I certainly enjoyed reading this book on calculation (and plan to give Aagaard's book on calculation in his Grandmaster Preparation series a try), but have mixed feelings about it. First the positives and then the negatives.

On the positive side, even now in the golden age of chess books there are very few books on calculation, and Aagaard's is probably as good as any. I like Aagaard's emphasis on the importance of finding candidate moves because, as he says, the most important errors are often right at the beginning of the calculation process when a key possibility is ignored. Finding good candidate moves is, he argues, more important to success than the accuracy of long calculations. Aagaard gives some interesting suggestions about how get better at finding candidates. This part of the book is original and first rate. Otherwise, most of what Aagaard says about calculation techniques and when to calculate is not especially new. Aagaard draws extensively from the legendary trainer Dvoretsky as well as Jonathan Tisdall's discussion of the use of stepping stones in visualization in his book

*Improve Your Chess Now.*Not that this is a problem. Aagaard freely acknowledges his borrowings. His presentation of the key ideas is engagingly written, and most of his illustrative examples are excellent.
My reservations about the book have to do with the question of how to approach calculation in the age of chess engines. Much of Aagaard's analysis is engine reliant (whose isn't nowadays?), and some of the moves and variations he considers would be very difficult for all but the best players to get right the board. In fact, they are so difficult that some of Aagaard's computer aided analysis contains significant errors. One important example of this is his discussion of the 2003 game between Riazantsev and Arbakov on pages 79 to 82. Aagaard criticizes Arbakov for his 21st move and gives an alternative that he claims is better and makes black's defense easier. But the move he gives simply does not work.

(For those who want to explore this, in the above position Arbakov's move was 21..Nxd5, Aagaard's move is 21...Kg7, which does not work because of 22. Qd2, a move that Aagaard skims over, saying that it "will transpose in most lines."(page 80) Stockfish 11 at a depth of 49 gives a 3.33 pawn advantage to white after 21...Kg7; in other words, it considers it losing.) My guess is that in 2004, when Aagaard wrote the book, chess engines simply did not see the refutation of Aagaard's move that they now see in 2020. In actual fact, Arbakov played the best 21st move--that Stockfish 11 can find. This would not be all that important except for the fact that Aagard uses Arbakov's supposed error to issue a more general criticism of him. "Arbakov is not really interested in calculation" (page 81) and basically became a grandmaster because of his natural talent, Aagaard argues. He has not progressed beyond being a normal grandmaster, Aagaard suggests, because he has not put in the hard work needed to go further. Am I wrong to detect a touch of resentment here by Aagaard who had put in hard work and had not yet become a grandmaster when he wrote these lines? Similar insinuations about GM Joel Benjamin (p. 51) indicate that talented players who don't rise to their full potential are a pet peeve of Aagaard.

Putting the criticism of Arbakov aside, this example points to a larger problem with Aagaard's book. If Aagaard (a conscientious author and international master when the book was published) can't get his home analysis right with the help chess engines, how can an ordinary player hope to get it right over the board? Of course, the best players will get it right most of the time, but how do these examples help improving players (who are, after all, the audience for his book) improve? Some easier examples showing typical errors of less illustrious players playing simpler positions would be helpful for the target audience, described by the publisher as "club and tournament players." After all, as Aagaard himself, wisely says, "one of the most important aspects of training is to build confidence and motivation which is not achieved by trying to solve far to difficult exercises." (page 17) Part of the problem, I suspect, is that Aagaard did not really write this book for "club and tournament players," but rather for himself as part of his eventually successful effort to become a grandmaster. This shortcoming of Aagaard's book is symptomatic of a larger problem with chess books, which rarely give much thought to issues of pedagogy, but that is a topic for another day.

Beyond this, what is missing from Aagaard's book is serious reflection on how incredibly difficult it is to consistently calculate accurately and what this means for practical, over the board chess. The great world champion Mikhail Tal used this to his advantage by forcing his opponents to calculate and repeatedly won games in which his attacks were objectively flawed, but too difficult for his opponents to refute over the board. Other great players, (I think of Ulf Andersson) although excellent at calculation when they had to do it, preferred to avoid its risks and often won by putting positional squeezes on their opponents that did not require difficult calculations. It may seem strange to want to talk about games won without complicated calculations in a book on calculation, but it is important to know when and how to steer a game toward or away from calculation. More attention to how calculation fits into broader practical, human strategies for winning games would be useful.

Finally, Aagaard said on the Quality Chess blog that "the exercises are not that great [in this book]; I could skip them." I did not try them, so I can't say if he is correct, but I will take his word for it.

For the record, I play over the board tournaments, and my rating is currently 1887 USCF. I know it is a modest rating, but it places me in the 93rd percentile of active USCF tournament players, which should make me part of the intended audience of this book.

I don't imagine that this book would be very helpful for a player rated below about 1800 USCF. Lower rated players might find Andrew Soltis's

*The Inner Game of Chess: How to Calculate and Win*a better book for them. I read it when I was rated around 1600 and found it useful.
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