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"Warriors Of The Mind,"
  '(a quest for the supreme genius of the chess board)' 

  by GM Raymond Keene and Nathan Divinsky 

  This page is an off-shoot of my  "Best Players"  page.  

This will be my page devoted to this book. ("Warriors of The Mind," by Keene and Divinsky. ISBN:  # 0-9513757-2-5 This is not the original edition, {someone ran off with mine}; but a Hardinge-Simpole reprint.)  While I am pretty sure I do NOT approve of this book completely, it is perhaps the ONLY book ever written that truly attempts to answer this question in an intelligent manner. 

 The question is ... of course! ...    WHO IS (or was)  ...  THE GREATEST CHESS PLAYER WHO EVER LIVED?

There are many authors who have touched upon this topic. Another good book - that I believe is out of print - is:  "The Ratings of Chessplayers, Past & Present," by Arpad E. Elo. (Copyright © 1978, published by Batsford Chess Books.  ISBN: # 0-7134-1860-5; hard-back.) The author {Elo} does not really attempt to answer the question in its entirety, but does come to the conclusion that Fischer was the highest-rated player of all time. Another book - which seems to be just the research for the "Warriors" book - is the volume: "LIFE MAPS ... of The Great Chess Masters," by Nathan J. Divinsky. (Copyright © 1994, published by International Chess Enterprises, {I.C.E.} ISBN: # 1-879479-17-6; hard-back.) This is a handy book to have if you wanted a book full of tables - with the answers to questions like: "How did Capablanca, {or other great players}; score against the best players ... that he faced over the board?" 

 "There are lies, DAMN LIES, ... and statistics."  -  Mark Twain

 (Book) Review of  "Warriors of The Mind."
(Keene & Divinsky)

By LIFE-Master A.J. Goldsby I.


First you should know I am a Life-Master of chess. You should also know I have written extensively on the subject of "The World’s Greatest Players," … many different state chess magazines have printed my thoughts on this subject. (I also have several pages on my web site that cover this.)

For example, some of the factors to be considered are:
#1.)  Strength of opposition, How and when did this player face the other 64 on this list? (Who did he play? Were they any good?); 
  The aging factor, (These authors call this the "era effect." In chess, a player’s strength decreases dramatically after about age 45.);  
#3.)  Career span, The length of time a player's career lasted. 
(How long did a player play, and for how long was he really good?). 

Some of the factors these authors do NOT address is the accumulation of general theory, (Could a player of 1850 beaten a player of 1950?); player effectiveness, and how much a player contributed to the overall advancement of the science/theory of the game. They also touch upon, but do not really delve into, one of the most effective measuring tools one could use for this task: i.e., how far was this player ahead of the rest of his generation of players … especially at their peak?

This book is a re-print of a book that first came out I 1989; much of the material in here is already rather dated. (This means that players like Anand and Kramnik are NOT even mentioned, as they had yet to make their mark on the chess world.)

The object of this book is to find the greatest {CHESS} player who ever lived. The authors say that they are embarking on the on this mission with zeal, yet they are going to be more objective than anyone has ever attempted to be. Yet it seems to me that the authors started out with a preconceived notion of who the best player was, and then constructed an elaborate artifice to justify their conclusions. (In one of their early lists, Andrei Sokolov comes out as number FOUR. The authors then attempt to "massage" their data in an effort to make this unbelievable blooper go away!) The authors also start out with a fairly small number of players, (64); statistically this – in and of itself – is a tremendous blunder! (Then they map out every game every played between this pool of contestants.)

I was considered an adept at math … and I once had a student who eventually received his Doctorate in Math as a Statistician. But even so, some of the formulas here, (pages # 320-321); are beyond the ken of virtually anyone but a trained mathematician.

Their final results will also generate controversy; some of their lists are almost laughable in their conclusions. For example: Many EXPERTS, GM’s and authors strongly feel that Alekhine was one of the greatest players who ever lived. Yet these two authors (initially) do NOT rank him in their top 25!!

This book will not make you a better player, so don’t buy it for that reason. Buy this book because it is perhaps the ONLY book to even TRY and deal with this topic in a really intelligent manner. It is also a great "FUN" book. You get a game or two for each player discussed and they also give a brief sketch/(bio) of the careers of each of the players covered in this book. A rousing read which is stimulating AND thought-provoking!!


