Depth, Width, and Tenacity: Lessons in Calculation
Rhys Goldstein, March 2013
Omar Shah recently gave an excellent lecture to Toronto’s Annex Chess Club in which he identifiedvisualization as “the most important skill for a club player”. Visualization is one’s ability to correctly foresee what the board will look like after a sequence of moves. Effective calculationrequires one to not only visualize a sequence of moves, but also choose which sequencesto visualize.
Strong players know when to calculate with greater depth, seeinglonger sequences of moves. They know when to focus on width, seeingmore alternative sequences. And they know when to play with tenacity, calculatingevery move instead of a few key moves. This game I lost to the defending club champion illustrates the importance of these three aspects of calculation.
White: Rhys Goldstein (2022)
Black:Michael Humphreys (2281)
Annex Chess Club Championship, Toronto, 2013
1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Nf3 b6 5.Qb3 c5 6.Bg5 Bb7 7.O-O-O
After the game, David Southam described the opening line I adopted as “hyper-aggressive” yet “fun”. Now that the pin is broken, I am thinking about maneuvering the c3 knight to b5 and then d6. Black puts a quick end to that possibility.
7…Bxc3 8.bxc3
After 8.Qxc3 Ne4 9.Bxd8 Nxc3 10.bxc3 Kxd8 11.d5, Whitewould headto the endgame with a space advantage but a worse bishop and pawn structure.
8…cxd4 9.Nxd4
Evidently I was determined to land a knight ond6. Black prevents this temporarily by covering b5.
8…a6 10.f3 Qc7 11.e3 d6
Position after 11…d6 (White to move)
12.Bf4!?
I thought fora half-hour or more before offering this piece sacrifice. Slower play allows Black to castle and consolidate with …Nbd7 followed by …Nc5 or …Ne5. Black would then have a much better position due to White’s queenside pawn islands and vulnerable king.
12…e5
Playing to win, Black accepts the sacrifice and allows White to finally get a knight on d6. The alternative, 12…O-O 13.Nxe6 fxe6 14.Bxd6, followed by 15.Bxf8, appears roughly equal.
13.Nf5 exf4 14.Nxd6+ Kf8 15.c5?
This mistake provides our first lesson in calculation. The lesson is that one should calculate forced lines a little deeper, simply because one can. The most forcing move would have been 15.Nxb7!asBlack must recapture with 15…Qxb7. Then 16.Rd8+ forces 16…Ne8 if Black is to save the rook on h8. Next we have 17.Qb4+ forcing 17…Qe7 since the knight may not be abandoned. I saw this line when I played 12.Bf4, but rejected it because White must submit to an exchange of queens. I reconsidered the line at move 15, but rejected it again for the same reason. Myassumption was that a queen trade would end my attack and leave Black a piece up, so I chose not to look any deeper.
Suppose that I had looked deeper. Again, the forced moves are 15.Nxb7 Qxb7 16.Rd8+ Ne8 17.Qb4+ Qe7. The only logical follow-up for White is 18.Bd3 to get the remaining pieces into the game. It turns out that this move threatens Be4, hitting the Black rook on a8 that defends the pinned knight on b8. Strangely, Black has no response that maintains a clear material advantage. For example, after 18…Qxb4 19.cxb4 Ke7, White keeps both Black knightspinned with 20.Rc8. Note that 20…Kd7 would be met with 21.Bf5+, saving the rook on c8 and gaining a tempo to develop the rook on h1. If instead 20...fxe4, then after 21.Be4Ra7 22.Rxb8, material is equal and White has a small advantage.
After 15.Nxb7 Qxb7 16.Rd8+ Ne8 17.Qb4+ Qe7 18.Bd3, Black’s best line is likely18…a5 (keeping White’s pawns doubled) 19.Qxe7+ Kxe7 20.Rc8 g6 (preventing Bf5) 21.Be4 Kd7 22.Bb7 Ra7 23.Rd1+ Nd6 (preventing Rxb8) 24.Rxh8 Rxb7. Material is then equal and Black has only a tiny advantage.
Even without calculating all of these variations, I may well have appreciated the power of 18.Bd3 had I bothered to consider it. It is true that the line involves a queen trade, which seems unfavorable for White. But since the line is forced, I should have looked a little deeper.
The move I actually played, 15.c5, threatens cxb6as well as the developing move Bc4. Unfortunately for White, these threats are easily parried.
15…b5
Position after 16…b5 (White to move)
16.Bxb5?
Clearly this is desperation, but what else was there? I might have played 16.exf4, but this gives Black time to play 16…Nc6 while doing nothing to develop White’s kingside pieces. I preferred to move the bishop immediately, but where? We can reject 16.Bd3 on account of 16…Bd5,hitting White’s queen and threatening 17…Qxc5. The alternative 16.Be2 allows the rook on h1 to occupy the e-file, but at the same time it blocks this file. I also considered 16.c4 to clear space for the bishop on the queenside, but dismissed this move because it blocks White’s queen. Black would respond with 16…Nbd7, hitting c5 without fear of mate on f7.
I played 16.Bxb5 after rejectingevery alternative. However, my list of ideas had become a little too narrow. This mistake serves as our second lesson in calculation: to recognize situations where one must look not necessarily deeper, but wider.
