The Butterfly Effect

By Daniel Gurevich

In the 1952 short story by Ray Bradbury, “A Sound of Thunder”, the killing of a butterfly by a time-traveler during the time of dinosaurs causes the future to change in subtle but meaningful ways. The term “butterfly effect” was popularized by a meteorologist Edward Lorenz who in 1961 discovered, by using a numerical computer model, that slight changes in initial conditions could result in a completely different weather scenario. The poetical “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” became the literary expression of this unexpected and counterintuitive result. The idea that a seemingly insignificant event can have very profound consequences, which lies at the foundation of mathematical chaos theory, turned out to be remarkably general.

In chess, the butterfly effect manifests itself when an innocent-looking transposition, or a slightly different knight move, or a small difference in the king’s position completely changes the outcome of the game. One move may win, but the other, although looking very similar, may fail catastrophically. When considering two similar candidate moves, it is possible to think, “Oh, they’re both the same! I’ll just play one at random!” This kind of approach invites the butterfly effect. Therefore it is important to think about the differences, not the similarities. In which lines does the king on b1 instead c1 change the evaluations? What does this move order potentially allow? Becoming a victim of the treacherous butterfly effect is not uncommon, but thinking about the differences between two similar moves helps avoid this pitfall. Now, here are some examples of the butterfly effect from a couple of recent tournaments:

(1) Lauria,Michael (1862) – Taylor,Paul R (2034)
GA Class Championships (3), 21.11.2009

1.e4 e5 2.Nf3 Nc6 3.d4 Nxd4!? An interesting weapon against the Scotch Gambit and the Scotch Game. 4.Nxe5 The alternative is 4.Nxd4 exd4 5.Qxd4 Ne7 6.Be3 Nc6 7.Qd2, also with an advantage for White. 4…Ne6 5.Bc4 d6 6.Bb5+!? Leading to an unclear material imbalance. 6.Nf3 Nf6 7.Nc3 is also good. 6…c6 7.Nxc6 bxc6 8.Bxc6+ Bd7 9.Bxa8 Qxa8 10.Nc3 Nf6 11.f3 Be7 12.0–0 0–0 13.Be3 White should be slightly better because of the weaknesses on d6 and a7. However, if Black activates his pieces, a mating attack might result. 13…Bc6 14.Qe2 Qb7 15.Rfb1 Better was Rab1, letting the other rook go on d1 to prepare for d5. 15…Rd8 15…Rc8 is another possibility. Black will take advantage of the weak c2-pawn if White plays b4. 16.b4 d5 17.exd5 Nxd5 18.Nxd5 Rxd5 Black’s initiative could get dangerous, but White’s pawns are very mobile. 19.c4? This is an instance of the butterfly effect. 19.b5 Be8 20.c4 Re5 transposes to the text, with one critical difference. 19…Re5 20.Qf2 Now b5 is impossible! 20.b5?? Rxe3!! 21.Qxe3 (21.bxc6 Qxb1+ 22.Rxb1 Rxe2–+) 21…Bc5 22.Qxc5 Nxc5 23.bxc6 Qc7–+ Black will play g6 and win soon. 20.Qd3? Bxf3! 21.gxf3 Qxf3 22.Re1 Bg5–+ 20…Bf6 21.Rd1 h6? With only one rook, Black’s back rank is very weak, but a better move is 21…Ba4! A rook move invites …Rxe3, followed by either …Bd4 or … Bxa1. 22.b5! Must push those pawns! 22…Bxd1 23.Rxd1 Qc8! (23…Qc7 24.c5!) 24.f4 Re4 25.c5 Black is objectively winning, but there is a lot of play left in the position. 21…Qxb4! 22.Rab1 Qxc4 23.Rb8+ Nf8 Here too Black should be winning. 22.b5 Be8 22…Bxf3!? 23.gxf3 Ng5 24.Bxg5 Rxg5+ 25.Kh1 (25.Kf1?? Qc8!! 26.Rac1 Qh3+ 27.Ke1 Rg2–+) 25…Bxa1 26.Rxa1± Black is in trouble. However, White has a huge probability of blundering in this line. 22…Bxf3 might or might not be a better practical decision. 23.Rab1 Be7 24.Kh1 Stopping the threat of Rxe3. 24…a6 25.a4 axb5 26.cxb5 Kf8 26…Nc5 27.Bf4 Rh5 28.Rbc1 Nxa4 29.Rc7 Rd5 30.Rxd5 Qxd5 31.Rxe7 Bxb5 32.h3+- doesn’t help. 27.Rdc1 Rd5 28.Rc4 Bd6 29.Rbc1 Rh5 30.Rh4 Qd5 31.Rxh5 Qxh5 32.g3 Now Black cannot create an attack, while the passed pawns march on and on. 32…Ng5 33.Bc5 Bxc5 34.Rxc5 Qg6 35.Rc8 Qe6 36.Rc3 Nh3 37.Qd2 Ng5 38.Re3 Qc8 39.b6+- The rest of the game is perfunctory. 39…Bc6 40.Rc3 Bxf3+ 41.Rxf3 Nxf3 42.b7 Qb8 43.Qd5 Kg8 44.Qxf3 Qc7 45.Qe4 g6 46.Qe8+ Kg7 47.b8Q Qc1+ 48.Kg2 Qc2+ 49.Kf3 Qd3+ 50.Qe3 Qf1+ 51.Ke4 f5+ 52.Kd4 Qd1+ 53.Kc5 Qc2+ 54.Kd5 Qg2+ 55.Ke5 1–0

