Gordian Knot

In an ancient city called Gordium, legend has it that Alexander the Great cut the Gordian Knot which carried an Arthurian style prophecy that whosoever loosened the knot would become ruler of Asia. In today's parlance, cutting the Gordian Knot usually means thinking outside the box to solve a complex problem. Gordian Knot is also often used to refer to bureaucratic red tape.

As a training exercise, a friend who is an expert presented a position from Dvoretsky's Secrets of Chess Tactics. On page 69, Polugaevsky-Tal, 1956 Soviet Championship opens as a Tarrasch Defense and progresses toward White having the isolated queen's pawn. After White's 15th move 15.Qe2, they reached this position:

I noticed that this position shares some superficial resemblance to the Siberian Trap of the Morra Gambit, shown here after White's 8th move 8.Qe2.

The specific common elements I refer to are the placement of the four knights on c3, f3, c6, and f6, the White queen on e2, the Black queen on c7, and the White king having castled. The Siberian Trap proceeds: 9...Ng4 10.h3?? Nd4! White's f3 knight whose job it is to defend his queen from the Black knight cannot capture 11.Nxd4 or else Black plays 11...Qh2 mate! White has to play 11.hxg4 and Black captures the White Queen with 11...Nxe2+. I'd like to mention two tools in the midst of complicated variations. The knife is the title of Charles Hertan's book Forcing Chess Moves. Priority is given to moves that checkmate, then to moves that check, then moves that threaten the queen, and then progressively smaller threats. This prioritization can help cut the knot. THE move order is a little more obvious so that variations don't have all permutations of move orders. The other tool is a chainsaw in the form of a computer analysis engine. Yes, it takes much of the learning and training of working through a position away, but it also supplies gold standard and there is a large degree of truth to its analyses. After I see the truth, perhaps I can recalculate the variations in an imitation of the calculation. Still valuable, albeit less than actually working through all the variations.

Polugaevsky-Tal is extremely complicated for tactical analysis, but it starts similar to the Siberian Trap. Tal presented the Gordian Knot with his move 15...Ng4.

Let's enumerate the various things that are happening:

