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<Komodo 9.2>, PV=1, [-0.53], d=27: 18.Rhe1 Bd8 19.Qh3 Ne5 20.Qh6 Bb6 21.f5 Bxf5 22.Bxf5 gxf5(1) 23.Rxe5(2) dxe5 24.Bxb6 Qc8 25.Qf6(3) Re8 26.d6 Qd7 27.Ba5 Rab8 28.h4 Rb7 29.Bc7 e4 30.h5 Re6 31.Qxf5(4) Rb5 32.Qf4 e3 33.Re1 e2 34.Qd2 Rbe5 35.Qxb4 Rxg5 36.Qf4 h6 37.Qc4 Ree5 38.Qxa6 Re4 39.Rxe2(5)

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(1) Only here does Komodo deviate from Houdini's 22...Re8, not giving back the piece and apparently unconcerned about the opening of the g-file.

(2) So, in return, White gets 2 pieces for its rook and a passed d-pawn, remaining down only the exchange. But Black has 2 connected passed pawns of his own.

(3) If White tries 25.Rd3 to try to get its rook to the h-file, then Komodo assesses that White equalizes in spite of his material disadvantage, evaluating the resulting position at d=29 at:

(3a) [-0.27] after 25...f4 26.d6 Qd7 27.Rh3 Qf5 28.d7 Rfd8 29.Rd3 f3 30.Qf6 Qxf6 31.gxf6 f2 32.Bxf2 Rab8 33.Bc5 e4 34.Rd4 Rb7 35.b3 Rbxd7 36.Rxe4 Rd1+ 37.Kb2 R1d2 38.Rxb4 Rxh2 39.Rg4+ Kh8 40.b4 h5 41.Rg7 Rd7 42.a4 Re2 43.Rg5 Kh7 44.Rxh5+ Kg6 45.Rh4 Kxf6 46.Rh6+ Ke5 47.Rxa6 Rdd2 48.Rh6 Rxc2+

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Black has a R vs. B+P advantage and coordinated rooks, but apparently doesn't have any winning chances. Restarting the analysis from this position Komodo evaluates the resulting position at [0.00], d=29 after 49.Kb3 f5 50.a5 f4 51.a6 f3 52.a7 Ra2 53.Rh8 Reb2+ 54.Kc4 Rc2+ 55.Kb5 Rxc5+ 56.bxc5 (this position is a tablebase draw) 56...Rxa7 57.Rf8 Ra3 58.c6 Rc3 59.c7 Rxc7, and after 60.Rxf3 with only kings and rooks remaining, the position is a clear draw.

(3b) [0.00] after 25...Qc4 26.b3 Qf4+ 27.Kb2 Rfc8 28.d6 e4 29.Rh3 Qe5+ 30.c3 Qg7 31.d7 Rcb8 32.Qxg7+ Kxg7 33.Rh6 Rxb6 34.Rxb6 Rd8 35.Rd6 Kf8 36.cxb4 Ke7 37.Rf6 Rxd7 38.Kc3 Rd5 39.Rxa6 e3 40.Ra7+ Ke6 41.Ra6+ Ke7

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And a draw by repetition since White would win after 41...Ke5 42.Ra5. So 35...bxc3+ 36.Kxc3 Kf8 might have been advisable to eliminate the Pb4 after 36.cxb4, but then White would gain the advantage by eliminating White's passed pawns after 37.Rd5 f4 38.Rd4 f3 39.Rxe4 Rxd7 40.Rf4. So the draw by repetition seems to be the best that Black can achieve.