The best move for White would have been the useful waiting move 16.exf4. If Black responds with 16…Nc6, which I had expected and feared, then …Nbd7 is no longer an option so White is free to play 17.c4. After these moves, one possible continuation is 17…Na5 18.Qb4 Bc6 19.cxb5 axb5 20.Bxb5 Rb8 21.Rhe1. Perhaps Black should still win after this sequence of moves. But at least all of White’s pieces are developed, and material is in fact equal in terms of point value.
It was correct on my part to dismiss c4 on move 16. However, I should not have dismissed this pawn advance in all lines, as it becomes a viable option after …Nc6. Had I included this idea in my calculations,I would have had a considerably better chance of drawing the game.
16...axb5 17.Nxb5 Qa5 18.Nd6
Position after 18.Nd6 (Black to move)
It is time for the third lesson in calculation. The lesson is to be tenacious; calculate every move when necessary. The importance of tenacity is illustrated in the way Black pursues the winover the next several moves.
Black’s first step is dealing with the threat of Qf7#.
18…Bd5!
Black gives up a knight and bishop for a rook, leaving all of his remaining pieces on the rim of the board. Even more surprising, he passes up the option of forcing a queen trade, which would have eliminated threats of mate or perpetual check. It is true that exchanging queens with 18…Qa3+ would cost Black the bishop on b7, but White has already sacrificed two bishops. Should Black not return a piece in order to bring about a safe endgame?
With 18…Bd5, Black is being tenacious. He is willing to calculate a line that is tactically winning rather than playing safe but inferior moves.
Inferior would have been 18…Qa3+, for example, as after 19.Qxa3 Rxa3 20.Nxb7 Rxc3+21.Kb2 Rxe3 22.Rd8+ Re8 23.Rhd1, Black has the arduous task of subduing White’s passed pawns while creating and promoting his own.
Interestingly, an attempt to simplify the position with 18…Qxa2would only complicate matters for Black. Suppose play continues19.Qxa2 Rxa2 20.Nxb7fxe3 21.Kb1. Black can win with the deeply hidden combination21…Rf2!! 22.Rd8+ Ke7 23.Rxh8 e2 24.Re1 Rf1 25.Kc2 Rxe126.Kd2 Rb1 27.Kxe2 Rxb7. But the obvious 21…Ra8, protecting the knight on b8,allows 22.Rd8+ Ne8 23.Re1 f6 24.Rxe3 Kf7 25.Rexe8 Rxe8 26.Nd6+ followed by 27.Rxe8, and White should win easily.
It is notable that on move 15, White should have considered a queen trade despite being on the attack. And here, Black wisely avoids a queen trade despite the need to defend.
19.Rxd5 Nxd5 20.Qxd5 Qxa2
Black defends f7 from a distance and offers an exchange of queens. With Black’s bishopno longer hanging on b7, White must now keep queens on the board to have any chance of drawing the game.
21.Nc4g6!
Many players may have growntired of calculating at this late stage in the game. When weary, it is tempting to throw in a quick check or two and defer the task of thinking. But Black accomplishes nothing with 21…Qa1+ 22.Kd2, and following up with 22…Ra2+ 23.Kd3 would in fact lose since White ends up threatening both Rxa1 and Qd8#. Black is demonstrating tenacity by calculating that his king will be safe in all lines after 21…g6.
22.Qd6+ Kg8!
With both of our clocks winding down, I was hoping that Black would play the natural 22…Kg7. After all, he may have expected 22.Qd8+, in which case 22…Kg7 23.Qd4+ f6 is completely safe. But because I gave check on d6 instead of d8, 22…Kg7 can be met with 23.Qe5+ and White draws by perpetual check! If 23…Kh6 in this line, White ignores the loose rook on h8 and continues pursuing the king with 24.Qxf4+. And if 23…f6 instead, 24.Qc7+ draws since …Kh6 can again be met with Qxf4+.
Black’s actual move, the unintuitive 22…Kg8, leaves White with only a couple harmless checks. I gave these checks anyway in order to both protectmy knight and relocate my rook. On h1, the rook can be skewered with 23…Qa1+. It can also be picked off after 23…Qxg2, as White’s first priority would be the threat of …Ra1#.
23.Qd8+ Kg7 24.Qd4+ f6 25.Rd1 fxe3 26.Nxe3 Re8 27.Rd2 Qa1+ 28.Kc2 Ra2+ 29.Kd3 Qb1+ 0-1
Final Position after 29...Qb1+ (White resigns)
In the finalposition, I looked at only a few of my options, saw that they were unplayable, and resigned because I had only seconds remaining on the clock. It turns out that White should lose quickly in all lines. Observe that 30.Kc4is met with 30…Ra4+, that 30.Rc2 can be answered with 30…Rxe3+, and that 30.Nc2 allows 30…Qf1+. White’s best try would have been 30.Ke2, but Black can reply with the simple 30…Ra1 threatening …Qf1#. There is no defense. Both 31.Rd3 and 31.Kf2 allow 31…Qe1#, and 31.Rd1 Qxd1+ 32.Qxd1 Rxd1 33.Kxd1 Rxe3 is of course hopeless.
One could view this game as yet another case of a reckless attack by White giving Black an easy win. But such an interpretation would overlook everything that makes this game an instructive example of calculation in chess. In fact the reckless attack might have resulted in a fairly equal endgame hadWhite calculated a forced line a little deeper. Even after missing this opportunity, White could have put up a better fight by taking a wider look at the possibilities. In the final stage of the game, Black maintained a winning advantage by being tenacious andcalculating move after move.