Steinitz’ Theory of Perfect Play

Steinitz’ Theory of Perfect Play

Dec 5, 2009, 1:13 PM |

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 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 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 article about draws, GM John Nunn provides the following data:



short draws

Linares 2004



Wijk aan Zee 2005



Linares 2005



Dortmund 2005



San Luis 2005 World Championship 



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!]