(4) White might try to keep the pressure along the a1-h8 diagonal by 31.Qd4 and threaten mate by 32.h6 but then Black can block the diagonal by a timely ...f6; e.g. 31.Qd4 e3 32.h6 f6 33.gxf6 Kf7. But Komodo at d=25 indicates that White can then get an even game ([+0.35]) after 34.Qh4 e2 35.Qh5+ Kxf6 36.Bd8+ Qxd8 3.Qh4+ Kf7 38.Qxd8 exd1=Q+ 39.Kxd1. But Komodo also indicates that Black can retain a small advantage ([-0.61]) by a better placement of its rooks before advancing the e-pawn by 31.Qd4 Rb5 32.Qa7 Re8 33.Qe3 f4 34.Qxf4 e3 35.Qd4 Rxg5 36.Qxb4 e2 37.Re1 Rxh5.

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<Stockfish 7>, PV=1 [-0.79], d=36: 18.Rhe1 Bd8 19.Qh3 Ne5 20.Qh6 Bb6 21.f5 Bxf5 22.Bxf5 Re8 23.Bxe5 Rxe5 24.Rxe5 dxe5 25.Be4(1) Be3+ 26.Kb1 Qb5 27.Qh3 Bxg5 28.Qg2 Bf4 29.h4 Rd8 30.h5(2) Kg7 31.hxg6 hxg6 32.Rh1 Rh8 33.Rd1 a5 34.d6 Rd8 35.Qh1 a4 36.Bc6 Qc5 37.d7 a3 38.Qd5(3) Qxd5 39.Rxd5 f5 40.c3(4) bxc3 41.bxa3 g5 42.Kc2 Kf6 43.Kxc3 g4(5)

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(1) Only here does Stockfish deviate from Houdini's 25.Bh3.

(2) White does not have sufficient material to force its way through on the k-side, and Black can initiate a pawn storm of its own.

(3) Seems like a mistake to me, the queenless ending seems hopeless for White. But there's no horizon effect at work, restarting the analysis after 37...a3 Stockfish at d=33 still considers 38.Qd5 to be White's best move, evaluating it at [-1.43] when compared to 38.Qf3 ([-1.50]) and 38.Ba4 ([-1.57]).

(4) I would think that White does better with 40.bxa3 bxa3 since then Black's a-pawn looks week and White's c-pawn can advance at will. At d=35, Stockfish evaluates the resulting position after 40.bxa3 bxa3 and either 41.c3 or 41.Bb5 at [-2.22] or 41.c4 at [-2.2.1] which is not as good as its initial evaluation. But it turns out to be better than its evaluation of the resulting position after 43...g4 (see below).

(5) Restarting the analysis from this position Stockfish evaluates the resulting position at [-3.24], (winning), d=35 after 44.Kd3 e4+ 45.Ke2 g3 46.Kf1 Bc7 47.Rc5 Bd6 48.Rb5 Rh8 49.Kg1 Be7 50.Rd5 Bd8 51.Rb5 Ke6 52.a4 Rh2 53.Rb3 Rc2 54.Ba8 Kxd7 55.Rxg3 e3 56.Bf3 e2 57.Bxe2 Rxe2 58.Rd3+ Ke7 59.Ra3 Ba5 60.Kf1 Rh2 61.Kg1 Rc2 62.Rb3 Kf6 63.a3 Rc4 64.Kf2 Rxa4 65.Kf3 Rc4 66.Ke2 Rc3 67.Rb8 Rxa3 68.Rc8 Ke5 69.Rc5+ Ke4 70.Rc4+ Kd5 71.Rf4 Ke5

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And this position is clearly won for Black so Stockfish's initial evaluation of 17...g6 seems pessimistic. But again, this was just one line and there are many opportunities for deviation by both sides.

This used to be true many years ago, but engines have advanced a lot. An engine's evaluation is usually a linear combination of all the factors in their evaluation function multiplied by their weights. So it is quite possible that the weighted sum of all the non-material factors exceeds the weighted sum of the material factors. And, of course, each engine has a different evaluation function so it is possible, even likely, that one engine evaluates the material factors higher than the non-material factors and another engine does the reverse.

