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Steinitz’ Theory of Perfect Play

In my previous blog, I claimed that Wihelm Steinitz’ 1896 Theory of Perfect Play was the first occurrence of a scientific theory of chess, and I speculated that it may be the only scientific theory of chess yet offered.  Indeed, Steinitz’ theory is the only one discussed in the Oxford Companion to Chess under the entry for ‘theory’.

Some may wonder about Philidor’s famous claim from 1749 that “pawns are the soul of chess”, which predated Steinitz’ theory by nearly a century and a half.  But Philidor’s statement, elegant and insightful though it may be, is not a scientific theory simply because it makes no claim that is testable with observable data.  Philidor’s beautiful thesis dwells more in the realm of faith than science, and the game of chess has room for both.

In my first post I quoted Steinitz’ first statement of his theory in abbreviated form, but let us present it now in full because he appends a reference to White’s first move advantage at the end:  “In fact 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, and that the right of making the first move might secure that issue, but is not worth the value of a Pawn.”

Steinitz continues by discussing the grave danger to a chess player of losing a pawn unless the loss is made up very quickly, but does not again refer to the advantage of the first move.  Given his vaguely disparaging remark “but is not worth the value of a Pawn” it is clear that Steinitz did not believe that this small advantage was significant enough to invalidate his theory.

Steinitz wrote in accordance with his theory that when a game ends with a winner and a loser it is the loser that has determined the outcome by committing an error.  In Steinitz’ words, “Brilliant sacrificing combinations can only occur when either side has committed some grave error of judgment in the disposition of his forces.”

This is a blog, not an academic monograph, so I am not prepared to offer definitive evidence for or against Steinitz’ theory.  I can, however, present a few data points to indicate if the theory deserves further study.  Fortunately, there is some interesting data right here on chess.com at the players page for standard, live games.

There are several things of interest to notice here.  First, there is a large pool of players represented, almost 47,000 as I write this.  Second, the average player rating is only 1193, indicating that most players here are not particularly strong.  Hence, we would not expect to see very many draws if Steinitz’ theory is accurate, and indeed only 3% of the games end in a draw.

Weak players make lots of mistakes.

I myself am not a strong player by any means, but my rating on this site puts me far to the right of the bell curve, and we would expect that I would have more than 3% draws.  I have drawn 8% of my turn-based games.  A quick check of several turn-based players close to my rating revealed significant variability, but draw percentages for players with large numbers of games are almost all higher than 3% and not far from my own percentage.

I do not trust the statistics for titled players on this site because they tend to play significantly lower rated players here (which I view as a courtesy and a kindness) and so their win rates are extremely high.

However, a good site that records over-the-board games of generally high-rated players is chessgames.com and their statistics page tells us that of more than a half million games there are roughly 37% wins for white, 36% draws, and 27% wins for black.  The average Elo rating when known is 2226.  The site does not say how many rated players are in that set, nor how many players are represented in their database overall.

A good theory is predictive, and the tentative evidence above is in accordance with the prediction of Steinitz’ theory that stronger players will have more draws than weaker players.

Let us conclude with a longitudinal prediction of the Theory of Perfect Play.  There will always be detractors, but I believe most people would agree that the level of play among the world’s elite chess players has become better over the past century.  Thus, the theory would predict that today’s highest caliber players would have higher draw percentages than players of Steinitz’ day. 

In the Vienna tournament of 1882 in which Steinitz tied for first place with Winawer, we discover that among the 306 games played, there were 69 draws, or about 23% of the total.  Given that some of the games were forfeited when players withdrew from the competition, that percentage could have been even higher if the games had actually been played out.

In the famous Hastings tournament of 1895 where Steinitz placed 5th behind Pillsbury, Chigorin, Lasker and Tarrasch, there were 231 games played with 56 draws for a 24% rate.

What about tournaments among the chess elite of today?

In a chessbase.com article about draws, GM John Nunn provides the following data:

Event

draws  

short draws

Linares 2004

79%

33%

Wijk aan Zee 2005

63%

19%

Linares 2005

65%

19%

Dortmund 2005

54%

13%

San Luis 2005 World Championship 

58%

18%

I wish to avoid the issue of ‘short draws’ or ‘Grandmaster draws’ for the moment.  Even if we subtract out the short draws from the draws overall, we can see in these recent tournaments that the overall percentage of draws is significantly higher than the 23-24% of Steinitz’ day.  This is in accordance with the theory’s prediction.