(2) Mundy,Jim (2041) – Piper,Alan (2084)
GA Class Championships (4), 22.11.2009

1.e4 c6 2.d4 d5 3.exd5 cxd5 4.Bd3 Nc6 5.c3 This is the Exchange Caro-Kann, once a rare continuation, now gaining popularity. In most of the lines, White wants to castle kingside and launch an attack. However, this game took a mostly positional turn. 5…Qc7 To stop Bf4. 6.h3 Also possible is Ne2 immediately: 6.Ne2 Bg4 7.f3 Bd7 8.Bf4 is one possibility. 6…g6 7.Qb3?! Ne2 is still good. 7…Nxd4 8.Qxd5 Nc6 Black could already try for more with …Bg7. 9.Nf3 Be6 10.Qb5 a6?! Weakening b6. Better is 10…Rd8 11.Qa4 Bd7?! Black loses his lead in development, while there are no good discoveries. 12.0–0 e5 12…Ne5 13.Qf4! Nxf3+ 14.Qxf3 13.Re1 Nge7 14.Qh4 Qd6 15.Bc2 h6? 15…Bg7 16.Nbd2 0–0–0 Developing makes more sense. 16.Nbd2 Bg7 17.Ne4 Qc7 18.Nf6+ Kf8 19.Nxd7+! White trades an active piece for a passive piece, but for a good reason: the bishop pair. 19…Qxd7 20.Be3 Nf5 21.Bc5+ Kg8 22.Qe4 Kh7 23.Rad1 Qe8 24.g4 White has complete domination. 24…Nfe7 25.Bd6? Now Black is back in the game. 25.g5 is much better because it stops …f5. 25…f5 26.gxf5 gxf5 27.Qh4 Qg6+ 28.Kh1 Bf6! 29.Qg3 Qxg3 30.fxg3 e4 Now Black has near equality. 31.Ng1 Rhg8? 31…h5 stopped the threat. 32.Ne2? 32.g4!+- 32…h5 33.h4?! 33.Bb3 33…Be5! 34.Kh2 Bxd6 35.Rxd6 White is the one who has to try for a draw! Black has a protected passed pawn, while White has weaknesses on g4 and f3. 35…Ne5 36.Red1 Ng4+ 37.Kg1 Ne3 38.Rd7!? This doesn’t change anything. 38…Rg7 39.R1d2 Nxc2 40.Rxc2 b5?! 40…Ng6 41.Rxg7+ Kxg7 42.Rd2 Re8 43.Rd7+ Re7 44.Rd5 Re5 is a sure draw. 41.Kf2 41…Ng8? Butterfly effect! Wrong square! 41…Ng6 42.Rxg7+ Kxg7 43.Rd2 Ne5= Black would definitely draw. 42.Rcd2 Ra7 43.Rxa7+- Black has too many weaknesses: f5, h5, a6 and b5. White can also get a passed pawn on the queenside. 43…Rxa7 44.Ke3 Rg7 45.Rd6 Rg6 46.Rxg6 Kxg6 47.Nf4+ Kh6 48.Nd5 a5 49.Nc7 b4 50.cxb4 axb4 51.Nd5 b3 52.a4 Kg6 53.a5 Kf7 54.a6 Ke6 55.a7 1–0 