I've seen computers make positional sacrifices where the end result could not be evaluated within the search depths achievable by current technology; see for example Aylerkupp / Rybka vs Kutztown46 / Stockfish, 2011 and the discussion about Stockfish's 11...c5 (Aylerkupp / Rybka vs Kutztown46 / Stockfish, 2011 (kibitz #49)).

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<Houdini 4>, PV=2, [0.00], d=29: 18.gxf6(1) Bxf6 19.Qe4 g6(2) 20.Rhg1 Rf7 21.Qe8+ Nf8 22.Bxg6(3) hxg6 23.Rxg6+ Bg7 24.Rdg1 Bg4(4) 25.Qxb8(5) Rxb8 26.R6xg4 Rbb7 27.R1g3(6) Nh7 28.Rg6(7) Rbd7 29.a3 bxa3 30.Rxa3(8) Rxf4 31.Bxg7 Rxg7 32.Rxd6 Rf1+ 33.Kd2 Rg2+ 34.Kc3 Nf6 35.Kb3 Ne4 36.Rc6 Rd2 37.c4 Rff2 38.Kb4 Rxb2+ 39.Ka5 Rb8 40.h4 Rc2 41.Ra4 Nd2 42.Rc7 Ne4 43.Kxa6 Ra8+ 44.Ra7(9)

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(1) Houdini immediately deviates from Tal's 18.Rde1. And that makes sense, if White's objective is a k-side attack it will be necessary to open files, and this is the quickest way to do that; there will be time for Rd1-Rd1 (or Rh1-Re1) later. The downside is that Black's DSB immediately takes up a good post, challenging White's DSB.

(2) So ...g6 was necessary after all!

(3) And White sacks a second piece for 2 pawns. No one can't accuse Houdini of not playing like Tal. It seems that almost all of Black's k-side pieces are pinned.

(4) The only move. According to Houdini other attempts to defend the 7th rank and the Bg7, 24...Ra7 and 24...Qb7, lose.

(5) White could now force a draw by 25.R1xg4 Qxe8 (attempts defend the 7th rank and the Bg7 by 25...Qa7 or 25...Qb7 fail even quicker than in the previous move after 26.Qxa8 Qxa8 29.Rxg7+) 26.Rxg7+ Rxg7 27.Rxg7+ Kh8 28.Re7+ Kg8 29.Rg7+ Kh8. But that's clearly not what White has in mind.

(6) The immediate smoke has cleared and White has 3 pawns for his piece, the initiative, and with the draw in hand since if Black tries to get out of the pin of the Be7 by ...Kh8 or ...Kh7, Rg4-h4 forces ...Kg8 and a draw by repetition.

(7) White can now force a 3P vs. N endgame by 28.Rxg7+ Rxg7 29.Rxg7+ Rxg7 30.Bxg7 Kxg7 and the following position:

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Is this a win for White? Apparently not, starting the analysis from this position Houdini (with 5-piece Gaviota tablebase support) evaluates the resulting position at [0.00], d=27 after either 31.Kd2 or 31.h4.

(8) Maybe White could take advantage of Black's tied up pieces by 30.bxa3 followed by placing his king in a more active position before simplifying to the 3P vs. N endgame. But Houdini does not think so, evaluating the position at d=28 at either [-0.19] after 31...Kf8 (getting the bishop out of the pin) or [0.00] after 31...Nf8 32.R6g4 Nh7 33.Rg6 and the draw by repetition.

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So I was surprised to find out after restarting the analysis from this position that Houdini evaluates the resulting position at d=30 as [-3.56], winning for Black, after 44...Rb8 45.Rc7 Rcb2 46.Ka7 Nd6 47.Ra6(10) Nc8+ 48.Rxc8+ Rxc8 49.Rc6 Rd8 50.h5 Rd7+ 51.Ka6 Kf7 52.h6 Rb1(11) 53.h7 Rh1 54.h8R Rxh8(12) 55.Kb5 Rh2 56.Rc5 Ke7 57.Rc8 Rh7 58.Kc5 Rh4 59.Kb6 Rh6+ 60.Kb5 Rb7+ 61.Kc5 Ra7 62.Kd4 Rh4+ 63.Ke5 Ra6 64.Rg8 Rxc4 65.Rh8 Ra5 66.Rh7+ Kd8 67.Kd6 Ra6+ 68.Ke5 Rc5 69.Rh8+ Kd7 70.Rh7+ Ke8 71.Rh8+ Ke7 72.Rh7+ Kd8 73.Rh8+.

