check by investigating the universe.
    2. Check it.  If it doesn't make sense, discard it; if it does, use it to make more guesses.

    The fact is that this method has, over the years, accumulated a staggering amount of what amounts essentially to very intelligently developed guesswork, but guesswork that has nonetheless withstood every critical test and falsification attempt thrown at it.  Interpretation of the results is left to the beholder, but I hope I can be forgiven for observing that the above-mentioned body of guesswork is remarkably internally consistent, and it seems, so far, to describe very accurately the characteristics of a universe in which your two propositions are true.  So far.

    And at any rate, "fewest assumptions yet discovered"...I like that.

    Full disclosure, by the way, in case anybody should feel inclined to continue this (tangential and only slightly relevant) thread of the discussion: I have a degree in physics from U.C. Berkeley.

  • 4 years ago

    enthymene

    So, maybe we should be calling it Steinitz' First Conjecture?

    Interrobang, it's possible MetalK hasn't had the benefit of clear and concise elucidations of science like Carl Sagan's Cosmos or The Demon-Haunted World. When you also consider how the terms "theory," "law," and "hypothesis," are routinely brutalized in public usage (if they're used at all), it's understandable. 

    I suppose I disagree with you on one point.  Attractive as your parallelism is, I have trouble with your claim that science makes no appeal to belief.  My misgivings were voiced more eloquently in a Psychology 101 textbook I once owned, so I'll paraphrase it here.  It really should be in the introduction of more science texts.

    The book asserted that you must accept two fundamental propositions in order to participate in science:

    1. The universe is orderly and rule-governed.
    2. These rules are discoverable by human beings (namely through experiment, via the scientific method).

    I personally don't think you even need believe that the universe is real; so long as it plays by the rules, you can do science in it.

    So maybe science does require some beliefs (or at least utilitarian assumptions), but it requires the fewest assumptions yet discovered.

    Aaand I'm just realizing that I got sucked into a debate about epistemology.  I'll stop now.  Thanks for the wikipedia link.  First move advantage is a very engrossing subject.

  • 4 years ago

    rumsim

    =========================================================================
    The First Scientific Theory of Chess
    ...
    But I have only found one explanatory framework in my research that satisfies what I understand to be a scientific theory of chess, and that theory is more than a century old.
    ...

    In the sixth chapter that begins on page xxxi, Steinitz wrote his humble but profound theory: “…it is now conceded by all experts that by proper play on both sides the legitimate issue of a game ought to be a draw…”   As if to underscore its importance by repetition, he wrote on the very next page that “The principal thesis of the modern school may be briefly summarized thus: … by best play on both sides a draw ought to be the legitimate result.”
    ...

    Why is this claim to be properly understood as a scientific theory of chess rather than a personal prejudice?  I will address this question when I post part 2 of this blog in a few days.
    =========================================================================

    What I would like to say:

    All this is not a theory but only some claims.

    I am waiting to see if in the second part you will address the John fon Neuman Theory of Games.

    This is the thing to be called scientific theory of games (including Chess).

    According to it, the claim of Steinitz is still not proven.

    And if you insist his claim is true then you will be the first to prove it or to find that Steinitz had proven it but nobody understood him.

    I will also say: There is no scientific theory where no scientific proof is given.


    I like your introduction and the differentiation you made between believes and scientific theory.


    But be careful in the second part! Read what I wrote above!

    I could be wrong only if Steinitz claim has recently been proven scientifically and you are going to present and/or comment such a proof!

  • 4 years ago

    Interrobang

    Enthymene, I think Lasker was making his point precisely because of the fact that White has a definite and easily measurable advantage in the first move.  Opinion in the chess sphere differs as to the degree of this advantage, with prominent masters having come out on all sides; some have asserted that Black draws with best play, and others that the game is theoretically won for White after either 1.e4 or 1.d4 (according to their preference).  In fact, statistician and chess analyst Jeff Sonas, a frequent contributor to chessbase.com, has calculated that in a game between two comparable opponents, White's first move is equivalent to an Elo rating advantage of about 35 points.

    It is obvious that Black must play to draw before he plays to win, as his opponent receives the only advantage inherent to the rules of the game.  The question under debate is whether this advantage is significant enough for White to secure the win in spite of Black's best efforts.

    Wikipedia has an informative article on this debate: http://en.wikipedia.org/wiki/First-move_advantage_in_chess.

  • 4 years ago

    Interrobang

    Well spoken, enthymene.  Unfortunately, it is our friend MetalK whose understanding of the word is woefully lacking.  Scientific theories do indeed fail to be theories when they are shown to be inaccurate or untrue.  A prime example would be the geocentric model of cosmology that he mistakenly cites as an example of his own misguided point: the idea that the earth is at the center of the universe was indeed grounded in observation and falsifiable prediction according to the technology and analytical mathematics of its era.  It began to fall out of favor after Copernicus showed that more detailed observation and analysis indicated a sun-centered universe, and subsequent refinements to the heliocentric model by Kepler, Galileo, and others further hastened its demise.

    This is exactly how science works.  Unfortunately, MetalK, a "science major still in college", has apparently failed to learn this most basic of facts about his chosen field of study.

    His ignorance of the (lack of) applicability of scientific methodology to religion is equally striking.  As enthymene rightly observes, religions are founded on ideas are fundamentally matters of faith, and thus unfalsifiable.  Ultimate appeal to belief denies the relevance of proof or disproof.  Since all religions are matters of belief, and the fundamental tenets on which all religions are based are ideas that cannot be disproven by experiment (as, ironically, MetalK also points out), religious beliefs do not constitute theories in even the slightest sense.  Indeed, Pope Paul V's 1616 decree asserting the truth of geocentrism has held little weight in light of 400 years of subsequent observation; and Galileo, who was later sentenced by the Inquisition to house arrest for life due to the incompatibility of his observations with scripture, was indeed as right about the universe as anyone in his time could have been.

    Simply put, just as religion requires no recourse to proof, science requires no recourse to belief; belief is, in the most literal sense, unscientific.  (This is a very, very different statement from the facetious assertion that science is anti-religious; real science simply does not concern itself with religion, as each lies well outside the other's purview.)  Neither, for that matter, are even the most augustly regarded theories of science held as immutable fact.  The greatest scientific theories of our time, from plate tectonics and germ theory to evolution and general relativity, are universally understood to admit further refinement, should observation warrant.  But with such overwhelming bodies of observation already supporting them and, crucially, a complete lack of observations contradicting them, our confidence in their fundamental soundness is indeed well founded.

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