Interestingly, Carlsen, who definitely does have the sporting killer instinct, shares Kramnik's view that extreme chess talent is not the proof of a generally superior intellect. True or not, it would be a wonderful battle of the brains if these two could one day play a full-scale world championship match against each other. Kramnik actually has slightly the better of head-to-head encounters with Carlsen, leading by three wins to two. 

Perhaps the most elegant was the following game from the Dortmund Tournament of 2009 — a win which ensured that Kramnik finished in first place above the ultra-competitive Norwegian. 1.d4 d5 2.c4 e6 3.Nf3 Nf6 4.Nc3 Be7 5.Bf4 (The standard move is 6.Bg5, but Kramnik prefers this more modest development) 0-0 6.e3 c5 7.dxc5 Bxc5 8.a3 Nc6 9.Qc2 Qa5 10.Rd1 Be7 11.Be2 dxc4 12.Bxc4 Nh5 13.0-0 Nxf4 14.exf4 (Kramnik's pawn structure appears compromised, but it gives rise to interesting attacking possibilities) g6 15.g3 Rd8 16.Rxd8+ Qxd8 17.Rd1 Bd7 18.f5! (A sacrifice justified by the weak black squares around Carlsen's king, but also by the variation 18...exf5 19.Qb3 hitting both b7 and f7) gxf5 19.Qd2 Qb6 20.Qh6 (Naturally Kramnik doesn't fall for 20.Qd7? Rd8 trapping White's queen) Be8 21.Ng5 Bxg5 22.Qxg5+ Kf8 23.Qh6+ Kg8 24.Qg5+ Kf8 25.Rd6! Qc7? (25...Qc5 was the best defence) 26.Qh6+ Ke7 (26...Kg8 is refuted by 27.Rxe6! fxe6 28.Bxe6+ Bf7 29.Nd5 Qe5 30.Nf6+) 27.Qh4+ Kf8 (27...Kxd6 loses the Queen to 28.Nb5+) 28.Qh6+ Ke7 29.Nb5 Qa5 30.b4 Nxb4 31.Rxe6+! (The coup de grace, requiring filigree calculation) fxe6 32.Qxe6+ Kd8 33.Qf6+ Kc8 34.Qxf5+ Kd8 (If 34...Bd7 35.Nd6+ wins the Queen) 35.Qf6+ Kc8 36.axb4 and Carlsen resigned. He would have seen that there is a forced checkmate in eight: 36...Qd8 37.Be6+ Bd7 38.Qc3+ Kb8 39.Qe5+ Kc8 40.Qc5+ Kb8 41.Bxd7 Qxd7 42.Qf8+ Qc8 43.Qd6+ and mate next move. A modern masterpiece.