(10) Hard to believe, given the loss of the exchange that follows, that this is White's best move. But White has no real options since after, say, 47.c5 Nc8+ 48.Ka6, then 48...R2b6+ 49.Ka5 Ra8#. So after 47...Nc8+, 48.Rxc8+ is forced. And, with only 3 pawns for the rook, White is lost.

(11) Rather than 52...Rh2 immediately, Houdini as Black apparently likes to either create drama or rub White's nose in it by allowing 53.h7. And, as White, gives as good as it can by underpromoting to a rook at 54.h8R.

(12) And, according to the Lomonosov tablebases, Black mates in 31 from this position. So clearly White should have taken the draw by 25.R1xg4 but, because of the horizon effect, Houdini could not search deep enough to determine the results of the position after 44.Ra7. I suspect that by some forward sliding that better moves for White could have been found to avoid the position that White found itself in at that point.

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<Komodo 9.2>, PV=2, [0.00], d=27: 18.gxf6(1) Bxf6 19.Qe4 g6 20.Rdg1(2) Rf7 21.Qe8+ Nf8 22.Bxg6 hxg6 23.Rxg6+ Bg7 24.Rhg1 Bg4 25.Qxb8 Rxb8 26.R6xg4 Rbb7 27.Kd2(3) Nh7 28.Rg6 Kf8 29.Bxg7+ Rxg7 30.Kd3 Rgf7 31.Rxd6 Rxf4(4) 32.Rgg6 Rbf7 33.Rd8+ Ke7 34.Ra8 Nf6 35.Ra7+ Ke8 36.Ra8+ Ke7(5)

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(1) Komodo, like Houdini, prefers opening up the g-file immediately instead of Tal's 18.Rde1.

(2) Here Komodo prefers "the other rook" compared to Houdini's 20.Rhg1. Which looks kind of strange, locking in the other rook on h1. But it really doesn't matter since the next 13 moves, through 26...Rbb7 are essentially the same (other than moving the other rook to g1), and the same position is reached as in the Houdini analysis after 24.Rhg1.

(3) And here Komodo, recognizing like I did :-) that Black's pieces are completely tied up, decides to improve the position of its king before proceeding.

(4) I think that Komodo played the position after 17...f5 better than Houdini. It still has 3 pawns for its knight but its king and both its rooks are more actively placed than Houdini's, it has a passed d-pawn, and Black's q-side pawns look somewhat weak.

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Enough to make a difference in the outcome?

(5) Apparently not. Restarting the analysis from this position, at d=22 Komodo does not find anything better than the draw by repetition by 37.Ra7+ Ke8 38.Ra8+ etc., and evaluates that it also has nothing better than the same draw by repetition after 37.Rxa6 Nxd5 38.Ra7+ Ke8 39.Ra8+ etc.

