The Chess Mind

First, a preliminary point. If Inky's claim is that Shabalov and Perelshteyn are admirable because of their last round fight, it's hard to agree. A draw meant around $1000 - and that's before the entry fee and hotel (and airfare?) were deducted; in short, next to nothing. A win, however, meant nearly $8,000, so the decision for them to fight it out was a no-brainer.

Now to the main event: were the eight leaders irrational for making a quick draw - should we be "amazed" by their actions? We shouldn't rush to answer - the question is insufficiently precise. There are different things we might, or might not, be amazed about.

(1) Psychologically, their action isn't amazing. At the end of a tournament players are tied, and as Vince Lombardi (or George Patton) said, fatigue makes cowards of us all. Further, many people are risk-averse, and the thought of forsaking a nearly $8k bird in the hand for $1k in the bush, if one is unlucky, is an unhappy one.

(2) Our focus, therefore, will be on the economic rationality of the decision, abstracted from questions of risk aversion and energy (though I will say more about those issues later). But we should make the question more precise still, because in working out the percentages, color matters. As Garry Kasparov writes in How Life Imitates Chess, the stats for GM games average 29% White wins, 18% for Black, and 53% draws. So the question I want to focus on is this:

(Q) Should a last-round leader with White take a quick draw in a normal, still-living position?

To solve this, we'll have to do some number crunching, and I'll make some simplifying assumptions. (Those who are willing to do a more thorough job are invited to write in with their more accurate conclusions.) Here goes.

Assumption 1: There were ten prizes in the Open Section (I'm going to assume the numbers given on the website):

$30,000, $15,000, $7,000, $3,000, $2,500, $2,000, $1,500, $1,000, $800, $700.

The actual prize fund was reduced, but I’m going to assume the reductions maintained the proportions and number of prizes originally offered.

Assumption 2: I'll assume that if any of the eight leaders lost, they'd make nothing. This is in fact untrue – there are scenarios in which they could make over $1000 – but I’ll generously assume they won’t. (It’s not that generous though, since Goichberg extracted the entry fee and (I think) the room costs from GMs’ prize money. So in many if not most cases they probably would have netted a goose egg.)

Assumption 3: Another kindness on my part: I’ll assume that no one could catch the leaders if they all drew. (In fact, Shabalov did catch them and two others might have.) This too improves the financial incentive for a draw, though perhaps not enough to justify not trying for a win. Stay tuned.

Assumption 4: One final generosity. While the odds of a decisive game are only 47% (29% + 18%), I’ll bump it up to 50% for ease of calculation – but only for our rivals. Since that increases the chances that one’s rivals will reach the higher score group, this too offers some support to the “let’s all draw” scenario.

Ok, let’s go to the numbers (I do a little rounding up and down on the cents, so the results are approximate).

There are three cases for our single player going for a win – let’s call him “HN”, for no apparent reason – each with four sub-cases:

(A) HN wins, and of the other three games either all are drawn, two are drawn, one is drawn or none are drawn.
(B) HN draws, and…the same four cases.
(C) HN loses, and…there are the same four cases, but we don’t care, since we’ll assume HN makes nothing – that was assumption 2.

Case (A1): HN makes $30,000
Case (A2): HN makes $22,500
Case (A3): HN makes $17,333
Case (A4): HN makes $13,750

Case (B1): HN makes $7,750
Case (B2): HN makes $5,167
Case (B3): HN makes $3,625
Case (B4): HN makes $2,750

Case (C): HN makes $0

There are still two steps left. We have to weight the cases by multiplying the totals by their likelihood. Thus in Case (A1), the odds of all three other games winding up drawn = 1/8 (1/2 x ½ x1/2), and his chance of winning is .29. So the expected value in this scenario = $30,000 x .125 x .29. We’ll leave the last multiplicand for the second step, though.

Case (A1): $30,000 x 1/8 = $3,750
Case (A2): $22,500 x 3/8 = $8,438
Case (A3) $17,333 x 3/8 = $6,500
Case (A4) $13,750 x 1/8 = $1,719

Case (B1) $7,750 x 1/8 = $969
Case (B2) $5,167 x 3/8 = $1,938
Case (B3) $3,625 x 3/8 = $1,359
Case (B4) $2,750 x 1/8 = $344

Case (C) $0

Now we sum up sub-cases and multiply by the appropriate percentages:

Case (A) $20,407 x .29 = $5,918
Case (B) $4,610 x .53 = $2,443
Case (C) $0 x .18 = $0

Add it all up, and HN’s expected value is $5,918 + $2,443 = $8,361.