Again let me repeat that this is only a blog, and while I do not claim we have found strong empirical evidence in support of Steinitz’ Theory of Perfect Play, I do claim we have found weak evidence.  As such, deeper study of the question is warranted.

In my next blog I would like to discuss how thinking on chess strategy is in accordance with Steinitz' theory.  In the meantime, I hope this blog generates as much fascinating discussion as the previous one; and as you continue your own quest to achieve perfect play, remember to choose your move carefully, in chess as in life.

 [Note: I'd like to thank NM Lonnie Kwartler a.k.a. GreenLaser for his clever comment pointing out my typo on the original date of the Hastings tournament, which I originally listed as 1885. Nice catch, Lonnie!]

Comments


  • 2 years ago

    sryiwannadraw

    I think that since white has 1 more move its a higher percentage he/she will draw more often, not by much and higher rated players draw more often due to experience obviously. Also, perfect play cannot be achieved in reality 100% of the time.

  • 4 years ago

    WarAndPiece

    I got 10% from the paragraph (in the article above) about chessgames.com especially this sentance

    "...tells us that of more than a half million games there are roughly 37% wins for white, 36% draws, and 27% wins for black..."

    To use the numbers that you pointed out, at Master level the difference is still noticeable, white wins 52% to 56%.  Which means that black wins between 48% and 44% respectively, which actually gives you white's spread of victory of 4% to 12%.  I'm not sure if "spread" is accurate here, so putting that aside and just looking at white having 2% to 6% advantage - this is still noticeable.

    The foundation stone of this theory is that starting first grants you little or no advantage (less than 1 pawn).  I would therefore expect white's advantage to be minimal, rather than anything from 6% to 12%.  This doesn't seem to add up.

  • 4 years ago

    Interrobang

    WarAndPiece, where did you get that statistic?  In master play, White tends to score between 52 and 56 percent.  That's adding the total of White's wins to half of the draw total.

  • 4 years ago

    WarAndPiece

    If having the first move results in less than a pawn of advantage why is that white wins 10% more often than black?

  • 4 years ago

    SpaceOddity

    Chess statistics can be interesting and informative, but I don't see how any of that is illuminated by a so-called 'scientific' 'theory' of chess of the kind attributed to Steinitz.  The relevance of chess statistics of past games for illuminating the question of whether Steinitz was right in asserting that perfect play always leads to a draw are like tic-tac-toe statistics accumulated from 5 year-olds.  Those statistics will also follow a bell curve, they will also show that the more highly rated 5-year-olds tend to draw more often when they play other highly rated 5 year-olds, but that empirical 'data' does nothing to help answer what is not an empirical question at all but a purely logical one--does chess, when played properly by both sides, lead to a draw or win?  Any finite set of 'data' (ie, past games) that does not encompass all logically possible chess games cannot determine that not all chess games lead to a draw.  A finite set of tic-tac-toe games can, however, show that all tic-tac-toe games, if played perfectly by both sides, will always lead to a draw.  In any case, the important point is that even though chess games can be treated as 'data', it is a misunderstanding of the phenomenon to compare it to empirical data of the sort found in the natural sciences because chess games, unlike natural, physical events, are purely formal and not physical.  The activity of playing chess is an event that happens by human beings in space and time, but in playing a game of chess, we only instantiate one of the logical possibilities of chess, one that is either an example of perfect play or (most likely) one that is not.  The set of chess games exists neither in space nor time, as could be said of geometry.  In short, the very idea of a 'scientific' theory of chess, based on the model of the empirical sciences does not seem plausible or even coherent since the object of study, chess, is only incidentally empirical but essentially logical.

    So Kurt Godden tells us in his first article on Steinitz that he wanted a scientific theory of chess as a sort of grounding or preparation for a discussion on chess strategy.  It seems that, by way of counter-example, we can simply point to all the other books on chess strategy (some better than others) that do just fine without such a grounding in a 'scientific' theory of chess.  