So, does White have anything better before Black recentralizes its knight? Restarting the analysis after 31...Rxf4 Komodo at d=20 evaluates the resulting position the same, [0.00] (draw by repetition) after 32.Rgg6 Rbf7 33.Rd8+ Ke7 34.Ra8 Nf6 35.Ra7+ Ke8 36.Ra8+ Kd7 37.Ra7+ Ke8 etc. And capturing the a-pawn immediately doesn't help,, Komodo evaluates the resulting position as effectively even, [-0.26], d=24, after 32...Nf6 33.d6 Kf7 34.Re1 Ne8 35.c4 bxc3 36.Kxc3(6) Rd7 37.Rd1 Rf6 38.b4 Nxd6 39.Kb3 Rf3+ 40.Ka4 Ke7 41.Re1+ Kd8 42.h4 Rh3 43.Rd1 Ke7 44.Re1+ Kf6 45.Rf1+ Ke5 46.Ra5+ Ke4 47.h5

(6) Komodo evaluates that it's better for White to have connected a- and b-pawns than c- and d- pawns, even though the former are less advanced. If instead 36.bxc3, Komodo evaluates the resulting position effectively the same at [-0.26], d=26, after 36...Rd7 37.Re7+ Rxe7 38.dxe7 Kxe7 39.a4 Nf6 40.a5 Nd5 41.Ra8 Nc7 42.Rg8 Rf5 43.h4 Rxa5 44.h5 Kf7 45.Rc8 Ne6 46.c4 Rxh5 47.c5 Kf6 (47...Rxc5 48.Rxc5 Nxc5 is clearly a draw, and 47...Nxc5 is no better for Black) 48.Ke4 Re5+ 49.Kd3 Rd5+ 50.Ke3 Rf5 51.Ke4 Rf2 52.Kd5 Rd2+ 53.Kc6 Rc2. It seems that once Black activates its knight the position is even, although White might be up a pawn.

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<Stockfish 7>, PV=2, [+0.10], d=36: 18.gxf6(1) Nxf6(2) 19.Rhg1 Rf7 20.Rde1 Qb7 21.Bxf6(3) Rxf6(4) 22.Qe4 g6 23.Qxe7 Qxe7 24.Rxe7 Rxf4(5) 25.Rf1 Rxf1+ 26.Bxf1 Bf5 27.Bc4 a5 28.Kd2 Bg4 29.Be2 Bh3(6) 30.Bd3 Rf8 31.Ra7 Rf2+ 32.Ke3 Rxh2 33.Ra6 Kf7 34.Rxd6 Ke7 35.Ra6 Bf5 36.Rxa5 Kd6 37.Bxf5 gxf5(7) 38.c4 bxc3 39.bxc3 Rh3+ 40.Kf4 Rxc3 41.Kxf5 (8) Rc2 42.Kg5 Rg2+ 43.Kf5 Rf2+ 44.Ke4

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(1) Stockfish, like Houdini, prefers opening up the g-file immediately instead of Tal's 18.Rde1.

(2) Stockfish immediately deviates from both Houdini and Komodo by recapturing with 18...Nxf6 instead of 18...Bxf6. This does not seem wise since it foregoes the exchange of White's DSB (unless White cooperates) but it opens up the diagonal of Black's LSB.

(3) This "cooperation" by White seems necessary since Black was threatening to gain the initiative by pressuring White's Pd5 and increasing the pressure by ...Bd7-b5, striking at one of its defenders and, if Bd3-e4, increasing the pressure by ...Bc4. But now Black's DSB has a fine uncontested diagonal, and g7 is amply protected.

Alternatives? Restarting the analysis from the position after 20...Qb7 Stockfish still considers 21.Bxf6 as White's best move, evaluating it at [+0.20], d=30 following the analysis continuation for several moves. It evaluated its other top 3 moves, 21.Qg2 and 21.Qg3, at [0.00] and [-0.26] respectively, even though they leave the Pd5 hanging. But Black does not capture it in either continuation; Stockfish must see something that I don't see. Without reviewing the lines, I'll go with Stockfish.

(4) And yet Stockfish recaptures with the rook and not the bishop, removing 2 defenders from g7 and denying the DSB the fine a1-h8 diagonal! Now I see (with Stockfish's "help") that 21...Bxf6 loses to 22.Re8+ Rf8 23.Bxh7+ Kxh7 (23...Kf7 24.Qh5+ g6 25.Qxg6#) 24.Rxf8 and Black loses a rook with mate after 25.Qh5 seemingly inevitable. In fact, at d=29 Stockfish claims a mate in 22 following several horizon effect-driven sacrifices to delay the inevitable. It shows that, while general plans and ideas are useful, they are useless without precise calculation.

