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Chess to Enjoy / Entertainment


You’ve Got My Number


You don’t have to be good at math to play good chess. But if you listen to players these days, you’d think we’ve all gone numbers


mad. By GM ANDY SOLTIS


A MAGNUS CARLSEN FAN, WATCHING one of his games live, in online coverage, will tweet: “MC outrates his opponent by 140 points. He’s got a 69 percent chance of winning!” Another couch-kibitzer will reply: “But he’s


Black. My database shows White wins 58 pct. in this opening.” A third fan chimes in: “Yeah, but Stockfish at depth 30 says this position is -0.48.” Debates like this are increasingly fueled by


the masses of data we have access to. But it also seems that chess doesn’t quite add up. The math of our game isn’t linear. It does


not neatly correspond to sequential jumps, like a number series.


DEAD DRAW


GM Fabiano Caruana GM Grzegorz Gajewski


Italian Team Championship, 2014


Then it becomes a fairly easy win. Okay, that makes some sense. A +2.00 posi -


tion, in the endgame, middlegame or opening, is supposed to be a win. But what happens if instead of one more extra pawn, we add two, on both h3 and f3? Of course, it’s even easier to win then. Yet


it is only slightly easier than when we added one pawn to the diagram. Sure, the computer’s numbers will rate the


three-pawn position as more won than the two- pawn position. But that doesn’t translate into “winnability” when you actually play it. Add a fourth white pawn and the numbers


go up again—but again it is only slightly easier to win than the three-pawn position. This is what could be called the Law of Disproportional Technique: The amount of extra material you have is not


directly related to the degree of difficulty in winning your position. It’s a variation on the law we all learned about diminishing returns.


DIMINISHING RETURNS GM Kateryna Lahno GM Humpy Koneru Kazan, 2012


In fact, White didn’t resign until 40 difficult


moves later. Analysis showed that Black couldn’t have shortened the game by much. There’s been some academic research that


suggests that a position with a +4.00 edge for White, the equivalent of four extra pawns, is won 85 percent of the time. After that, the winnability increases marginally: the difference between +5.00, the rough equivalent of an extra rook, and +10.00, an extra queen, is surprisingly minor. If you play chess long enough, you’re bound


to learn a lot about the game’s fuzzy math. Another example is the “two bishops.” If you and your opponent exchanged minor


pieces so that you have two bishops and he has a bishop and a knight, you probably have an advantage. But if you then trade bishops, your edge will


shrivel. It might disappear entirely. Why? Because two bishops are more than twice as strong as one.


WHITE IS BETTER GM Anish Giri GM David Howell Wijk aan Zee, 2010


AFTER 68. Kg3


Computers give White a solid edge. But any experienced player knows this is a dead draw. The defending king is in front of the pawn


and can stop it or the white king from advancing far. (Engines got it right after the game went 68. ... Kg5 69. Rb5+ Kg6 70. g5 Rg1+ 71. Kf2 Rxg5 72. Rxg5+ Kxg5, Draw agreed. With only kings left, they gave the only evaluation possible, 0.00.) Now suppose we improve White’s position. Let’s give him another pawn, say on h3 or f3.


16 March 2016 | Chess Life


AFTER 42. ... Rxe4 Computers spit out evaluations like -3.50 to


-2.50. That should make it a no-think win for a grandmaster.


AFTER 23. ... Ke8 If we remove Black’s knight and White’s c4-


bishop from the board, both sides have one minor piece, a dark-squared bishop. White has no compensation for being a pawn down.


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