If you’re still awake, here’s the bottom line: by going for a collective pre-arranged draw (which is against the rules, but common and capable of being arranged in a way that obeys the letter of the law while skirting its spirit) the player with White is, on average, tossing $611 out the window. (And that’s with the generous assumptions given above, and also ignoring that the actual HN outrated his opponent by 75 points, which would also improve his expected value.) In sum, if one has a reasonably high tolerance for risk, he or she should play for a win with White in the last round. Or should he? The argument has one last twist.

Some of you may be wondering, what about the player with Black? The calculation is easy – we keep the summed sub-case numbers and invert the multipliers: ($20,407 x .18) + ($4,610 x .53) + ($0 x .29) = $3,673 + $2,443 + $0 = $6,116. The answer this time is no. All things being equal, if the Black player goes for the win, he’s throwing away an average of $1,634 for his efforts. Note that on average, the drawing plan makes more for the players than going for a win, by an average of $512. If this is typical, then if one assumes the correctness and applicability of the game-theory strategy of tit-for-tat, then maybe Inky is right after all – at least for a player whose rating is likely to be near the average in such a situation.

There are many ways and materials that discuss this. Here's my suggestion, and I think it holds for anyone from "relative newbie" through master.

First, you need to pick a game. I recommend using games that are annotated, though you should make a copy of the game without the comments and cover up the moves, revealing each half-move only after you've made your guesses. (If you're using Fritz or ChessBase, that's easy. First, open a commented game, then use "delete all commentary" and save the result. (NOT "replace"!) Then use the "training" tab, which will hide all moves but the preceding one.)

Having picked out a game, go through it one half-move at a time (i.e. first one player's move, then the other's, etc.), starting from the end of your book knowledge, and try to guess the moves. (By "guess" I mean "work out as best as you can".) Do that all the way through, writing your guesses down.

Next, go through the game as played, a half-move at a time, and try to figure out why the players made the moves they did. Work out the positional moves, work out the tactics - the whole thing. Don't use your computer chess engines (and if you are doing all this on a computer, make sure you turn the heumas move-input tool off)! You might want to go through it twice - first without moving pieces to analyze, then moving them. If you can't figure something out, make a note of it.

Step four: see if you can figure out what was wrong with your mistaken guesses in part one. You could break this up into three sub-steps: working out mentally, then moving pieces, and then with a chess engine's help.

Now that you've extracted all you can from your own abilities and understand the game as deeply as you can, it's time to look at the annotated version. This should prove a real eye-opener after your preliminary work! I recommend you go through the notes the same way as in step three: try to understand all the analysis, and make a note of whatever you don't understand. (After doing this, you might make a second run-through with the chess engine, especially to check any tactical questions you might have.)

Finally, if you've done all that, ask a (sufficiently strong) friend or chess teacher to have a look at your analysis and to help you understand whatever leftover questions you might have.

Hypothetical Q&A;:

Q: Gee, that sounds like a lot of work.

A: Who said chess was easy?

Q: I don't have time to do all that.

A: You don't have to do it in one setting, though there are benefits to doing so. One is that tournament games take a long time to play, so this exercise will help improve your mental stamina. But if you can't, or can't always finish steps 1-5 in a single sitting, break it up into several sessions. Do make sure, though, not to let too much time elapse between sessions.

Q: When copying games, I see moves and annotations, and that ruins the whole exercise.

A: There are ways of avoiding or overcoming this problem. If you have a database, it's no problem at all, because you can open a game in training mode without seeing anything, delete the annotations without looking at them, and so on. If you don't have any databases and are using a game from a book, no problem: print the game from an online database (here's ChessBase's - find the game there, select it, choose "View* as PGN, paste it into something you can print from and you're good to go). Another thing you can do is to pick out a bunch of games, copy them out by hand, and then wait a while - give yourself time to forget what you've seen.

Q: Will this really help my chess?

A: Immensely.

Q: Why are you sharing this information with the general public?