I gave this book four - out of a possible five - stars. (Posted on around October, 15th, 2003.) 


There are literally hundreds of problems with this book, in fact there are so many flaws it is hard to take it really seriously. BUT ... it might be the only book {so far} where the players at least try to answer this question in a scientific manner. This web-page is also my in-depth look at this book, and an attempt to refute some of the sillier stuff these authors put forth. Another problem is they started off with ONLY 64 players ... their choice of who they picked was VERY arbitrary. They left OUT about a dozen great players, like RETI, TARTAKOWER, etc. 

  I must stress that in the following list, that these numbers are  NOT   ratings, but a numerical sum which probably represents several different factors!!!   
 (Things Keene and Divinsky consider important.) 

K&D's Top Ten Players

  1.  Garry K. Kasparov - 3096

  2.  Anatoly Karpov - 2876

  3.  Robert J. ("Bobby") Fischer - 2690.

  4.  Mikhail Botvinnik - 2616.

  5.  Jose R. Capablanca - 2552

  6.  Emanuel Lasker - 2550

  7.  Vicktor Korchnoi - 2535

  8.  Boris Spassky - 2480

  9.  Vassily Smyslov - 2413

  10.  Tigran Petrosian - 2363.

Of course there are many problems with this list. I agree that Korchnoi IS one of the greatest players of all time, but to rank him ahead of players like Steinitz??? (Remember: Korchnoi NEVER won the World's Championship!) Speaking of Steinitz, he is not even ranked in the top 30! This is both ludicrous and completely unbelievable. 

Other notables are: Morphy, # 11;  Tal, # 14;  Alekhine, # 17!, (After MUCH tweaking!); R. Fine, # 38; (Too many 'nobodies' ahead of him.);  A. Rubinstein, # 44!!!;  A. Nimzowitsch, # 50!;  and the WORST player ........ or at least, the lowest-ranked player out of the 64, is J. Zukertort, ... with ONLY a score of 873!!!!! I find this very hard to believe. (To say the least!)

If one is to take these numbers literally, Kasparov is more than TWICE as good as Rubinstein ever was, and almost FOUR times better than Zukertort. This is so incredulously stupid, inane, and unbelievable that only a moron would swallow this garbage. It really is hard (impossible) to believe that S. FURMAN is rated # 26, and guys like Nimzo, Rubinstein, etc; are left (far behind!) in the dust. 


Another common flaw of MANY books, (Keene and Divinsky, Elo, etc.); are that the older players invariably suffer. I.e., both Elo and K&D are under the influence of the OBVIOUS flaw that more recent champions gain stature, standing, or rating points by defeating earlier champions. 


More to come ... so stay tuned! 

(Sunday;  October 19th, 2003.)

I have now read this book, cover-to-cover, and read the front and back sections several times. Of course the authors keep insisting that their criteria is the only one that deserves to be considered; blah, blah, blah. Its silly and more than a little nauseating. And of course they continue to insist that  Kasparov is # 1  and  Karpov is # 2

But consider the following:

  •  -  They used a relatively small sampling of games. ANY statistician (worth his salt); can tell you that the larger the database, the 
         greater (the number of) the initial sampling, and the more "cross-sectional" your initial selection process is, the more likely the  
         final results will be valid and contain less error. These authors have thrown this consideration out the window. This puts their whole   
         process under a cloud, in my opinion. 

  •  -  They ARBITRARILY used a cut-off of 2600 as a consideration for their initial group of players. This could have just as easily 
         been 2550 or 2500. Their cut-off left out LEGENDS of the game like Richard Reti. (AND! ... many others as well.) 

  •  -  They considered ALL games played in their pool between the group of players selected. This meant that "fun" games, and 
         other "garbage" games like exhibition games carried the same weight as games played at the World Championship level.   
         This is so inept and foolish that it borders on retarded behavior. 

  •  -  The conclusions of their own raw data is simply ludicrous. After the first pass, GM A. Sokolov ... a player who never won the 
         World Championship, a Soviet Championship, or even ANY! major international tournament ...  is the number four all-time 
         player!! The authors then go through some major contortions nd have to work hard 'massaging' their data to move Sokolov 
         far enough down the scale to give their results any real measure of credibility at all!

