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Chess to Enjoy / Entertainment 2015 World Cup


No 2015 tournament had more elite grandmasters in it than the World Cup in Baku, Azerbaijan. Nine of the 128 invitees—including three of the five highest rated players— were Americans. But in the end the $120,000 top prize was won by Sergey Karjakin after a dramatic come-from-behind playoff against Peter Svidler. This month’s quiz features six positions from Baku. You are asked to find the fastest winning line of play. This will usually mean the forced win of a decisive amount of material, such as a rook or minor pieces. For solutions see page 71.


Problem I WGM Deysi Estela Cori Tello GM Vladimir Kramnik


Problem II GM Shakhriyar Mamedyarov GM Pouya Idani


Problem III


GM Vasif Durarbayli GM Le Quang Liem


BLACK TO PLAY


Problem IV GM Wei Yi GM Ding Liren


WHITE TO PLAY


Problem V GM Ding Liren GM Ernesto Inarkiev


BLACK TO PLAY Problem VI


GM Lazaro Bruzon GM Santosh Vidit


WHITE TO PLAY If we take the bishops on c4 and g7 off the


board, it’s bishop-versus-knight. White is at least equal. But in the diagram, thanks to his two bishops


White is much better. He can win by applying pressure with 24. Rd6 (24. ... Bxc3 25. Re6+ Kf8 26. Bh6+ Bg7 27. Rf6+!). Instead, he used the bishops to trap a rook


with 24. Be6, e.g. 24. ... Rc6 25. Bd5 or 24. ... Rd8 25. Rxd8+ Kxd8 26. Bd5. The game went 24. ... Nc6 25. Ra6! Ne7


26. Bd7+ Kf8 27. Bxc8 Rxc8 28. Rxa7 Bxc3 29. Bg5 Nc6 30. Rxh7 Be5 31. Rdd7! c4 32. Bf4 Bb2. Now consider the case of a rook on the


seventh rank. You know that it’s usually valuable in an endgame. It’s often worth a pawn. What about doubled rooks on the seventh?


They tend to be much better than just one rook. In fact, they are usually more than twice as valuable. That follows a basic—and non-linear—


principle of attack: When pieces coordinate, their strength is much greater than the sum of their parts. Here, however, this doesn’t apply. The fastest


way to win was to trade a pair of rooks, 33. Rc7!, because that eliminates any Black counter - play. Black resigned after 33. ... Nd4+ 34. Kd2 Rxc7 35. Rxc7 c3+ 36. Kd3 Ne6 37. Bd6+ Kg8 38. Rc8+ Kf7 39. Be5 Ba3 40. Kxc3.


WHITE TO PLAY You may have noticed the non-linear nature


of chess in a personal way. Your rating didn’t rise in a gradual, sequential way. Instead, you saw spurts and plateaus. Masters have tried to apply math to chess for


decades and their results have been, well, fuzzy. For example, Mikhail Tal proposed a formula


to gauge whether a mating attack will succeed: The “assault ratio” is determined by adding up the total attacking power of your pieces near the enemy king and comparing it with the total power of the defenders. But “near the enemy king” must be stretched quite a bit for the formula to work.


PETROFF DEFENSE (C43) GM Sergei Dolmatov GM Shakhriyar Mamedyarov Moscow, 2002


1. e4 e5 2. Nf3 Nf6 3. d4 Nxe4 4. Bd3 d5 5. Nxe5 Nd7 6. Nc3 Nxc3 7. bxc3 Nxe5 8. dxe5 Be7 9. Qh5 Be6


White has many options but two moves


stand out. One is 10. f4 with the idea of 11. f5!, seizing space and securing an advantage. The other is attacking the only thing Black has left unprotected, 10. Rb1. White rejected the rook move and drew after


10. f4 g6! 11. Qf3 f5. He explained that he calculated 10. Rb1 Qd7 (threat of 11. ... Bg4) and then 11. h3 0-0-0 and saw no significant edge.


WHITE TO PLAY But can he attack the queenside? Tal’s formula


suggests White’s lone queen rook, the only piece remotely close to the Black king, cannot be considered an attacking force. In fact, White can win immediately with 12.


Bb5! because of 12. ... c6 13. Ba6! bxa6 14. Qe2. Computer scientists ran into the non-linear


problems with chess in the 1980s. By then they had concluded that for each additional ply— that is, a move by one player—that a machine could search, its strength rose by roughly 200 rating points. If a program could see one full move further


ahead than it used to, it had gained an extra 400 points in strength. Thanks to a linear ground rule called Moore’s


Law (Simplified, that processing power for com - puters will double every two years. ~ed.), it was safe to bet that engines would be playing 4000- level chess by the early 21st century. But it didn’t happen. Top programs like


Stockfish, Houdini and Komodo have ratings in the 3200-plus range. But considering that they can crank out 16-ply analysis in seconds, they should be a lot stronger. In fact, Ken Regan, the international master


and computer chess authority, suggests on his always-interesting website that the absolute limit for chess, the highest rating that a computer can achieve, may be about 3600. Even perfect chess may have a linear limit.


www.uschess.org 17


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