A: I'm a nice guy! Besides, most people are lazy - probably all of us, at least some of the time - and they'd rather buy "Winning with the Four-Move Mate" or similar rubbish. You'll lose a game here and there to these trapmeisters, but you'll leave them in the dust if you make a habit of studying games in depth.

Q: I think I still see some dregs at the bottom of the cup: what else haven't you told me about studying a game for all it's worth?

A: Practically speaking, there's no end to what you can extract from a good game if you're willing to dig. Here are two more suggestions. First, you can look up other games that use the same variation, looking for similarities and dissimilarities, and doing so with an eye to solving whatever problems you became aware of while studying the first game. Second, you can do a search for games featuring similar motifs. (E.g. two bishops vs. two knights, a certain attacking pattern, endgames with a given material balance, and so on.)

Q: Should I just buy a "Solitaire Chess" book?

A: You can, but I have two caveats and a more serious objection. The first caveat is that if you use the book directly, you'll often be given information that helps you with subsequent moves, and the notes are almost always given for the winning side's moves. That means you'll get too much information (when you're doing the exercise) and too little (when you're working on step 5). Caveat number two is that it's only a temporary fix at best: what happens when you finish the book? Save your money and use the resources you already have. The most serious objection is that I dislike the "points" system and the imaginary ratings attached to them. The goal is to work and to learn, not to achieve a completely meaningless score. If you want to know how strong you are, play in tournaments, and you'll get a rating.

(Speaking of which, don't be one of those players (i.e. almost everyone) who says "my rating is x, but I'm reeeeeeeeeeeeeeally 200 points stronger." No, you're not, unless you're a sandbagger or a clearly improving player who has avoided tournaments for an extended period of time. Chess is a performance business, and your ability to score like an x + 200 player on a tactics test or your alleged possession of the "understanding" of an x + 200 player doesn't prove you're an x + 200 player when it counts, in a real life game. To paraphrase Bruce Lee, diagrams don't punch back.)

The first move is obvious: 1.c7, and now Black must start checking with 1...Rd6+. The next few moves can be easily found by a process of elimination: White can't go to the a-file because of Rc6, can't play Kb7 because of Rd7, and can't play Kc5 because of ...Rd1 followed by ...Rc1(+). So White plays 2.Kb5, Black has nothing better than checking with 2...Rd5+, and the next few moves reiterate the same ideas: 3.Kb4 Rd4+ 4.Kb3 Rd3+ 5.Kc2. Now black's rook lacks room to get under the white king, but there's another nice trick: 5...Rd4! Now 6.c8Q walks into 6...Rc4+! 7.Qxc4 stalemate, and 6.Kb3 Rd3+ is a repetition of moves. If you saw this, you did well, but it's not the last trick. White should promote, but to a rook: 6.c8R! White threatens Ra8, mating, and after the forced 6...Ra4, the double attack 7.Kb3 wins.

This solution, first published in 1895, has found plenty of followers. Here are three: two from Troitzky (of "Troitzky line" fame in the two knights vs. pawn ending) and one from Liburkin.


Troitzky 1911



Troitzky 1912



Liburkin 1931


It's White to move and win in each case. Again, when you're ready to see solutions and discussions, proceed to the next layer.

The (very well-written) review was largely positive, even enthusiastic, but the following passage has generated some controversy:

Just like Kasparov in his ‘’My Great Predecessors’-series, Morozevich, too, has worked with a co-author: IM Vladimir Barsky. What’s with these co-authors anyway? If they’re even necessary at all, then why not say (especially when one author is so much stronger than the other!) what’s by Morozevich and what’s by Barsky? But, of course, that’s not how it works. People would skip Barsky’s work and move directly to what the world’s number five has to say. More confusion is added by the fact that sometimes a text is preceded explicitly by a statement that Morozevich wrote it (’Alexander Morozevich: …‘). It seems a bit sloppy to me that the editors of New in Chess haven’t asked for more clarity from the authors on this point.

Barskij ("Barsky" on the book's cover, "Barskij" on the FIDE page) writes for Chess Today (as do I, as a book reviewer), and his fellow CTers, GMs Alex Baburin and Mikhail Golubev, have responded to the review. First, here's Baburin from Chess Today, issue 2264 (January 19):

The ChessVibes website posted a review of the recently published book "The Chigorin Defence", by GM Morozevich and IM Barskij. I think that the reviewer, Dutch chess player Arne Moll, is unfairly critical towards my friend and colleague Vladimir Barskij. If Kasparov did not need Voronkov to help him with the 'My Great Predecessors' series, he would have written it alone. And so would Morozevich – but he obviously appreciated Vladimir's contribution if he chose to work together. Apart from that the review is very interesting and well worth checking – as, I am sure, is the book itself!