• For now, we'll set aside the fact that White has a 16th move, but we'll come back later.
• Black now has Queen and Knight attacking h2, protected twice by Nf3 and Kg1.
• Black's Be7 now faces White's Bg5. Black's Be7 is protected twice by Nc6 and Qc7 while White's Bg5 is protected once by Nf3 (now doing double duty).
• Black's Nc6 and Rd8 doubly attack White's Pd4, protected twice by White's Rd1 and White's Nf3 (now doing triple duty).
• Because White's Nf3 is so crucial in protecting against Qh2+, it's likely that 16...Nxd4 leads to 17.Rxd4.
• After 16...Nxd4 17.Rxd4, Black now has the additional possibility of 17...Bxf3, gaining time because of the attack on Qe2 and removing the guard from Rd4.
• After 17...Bxf3, White's unguarded Rd4 can exchange with check 18.Rxd8+. Black could recapture with 18...Rxd8 if he wants the rook attacking down the d-file, 18...Bxd8 if he is concerned his Bishop hanging at e7, or least likely 18...Qxd8 which removes the queen from the attack on h2. It turns out 18...Rxd8 is the strongest.
• After 18...Rxd8, White seems to recapture 19.Qxf3, especially since 19.gxf3 leads to 19...Qh2+ 20.Kf1 Qh1 mate.
• After 19.Qxf3, Black then has the forcing variation 19...Qh2+ 20.Kf1 Qh1+ 21.Ke2 Qxa1. A count of material shows that Black has won the exchange plus a pawn and White's king position will continue to be a liability if both sides continue trading blows. e.g. 22.Qxg4 Qxb2+ (gaining another pawn for Black) 23.Kf1 (23.Kf3 leads to 23...Bxg5 and Black will soon deliver some devastating checks.) 23...Qxc3 24.Kg1 (other moves get mated starting with 24...Qa1+ 25.Ke2 Qxa2+ 26.Ke1 Qb1+) 24...Rd4 25.Qf3 Qa1+ 26.Kh2 Bd6+ 27.g3 Qxa2 and now White is a full rook and two pawns down.
• Instead of 19.Qxf3, White can try 19.Bf4 counterattacking Black's queen. Trading ensues 19...Bxe2 20.Bxc7 Rxd4 21.Nxe2 Rd2 22.hxg4 Rxc7 and Black is ahead by the exchange and two pawns.
• Now we return to the fact that White has a 16th move choice to make. It's fairly clear that the move that loses in the Siberian Trap, 10.h3?? also loses here with 16.h3?? Nxd4 17.Rxd4 Bxf3 18.Rxd8+ Rxd8 19.Qxf3 Qh2+ 20.Kf1 Qh1+ 21.Ke2 Qxa1. The pawn at h3 does not really alter the above analysis.
• 16.Bxe6, hoping for 16...fxe6?? 17.Qxe6+ Kh8 18.Qxg4 instead runs into 16...Nxd4! 17.Rxd4 and now instead of the variation above with 17...Bxf3 helping White to check Black with 18.Bxf7+ Kxf7 19.Qxf3+, Black switches to 17...Rxd4 (overloaded Nf3 still can't move) 18.Bxg4 Rxg4 19.Bxe7 Re8 20.Bd6 Qc6 21.Qd3 Qxf3 22.Qxf3 Bxf3.
• 16.Bxe7 also runs into 16...Nxd4! 17.Rxd4 Rxd4 and even though White has Bishop and Knight for Rook and Pawn, Black's attacks on White's kingside continue, forcing White to give up another piece. e.g. 18.g3 Qc6 18.Rd1 Rxd1 19.Qxd1 Qxf3 20.Qxf3 Bxf3 or 18.Nb5 Bxf3 19.Nxc7 Bxe2. In this line, 16...Nxe7 is mentioned, but is significantly weaker than 16...Nxd4.
• Instead of allowing the dynamism of Nxd4, Bxf3, and Rxd4, White can prevent it with the disruptive pawn sac 16.d5. The variation seems to peter out to equality 16...Bxg5 17.h3 exd5 18.Nxd5 Qb8 19.hxg4 Re8.
• 16.g3 is not mentioned in Dvoretsky's book. The line features Black sacrificing the his dark-squared bishop for White's e-, f-, and g-pawns. 16...Nce5!? 17.dxe5 Bxf3 18.Qxf3 Nxe5 19.Qe2 Bxg5 20.f4 Qc5+ 21.Kg2 Bxf4 22.gxf4 Ng6 23.Qf2 Qxf2+ 24.Kxf2 Nxf4.
• Finally, we reach the game continuation: 16.Nb5. Tal gives a variation which is 20 half-moves long, implying he saw it on the board. Dvoretsky's axe to grind at this part of the book was that Tal not infrequently had holes in his analysis, especially when the variations were long.
  • Play in the game proceeded analogous to the first lines above. 16.Nb5 Nxd4 17.Rxd4 Bxf3 18.Rxd8+. Here Dvoretsky takes issue with Tal's 18...Bxd8 and suggests 18...Rxd8 19.Nxc7 Bxe2 20.Bxe7 Rd7 regaining the piece. Dvoretsky also gives the variation 18...Rxd8 19.Nxc7 Bxe2 20.Nxe6 Rd7, but White seems to get a slight edge with 21.Rc1 Ba6 22.Bxe7 Rxe7 22.Nc7.
  • 18...Bxd8 19.Nxc7 Bxe2 20.Nxe6 Bxg5 21.Nxg5 Nh6 22.Re1 g6 intending to unpin with Kg7. When White fixes his back rank, Black plays Rc2 to defend his bishop. I'm not supplying diagrams for these positions not because I'm lazy, but because I'm at least trying to follow the variations in my head.

I'm going to try to untie the knot in my brain.