    So my questions for Kurt are: 1) why do we need a scientific theory of chess if many GMs can write successful and helpful books on chess strategy without needing a scientific theory of chess as a grounding? (ie, what would be added to this reservoir of chess books if we added one that was 'scientific' in the sense you mean, even if that were possible?) 2) Is chess in any relevant way different from tic-tac-toe in the way I describe above and in my blog  on why there cannot be a scientific theory of chess (in the natural science sense of 'scientific')?  If not, then again, there seems to be no motivation or desire for a 'scientific' theory of chess rather than simply an account of chess that accurately describes the different possible chess games that could arise--and we already have such a 'theory'--that would simply be a statement of the rules of the game.

    In physics, we don't know the 'rules' of the game, in that we don't know what laws of nature are out there, or if there even are strict laws of nature. So gathering data, finding patterns and testing hypotheses could be helpful in extrapolating, based on induction, what the 'rules' of the universe are.  But in chess the rules of the game are very clear, we invented them and program them into computers all the time.  So a theory of that sort is something we already have, and if it is not a theory of that sort that you are after, then I am befuddled as to what it is you are looking for in a 'scientific' theory of chess. 

  • 4 years ago

    Awick17

    Excellent article, I thoroughly enjoyed it!  Thank you very much, and keep it up!

  • 4 years ago

    jlueke

    Another interesting stat would  be to the results of evenly matched/rated players compared with matches with 100 point difference and again a 200 point difference.  Kasparov-Karpov had 131 draws with wins just 29-21 for Kasparov.

  • 4 years ago

    PeterArt

    Hi.

    You know the curve describes perfectly, what statisticans would call the gausian curve, or normal distribution. If you never heard of it, simple for a number of times lets say 100 times throw three stones and count the eyes of the stones you endup with the same figure for the total of eyes.  (100 is much maybe a computer or excel can do it for you..dont use 1 stone but 2 or 3 or more. ) (as 1 single stone behaves different chances are equal to get 1 to 6)

    I think in a good rating system (and i have some doubt the current ones) it shouldnt matter what level one person has if the difference is to big between the player the better player should not get much points, thats fair.. still it surprices me how high rated some people are here. But offcourse some are just better, as the curve is in most normal distributions. for example go and weight 100 people you get most likely the same shape :)

    So i'm not realy sure the shape itself is describing or proofing the chess theory.
    It is however a nice sample for statistics  (he in once studied statistics for a few month's) its kinda strange math. With an origin in gambling, no wonder we it aplies to games in general.

    I havent followed up mordern theories but if your interested you might find "game theory" invented by game developers interesting, it describes human gamble behaviour, and it is these days used in many fields.

  • 4 years ago

    psyduck

    i dont really see why this is such a groundbreaking theory. If prefect play leads to a white (or somehow black) checkmate, than i think we'd have discovered the way to sure victory by now. And if black (or white) wants to play for a draw from the get go, it seems pretty simple, play petroff against king's knight opening and play conservatively against queen's pawn. Even after 100 moves, there are still limited possible positions in chess

  • 4 years ago

    merchco

    Here is my theory In tournaments always play to win, anything else is nonsense.

     If its a friendly game where there are more important things than winning, ie using friendlies to practice new ideas or just to learn more well then loosing is definitely good as thats how we learn from making mistakes.

    The harder you work the luckier you become and most succesful people in this life have usually worked for it be it in sport or business, the old sayings handed down from our parents Practice makes perfect. 

    So to sum up draws are a human answer to deeper human emotions and feelings namely fear.Either the fear of winning(may not want to show your hand to early in a tournament, may not want any attention   ) the fear of loosing (afraid of being humiliated by a percieved lesser opponent) etc. etc. etc.

  • 4 years ago

    merchco

    I usually agree with your posts but on this one i totally disagree.

    I believe very few games should be drawn there are millions of moves in chess and no human being could predict them all let alone computers.(I found a new opening which does not exist in the data base and i am only playing a year so since most master games are in the data base it proves to me that only a limited number of moves have actually been discovered). 

    Even when computers are pitched against each other a draw is not definite.

    To me there is more to Chess than maths and science there is also psycology,and all that entails as to what motivates a certain move and this may go more to explaining the high percentage of draws amongst titled and higher rated players than any science -namely pride and other emotions and motivations. 