I wrote Baburin, and that letter, along with his response, was published in today's (Tuesday's) issue (CT-2268). First, the relevant excerpts from my letter:

I read the Chess Vibes review a couple of days ago, and my reaction was a bit different from yours. I agree that the reviewer was too dismissive of the weaker co-author's contributions: even if Barskij isn't Morozevich, he is still a good IM, and IMs can do excellent work (as e.g. Dvoretsky, Aagaard, and Watson demonstrate in spades).

That said, I share his concern about who wrote what in such books (a concern I express in my forthcoming review of Khalifman's (or is it Khalifman & Soloviov's?) presumed works on the French), and I think many other readers will feel the same way. [DM's update: I've since learned that Khalifman is the sole author of these books.] To worry about this isn't to denigrate the lower-rated player's abilities but to address a question of honesty, of truth in advertising. Most people who buy the book will do so because it is presumably written by one of the best and most unusual players in the world, not because it is on the Chigorin. And those who do buy it because they are interested in the opening will probably evaluate the book's suggestions and its overall importance differently, depending on who they think produced the analysis.

So granting that part of the reviewer's commentary was unduly dismissive, what do you think about the particular point I've raised?

And now Baburin's reply:

First, I should correct one small mistake – Kasparov's co-author is Plisetsky, not Voronkov.

I agree with Dennis that lesser players (and, unfortunately as it may be, we are all lesser players compared to Kasparov, etc) can write excellent books. As one does not have to be a GM or IM to write a great chess review.

Secondly, I agree with Mikhail Golubev (who, like me, left comments concerning that review at the ChessVibes website) [DM: See below for both.] that authors do not have to disclose how they split their work. I recall a witty comment from famous Russian satirists Ilf and Petrov on how they did that: "While one of us is working on the book, the other one runs around different publishers, trying to sell it!" I think a complete disclosure or exact breakdown is not necessary, though sometimes the authors may stress that certain comments belong specifically to one of them. Evidently, this is what Morozevich did in that book.

Finally, I don't think that there is a problem of "truth in advertising" in this case. If, for example, Vladimir played 1.b4 a lot and then got Morozevich's to co-write a book on that opening, readers might have a problem. But Morozevich is the main expert on the Chigorin, so it is clear that he had major input into the book. If a player simply "lands" his name to publications in which he is not really involved, very soon he will lose credibility – and I bet that leading chess players are smart enough to realise that.

To complete the picture, here are some excerpts from the back and forth at the Chess Vibes site. First up, GM Golubev:

When people are working together, why should they always explain what exactly was done by whom? As there are two co-authors, it is quite clear that two persons are responsible for the work, and not just one person. Of course, one may wish to know what exactly was done by Morozevich (or to know other things about Morozevich), but he is simply not obliged to provide this information. In general the author can not be obliged to explain how exactly he worked on his product, it could be a nonsense to ask.

Next, Arne Moll's response:

Hello mr. Golubev,

thank you for your comments on our website. It’s always interesting when a strong player says something about it! WIth regard to your comment about co-authors, I can say that my criticism was mainly triggered by the fact that the name Morozevich is used to attract readers, while it is not clear if Morozevich even wrote most of the book. Thus, to be completely fair to the reader, the book should have been called “The Chigorin Defence according to Morozevich and Barsky”, don’t you agree? And also, the subtitle should have been “A world class player and an IM on the opening he made popular”. Why mention Barsky only as the co-author and not in the title? If anything, this seems unfair to mr. Barsky not by me but by the editors, in my opinion.

Don’t get me wrong: I am not saying it’s wrong for authors to write together, but I do think it’s sort of misleading of commercial editors to attract potential readers by mentioning only the most attractive author and not the other in the title. Let’s be fair, how many people would have bought the book if it would have been called ‘The Chigorin Defence according to Vladimir Barsky’? Not as much as now, I think. So, in fact I am not critisizing mr. Barsky at all, I am criticizing New in Chess editors for not being clear who was the main author and being honest about it. Now, they leave it up to the reader to guess who wrote most of it. My personal guess is that mr. Barsky did most of the analysis work and I would be glad to here otherwise. Anyway, I think he actually deserves a compliment for this, rather than being mentioned only as the co-author, don’t you agree? If he did most of the work, then why is he not mentioned in the title?