(3) Piper,Alan (2086) – Wiley,Chris (1956)
Boris Kogan Memorial (2), 07.11.2009 

1.d4 d5 2.c4 e6 3.Nc3 Nf6 4.cxd5 exd5 5.Bg5 c6 6.Qc2 This is the main line of the Queen’s Gambit Declined Exchange Variation. The long name foreshadows equally long lines. The QGDEV is one of the simplest ways of getting the Karlsbad pawn structure: the e- and c- pawns exchanged. In the Karlsbad pawn structure, White tries either to play e4 eventually or push the queenside pawns, while Black tries to get an attack. Interestingly, both sides made little headway in their plans before move 30. 6…Be6 7.e3 Bd6 8.Bd3 Nbd7 9.Nge2 Qa5 10.0–0 h6 11.Bf4 Be7 Black does not want to trade pieces because he plans on attacking. 12.h3?! This move will later only speed up the attack. 12…g5 13.Bg3 Nh5?! The knight stands better on f6, preventing e4 and helping play g4. 14.Bh2 Ng7 15.Ng3 Bd6?! White can now force a few trades. 16.Nf5! Bxh2+ 17.Kxh2 Nxf5 18.Bxf5 Qc7+ 19.Kg1± Nf8 White is obviously clearly better. Black is furtherfrom his goal than ever, while White can soon play e4 and open up the position. 20.Rfc1?! White is much closer to playing e4 than  b4, a4, b5, Rab1, bxc6, etc. 20.Rfe1 makes much more sense. 20…Qd7 21.Bxe6 Nxe6 22.Qf5 Qe7 23.Qe5 f6?! Creates weaknesses with no compensation. 23…0–0! This is the best, no matter how ugly it may appear. 24.Qf5 Qf7 25.Na4 Now e4 doesn’t make much sense because Black can castle and play …Re8. Therefore, White correctly starts improving on the queenside. 25…Ng7 26.Qc2 0–0 27.Nc5 Rae8 32…f5 33.bxc6 bxc6 34.Nd3 f4 35.exf4 Re2 36.Qxc6 Qe4 White has played wonderfully up to this point. All White has to do is stop the attack and he will be winning. 37.Qc3? Too passive. 37.Rd1! Ne6 38.Rb5! g4 39.Qxd5 Qxd5 40.Rxd5 Nxf4 41.Re5! Rxe5 42.dxe5 gxh3 43.Nxf4 Rxf4 44.gxh3+- The attack is gone, but White’s extra pawns aren’t. 37…Nf5 38.Kf1 Ng3+ 39.Kg1 Nf5 40.fxg5?? Butterfly effect! White overpresses. He should have repeated the position. After Kf1, …Ne3+ is impossible because of Kxe2! 40…Ne3!–+ Game over. 41.f3 Rxg2+ 42.Kh1 Qxf3 43.Nf4 Rg3+ 44.Kh2 Qxf4 45.Kh1 Qf3+ 46.Kh2 Qg2# 0–1

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