    Its not just pride there are many different reasons for settling for draws.In early stages of a tournament where a draw is enough for both players why unless the rules state otherwise should either player tire himself out by going for a win when the draw suffices.  

    Steinitz was a great chess player but lets not turn him into a false idol he was no God.

    Yes he had a theory but for such a great chess player his theory sound totally incomprhensible to  one would presume logical thinker,as his theory was not backed by any science ie no evidence.

    Here is the flaw in his theory since no two human beings are the same it is impossible for their to be perfect moves all the time and since that is impossible it is not logical to assume that with best moves all games should be drawn.

    So since this can never happen why talk about it and even if human beings where perfect and played with no emotion and made all the perfect moves computers can prove that answer, and usually one side wins.

    If we take the logical conclusion from steinitz theory Chess is a total waste of time and resource since with best moves according to his flawed theory a draw would result so the logic would be not to play the game at all since as a draw will result both parties could have used their energy and limited time doing something more advantageous to themselves and obviously their families. 

    So as i say its all bullshit chess is a game between two human beings no computer can ever match since the computer will never play with feeling and emotion and fear of winning and loosing it can never claim to be as good as the Human Being.

  • 4 years ago

    NM GreenLaser

    The idea of chess theory is interesting. Hastings 1885 should be 1895. Human error affects balance in chess and writing. Perhaps, one day we can get Fritz or Rybka writers.

    notser3, http://www.chess.com/article/view/ruy-lopez-open-to-rudeness is an article that shows one way to deal with what you call a "jerk."

  • 4 years ago

    SisyphusOfChess

    This is an interesting thesis.

    Another set of empirical data you might consider looking at is games from top level computer chess events - as computers have now reached superhuman strength.

  • 4 years ago

    notser3

    I believe Steinitz was on to something. Logically both sides start off with equal forces Space I.e. resources. The only advantage in chess comes via a disadvantage that is created at some point in the game. The only pure advantage that can qualify as an actual advantage is white’s first move. However this advantage can be equalized in the game if black takes on its proper role as the submissive. As in Chinese philosophy the Yin and Yang are not described as stronger or weaker yet in balance or harmony. Like two dancers there is the lead and the follower and if both make all the correct moves what remains is a perfect choreographed balance of movements. Balance is the key in chess and breaking an opponent’s balance is the key winning. This fact also explains why a lot of jerks in the world are excellent in chess because they are great at disturbing their opponents balance both on and of the board. It’s also amazing to me when one of these jerks claims to be intelligently superior to others because he or she is so good at being a jerk! Maybe a little evidence for this is the late Bobby best player to ever live but very jerky.

  • 4 years ago

    ChessPaladin2009

    SmileAs I stated under the first blog on this subject, science can study and analyze and take measurements of chess - BUT chess is a mind game, and as such cannot be scientifically postulated no matter what statistical data is gathered!  WinkAll factors in a game of chess can never really be "equal", hence the assumption of a draw is not correct(not likely to be produced!)!  In science, if your primary assumption(s) are wrong, your conclusions will also be completely wrong no matter how accurate the data gathered on the subject being studied is!  Players offer and accept draws for a variety of reasons - some good(the position really is a draw) most are not so good!  SurprisedSteinitz was no scientist and his observations are also not a scientific theory on chess either!  -  ChessPaladin2009Cool   

  • 4 years ago

    jlueke

    Kurt,

    I tend to agree with your position for many of the reasons you cited in this post.  I wonder if there are also statistics from long games played computer vrs computer and what those results might look like?  One would think, if your theory is true, that the same engine running on the same hardware playing itself should always draw unless it has a programmatic flaw where it will always generate an error.  But even computers playing each other with different engines on the same hardware should ahve trouble coming up with wins since they are incapable of making mistakes due to psychological pressure or time.

  • 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.

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


  • 4 years ago

    Anatoly_Sergievsky

    Classy. Most blogs are.... not great. But this is good stuff all around. Scientific and well written, and not arrogant either. I like it a lot. Gold star.

  • 4 years ago

    nico101rsa

    Very nice post!

  • 4 years ago

    KiwiJuise

    This is sheer amazingness. I can't wait to discover the conclusion in your future blogs!

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