Same with Kasparov. If it turns out Plisetsky did most of the historical research and in fact did most of the writing and sorting the material, then why is the book not called “Kasparov and Plistesky on My Great Predecessors?” The reason is commercialism, and this, I think, is misleading towards the reader. But if anything, I wouldn’t call it criticism on Plisetsky, but on Kasparov or the editors of the book.

Best regards, Arne

And finally, part of GM Baburin's comment:

Dear Mr Moll,

While I find your review very interesting, I think that you are not fair to my friend IM Vladimir Barskij - or in fact to any such co-author! Nobody wants to write a bad book, so if Morozevich was happy to work with Barskij, we should trust his judgement.

Maybe Barskij prepared reference material, maybe he checked lines with computer - or perhaps he helped to better explain things to the main target audience (ie. club player). I don’t know what his role was - and neither do you. But, as long as the book is good, I don’t care.

One cannot seriously speculate that Morozevich’s name was just used to sell the book - he IS the main expert on the Chigorin.

For those readers who have persevered to the end of this monster post, what say you? Should we trust that Morozevich's integrity and desire to maintain a good reputation ensure his substantial participation in the project, to a degree sufficient to show that worries like Moll's and my own are mistaken? Or do you find the absence of clarity here unsettling, leaving open a range of possibilities from heavy Morozevich participation to contributing a few notes and a little editorial checking?

To summarize, we can find three objections to (most) negative book reviews in these quotes: (1) they are insensitive to the author, who has spent a great deal of time on his work, (2) the reviewers are generally relatively unqualified, and (3) those reviews aren't even the most effective way to "punish" unworthy books; silence works better. Let's consider each in turn. On (1): The suggestion is that it's insulting to tell the (conscientious) author who has spent a good deal of time producing a book or CD that he has essentially wasted his time; that's what a negative review does. To this, I have five responses:

(a) This seems to assume an unqualified bad review. But it might be that the work is of value to some readers, even if not the ones (or not all the ones) the author had hoped. Thus a book might be a poor effort overall, but with some value nonetheless.

(b) It's not clear that it's better to waste the time of the readers who will buy the volume than to make the author feel better about the time he spent writing it. (And when one adds up the time of all the individuals who buy the book, it will easily exceed the time invested by the author.)

(c) Not only the readers' time, but their money as well ought to be protected. The reviewer exists primarily to serve his readers, not authors or publishers.

(d) It's not a waste of time if the author can learn something from the review. The reviewer should be as conscientious as the author, not only in calling 'em as he sees 'em, but by trying to explain why the book falls short, in what areas, and how it could have been improved. If reviewers stay silent (objection (3)), how will the author learn?

(e) Reviewers can write with sensitivity: it's not necessary or beneficial to write scathing, excoriating reviews when the work reviewed was the product of a genuine effort. (I'm far less sympathetic to those who put in half-donkeyed efforts.) If the author has something of value to offer his readers, then the reviewer, as the audience's advocate, should ideally help the author to ultimately better serve that audience. On (2): The objection is that in most cases, the reviewer is less of a specialist than the writer, or to take a different example not given by Golubev, it's also true that reviewers are often weaker than the authors.

This criticism may be legitimate in some cases, but in others it's not. For instance, suppose I'm reviewing an opening book. I might spot check some sharp variations of interest with a chess engine. If it regularly turns out that the engine busts the author's analysis, isn't that relevant? Why do I need to be stronger than the author, or more of a specialist, to note that his work was sloppy? Maybe the author doesn't want to be told that he has wasted a few months on the book, but I don't think the reader will be thrilled to lose a few hundred - or a few thousand - dollars losing a big money game following bad analysis.