(5) After a series of forced moves White has recovered the piece and has an apparently better position with a rook on the 7th rank.

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But, restarting the analysis from this position, Stockfish does not consider that White has much of an advantage, evaluating the resulting positions at [+0.12], [+0.11], and [+0.10] at d=33 following 25.b3, 25.Re8+, and 25.Rc7 respectively. Note that the analysis continuation, 25.Rf1 is now not one of Stockfish's top 3 moves, indicating the benefits of forward sliding.

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(6) White was unwise to try to exchange bishops and Black was equally unwise to decline since after 29...Bxe2 30.Kxe2 Stockfish reassess the position to Black's advantage, [-0.32], d=33 after 30...Rc8 31.Kd3 Rc5 32.a4 Rxd5+ 33.Kc4 Rh5 34.Ra7 h6 35.Kb3 Rh3+ 36.Ka2 Rxh2 37.Rxa5 g5 38.Rd5 Rxc2 39.Kb3 Rc8 40.a5 Kf7 41.Kxb4 Ke6 42.Rd1 g4 43.Rh1 Rg8 44.Rxh6+ Kd5 45.a6 Kc6 46.a7 Kb7 47.Rxd6 g3 48.Rd7+ Ka8 49.Rd1 Kxa7 50.Rg1 Kb6 51.Rg2 Kc6. But, aren't all rook endings drawn?

(7) Now White is a pawn up with the better pawn structure. Shouldn't that be a substantial advantage?

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Perhaps, but restarting the analysis from this position Stockfish evaluates the resulting position at [0.00] after each of its top 3 moves, 38.c4 (the initial analysis continuation), 38.Ra4, and 38.Rb5. So, yes, all rook endings are drawn.

(8) And this makes it official; this position is a draw per the Lomonosov tablebases. So Stockfish's initial evaluation was reasonable.

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So it looks like these 3 engines agree that Larsen's 17...f5 was just as reasonable as 17...g6, and Larsen's mistake(s) came later. It doesn't seem like the immediate opening of the g-file gives White significant attacking chances since it leads to several piece exchanges. It may be that Tal sensed this (he couldn't have calculated the consequences) and so played 18.Rde1 rather than 18.gxf6. And of course, the finishing salvo 37.Qf7 was a delight. I wonder at what point in the game he saw this possibility?

It's already been pointed out, but this view is now many years out of date. The old days of goading the computer into taking (dangerous) material so that you can mate it are long gone. The top engines very much take positional factors into account. On top of that, it seems like the application of machine learning algorithms (like the ones used for AlphaGo) will put machines onto another level. They're already practically unbeatable for humans anyway, but the combination of current engine algorithms, machine learning, and endgame tablebases is going to put computer chess way beyond human reach.

<According to stockfish your line runs into problems after h5 instead of f5. Like so... 18. Rde1 Bd8 19. h4 Nc5 20. Bxc5 dxc5 21. h5 Qd6 22. Re5 f6 23. hxg6 fxe5. Stockfish gives white +0.43 in this position. A slight advantage that will only get larger.>

Not sure about a number of moves in this line (21.f5 and 22.Bxf5 look distinctly suboptimal) but 22….Re8 is simply absurd. 22....Bxd4 is crushing.

<23.Lxe5 Txe5 24.Txe5 dxe5 25.Le4 Le3+ 26.Kb1 Db5. Analysed with Stockfish 7.>

18 ... Bd8 ?

E.g. 19 Qh3 Nc5
20 Bxg7 Nxd3+
21 cxd3 Qc7+

I've just done this calculation in my head and have no computer program analysis, so would be interested to see what your programs might come up with.>