  •  -  Their formula's are serpentine and without reason. I am not a math professor, but the insight of a top-flight mathematician 
         would probably be greatly illuminating. (And I would be almost willing to bet would reveal many flaws and inconsistencies.)

  •  -  Just as with the  PURE RATING  formula's, the older players clearly suffer and the later players gain in stature by defeating 
         the previous champions. To even suggest that Kasparov is 2800, but Morphy is only 2500 is both foolish and ludicrous. 
         (It seems no one can come up with a system that is equitable to the older players. And every time a comparison is made 
          between the players of yore, and modern players; it seems that the older players invariably get the short end of the stick!) 

  •  -  One of the greatest mathematicians and chess scholars who ever lived was  Arpad Elo.  He said that you could  ONLY 

  •  -  Many  factors ... like a players' contribution to the overall theory and the advancement of the science of the game ... 
        are NOT even considered by these authors! 


Some other points to ponder are:  

# 1.)   In terms of pure ratings and peaks,  Bobby Fischer  would clearly be the best player of all time. (They even admit this on page 334!)

# 2.)  On page # 307,  Paul Morphy  is clearly the best player of all time. They also admit in this chapter that Morphy was the best by 
          a purely 'arithmetical' standard, and this is why this method alone is NOT a sufficient tool to find the best player of all time!!! (They 
          later say that Morphy's real strength is unclear and fogged by the mists of time.) 

# 3.)  According to quality of play, life-time percentages, and the table found on  page # 314,  the greatest player of all time is ... {easily} 
          Jose R. Capablanca!!!  {Capa also comes in the  TOP  spot according to  Jeff Sonas's  ONE-YEAR,  THREE-YEAR,  FIVE-YEAR peaks!!  
          In fact, he dominates all of these lists!) 

# 4.)  According to pure domination of their contemporaries, they rate Emanuel Lasker  as the BEST player of all time. (Page # 334.) 
          They go on to note that Lasker's performance(s) during the period of 1910-1918 has virtually no peer. (And they also admit that  
           Lasker held the title the longest, played many tough matches, and won the most 'super-tournaments' of any World Champion.) 

# 5.)  On page # 335 is another table, and one that I would be inclined to give much more weight to. It considers  ONLY  those games 
          played at The WORLD CHAMPIONSHIP level. Then they rank the players by their percentage level. IN CLEAR FIRST Place is 
          Emanuel Lasker  with a percentage of nearly 67%. Number two, at 59.52% is  Robert J. Fischer!  And number three, with a 
          winning percentage of 56.79% is:  Alexander A. Alekhine!!! (And Kasparov is nowhere to be found, at least NOT near the 
           top of this list!!) 


 --->    In the book of  "Chess Lists," (2nd edition); by GM A. Soltis ...  we find a somewhat up-dated version of this same list. 
           (On page # 44.) The top three players of that list are:  
           # 1.) Emanuel Lasker,   # 2.) Bobby Fischer, ... ... ... and  # 3.) Alexander A. Alekhine.  
           (Once again, Kasparov is nowhere to be found, at least not in the top five.) This is not a repeat of information. In some cases,   
             the numbers of GM Soltis are radically different than those given by Keene & Divinsky. 


         (Steinitz is on many of the lists that deal with the best players of all time. He once went close to 15 years without losing a game. 
           His TEN-YEAR peak ... no matter whose rating system you use! ... puts him in the top 10. These two authors completely ignore   
           this little fact as well. 02/06/2004.) 


All this just brings us back to the quote by Mark Twain, and the fact that if you have your own favorite ...  I see no good reason why anyone ... especially THESE authors ... should be able to convince you otherwise! 

March, 2005:  Jeff Sonas has completely redone his website. His - new - list of three-year peak performances shows  Kasparov  at number one, (# 01);  Fischer  at # 2, and  Capablanca is at # 3. (This pretty much completely refutes Keene and Divinsky's claims of GK #1, and AK # 2.)  [ more

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This page was created in August of 2003.  This page was last updated on 01/06/13 .  

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