That's one response; here's another. It might be that the reviewer isn't ideally qualified to assess the content. Nevertheless, again, the reviewer is there to represent and advocate for the audience, not the author and publisher. And if the content is wonderful but the presentation awful, prospective readers should know this. The reviewer might be the author's inferior when it comes to producing the material, but he might have a better understanding of the audience's pedagogical needs (in terms of form, not content). This in turn helps authors, by helping them understand how to reach their audience. On (3): The objection is that silence is a better way to "punish" bad work than a negative review. In my view this might be true on occasion, but probably not most of the time. Here are some objections and considerations to take into account.

First, by responding with silence rather a review, learning opportunities are lost all around. The conscientious writer doesn't learn what's wrong with his book, the audience doesn't learn from the insightful reviewer what sorts of things he should look for in a good chess book, and in case of disagreement about the merits of the review, the reviewer doesn't get to learn anything either.

Second, just because one reviewer is silent doesn't mean everyone will be. Assuming a book is borderline-bad, or is more attractive to reviewers more inclined to think from certain perspectives and less to others, then the upshot of Golubev's policy is that a weak book will be helped, not hindered, by having only positive reviews in print!

Third, the silence of the reviewers doesn't mean the book will die of obscurity. If the book comes from a major publishing house, or gets good blurbs by the author's friends, or is the umpteenth effort by an already successful author, or is promoted by effective supply chains, etc., it will find its way into the hands of unwary readers. They will waste their time, waste their money, not improve, and then rush out to buy the next weakly written but well-marketed work by that author, thinking that maybe this next book will push them over the hump.

In sum, while Golubev's concern for the feelings of chess authors (and a concern for their livelihood as well, I'm sure) speaks well of him, I think his opposition to negative reviews is misplaced - as long as the reviewer is writing conscientiously and to inform, not to "score points". The reviewer, even when negative, is performing a useful function: protecting the potential buyer's time and money while helping teach writer and reader to know what to expect from each other.

(P.S.: I have two of Golubev's books and have seen many of his analyses on Chess Today, and I'd like to say that he has always struck me as a hard-working analyst who does consistently excellent work.)

First, to clearly set up the position he is critiquing, here, from his book, is a quotation from Richard Ivry of the University of California at Berkeley:

The study of eminent performers across many careers leads to the startling conclusion: Elite performance results from intense, demanding practice, and those who excel are more willing than their peers to engage creatively in this regimen for countless hours. It is their drive that produces talent. If young Michael Jordan's interests had been taken up with physics at a young age, I have little doubt that he would have succeeded admirably in that field. A Nobel Prize might have been the alternative to his six championship trophies. (The Ethical Brain (New York & Washington D.C.: Dana Press, 2005), p. 59.

About the view that practice is the key, which stems largely from the work of Anders Ericsson, Gazzinaga says this:

While these studies are impressive, they have a basic flaw...a confusion of correlation with causation. According to Ericsson's reports, children who practiced the piano more throughout life wound up better at it; but it might well have been the case that hte children practiced more because they were better at it in the first place--therefore they found it more reinforcing to practice. This "self-selection" of groups makes it difficult to understand these issues in a causative context. It is likely the case that innate capacities and practice work in some kind of combination. (Ibid., p. 60.)

Gazzaniga then refers to a 2000 study by Siamak Baharloo et al showing that the development of absolute or "perfect" pitch has both a developmental (training starting at an early age) and a genetic basis. He concludes:

Ivry's bold conclusion, then, seems hard to believe. While it is clear that everyone who is an expert has to practice a lot, other factors seem to me to be in play. Surely Isaac Stern, one of the foremost violinists of the past century, has something that Bob Wills, the fiddler for the country-western swing band The Texas Playboys, doesn't have. And Larry Bird, as great an athlete as he is, is no Michael Jordan. Stern and Wills and Bird and Jordan likely put in a comparable amount of practice over their careers, yet something separates Stern from Wills, and Jordan from Bird. (Ibid., p. 61.)

Some might find this depressing, but I don't. That some people have special gifts strikes me as something worth celebrating. Despite our common humanity, we aren't all fundamentally interchangeable, and that's a very good thing. And here's an application: hard, smart work will take us a long way, but we should ideally apply our labors to fields we enjoy and to which our strengths seem well-suited. That will give us the best chance of a useful, successful and happy career (and ditto for our avocational life). Chances are, we won't be Kasparov or Einstein, Andres Segovia or Carl Lewis. But who said we would be, and why is it a problem if we're not? Speaking for myself, my job is to apply the gifts I do have, not those I don't!