THE LOGIC AND BEAUTY OF THREAT CORRECTION

by David Shire, in collaboration with Marjan Kovačević and Valery Shanshin

Part II

In Part I of the article Valery defined forms of threat correction (TC) and tertiary threat correction (TTC) in terms of alphabetical formulae. This is right and proper, if only for the sake of clarity. However, the existence of a mere pattern does not alone make a good problem. Ideally a composer also incorporates unifying factors that are essential in a successful multi-phase twomover and I will try to develop this theme.

Pieter ten Cate was one of the first authors to explore the potential of threat correction; No 13 is an early favourite of mine. 1.Bc3? ( -2.Sg5) 1...Bd8!/Rg8! 1.Bg7!? Bd8! 1.Bf6!? Rg8! Already we see an echo in the way in which the improved moves of the wB pre-close the defensive lines of bRc8 and bBa5. The threat correction key relinquishes a guard of d4 and unpins bSb4. (The element of surprise lies at the heart of TC!) 1.Bd4! ( -2.Sc3) 1...Sb~/Sd5 2.Sg5/Sc5 and 1...Sc~/Sxd4 2.Re5/Sg5. With delight we recognise the different roles of bBa5 and bRc8 post-key. The play introduced by bSb4 is a particular joy. The primary threat returns as a variation mate following the random move of this unit and after the correction move of its stable mate. The sense of unity is pervasive; this is not always apparent in pioneering problems.

The wP may not be an obvious candidate for developing threat correction, but Barry always thrived on a challenge! His No 14 has two excellent TC phases. 1.dxc5? ( -2.Sfd4) 1...Bxf3/Sxf1/e4 2.Rxf3/Be4/Qf6 but 1...Rc6! 1.d5!? ( -2.Qxg5) 1...Se4 2.Sfd4 but 1...c4! 1.dxe5! ( -2.Qf6) 1...Bxe5/Rxe6 2.Sfd4/Qxg5 and 1...Se4/Rf8/Sf7+ 2.Bxe4/Sg7/Qxf7. Barry would never describe himself as a theoretician but instinctively he valued the transfers of 2.Sfd4 and 2.Qxg5 because “it felt right”. However, there is a further unusual transfer of 2.Qf6 with a subtle foreshadowing of the actual threat by 1.dxc5? e4! Another valuable feature of No 14 is the cutting of white lines by both parties.

I have always appreciated the TC #2s of Yuri Sushkov; No 15 is a prime example. In the set position the b5 and d4 squares are both doubly guarded by White and blocked by Black... but watch what unfolds! 1.Be8? ( -2.Rbc6) 1...b4! and 1.Rd8? ( -2.Bd6) 1...Bh2/Se8 2.Bxd4/Rxb5 but 1...d3! Consequently White corrects the threats. 1.Bxb5!? ( -2.b4) 1...Sxb5/Sd5 2.Rbc6/Rdc6 but 1...Sa6! (2.Rxb5??) 1.Rxd4! ( -2.b4) 1...Bxd4/b4/Sa6(Sd5) 2.Bd6/Rc4/Rxb5. Here the mates on b5 and d4 together with the refutations that unblock both those same squares enable the concept to cohere quite admirably.

No 16 is another “Sushkov special” that I particularly enjoyed. 1.S4~? ( -2.Rxd3) 1...f5! Now the blunt 1.Sf6!? fails to 1...e4! (2.Bf6??), so White changes tack by ensuring that the thematic wS provides anadditional guard on d3. 1.S4c5!? Bc3! (2.Bb6?) and 1.Sf2!? Sc3! (2.Qg1?). Black defends successfully by unpinning bSb2. The solution is for White to unpin bSb2: Caprice! 1.Sc3! ( -2.Sb5) 1...e4/Bxc3/Sxc3 2.Bf6/Bb6/Qg1. Naturally the flight capture promotes the desirable transfer, 1...Kxc3 2.Rxd3. TC proves effective where white correction is found wanting and there is an impressive unity between the phases.

A potential c6 flight is the gelling factor in the French No 17. Fortunately, the only genuinely random move of the thematic white piece closes the potential line from f1 to d3. 1.Se2? ( -2.Rd3) 1...b5! is the unique refutation securing a flight for the bK. By means of two TC tries, White seeks to establish new mate threats which will themselves cover c6. 1.Sdc2!? ( -2.Sxb4) 1...bxc5/Kxc5 2.Rd3/Qb5 but 1...Rg4! and 1.Sf5!? ( -2.Se7) 1...Re6/Ke6 2.Rd3/Qc6 and 1...Rg4 2.Qd7 but 1...Bh4!. The Caprice element determines that White must cede c6 immediately. 1.Sdb5! ( -2.Sxc7) 1...Rc6/Kc6 2.Rd3/Qa8. The position is perhaps a little rough around the edges but this is understandable when the bK is allowed to flee in three different directions.

The more lasting memory is the overwhelming oneness achieved by the strategy of flights and blocks on flight squares across the TC phases. I assume that the French duo regarded the transfer of 2.Rd3 to the TC phases as a means of underlining the mechanism by which the primary threat had been suppressed, for in this way the logic of the threat correction is clarified. Readers may be amused to know that Jean-Pierre Boyer, the French author of the excellent No 12 of the first article, wrote of his early TC twomovers “La vérité est que j’ai composé ces problèmes sans connaître la correction de menaces”. (I composed these problems without knowing about threat correction!) And here lies the rub: J-P B also ensured the transfer of the primary threat to the TC phases. In equal measure, Yuri Sushkov also had the same unerring instinct in his early investigations of TC. This transference of the primary threat to subsequent phases of TC problems has been incorporated into an implicitly agreed theory of threat correction. Chess problemists along with composers of music have valued the “un-repetitive repetition” that the inner psyche finds so satisfying. There is little room for depth in the #2 genre (we have only three half-moves!) and so we value width: the transference of TC problems gives a “structured width” that provides harmony and crucially helps the composer to communicate effectively with the solver.

One key black defender, bRg5, binds the extraordinary concept of No 18 into a whole. 1.Sd~? introduces a triple threat, 2.Rxb5/2.Bxd4/2.Re8, but no genuinely random move exists. 1.Sde7? ( -2.Rxb5/2.Bxd4-2.Re8?) Rb4 2.Rd5 but 1...Rxf5! and now the bK has access to e4/e6. 1.Sdb6? ( -2.Bxd4/2.Re8-2.Rxb5??) Sxc6 2.Sc4 when after 1...Rxg4! the bK escapes to f5. 1.Se3? ( -2.Re8/2.Rxb5 -2.Bxd4??) fxe3 2.Bg3 fails to 1...Rg6! gaining the f6 flight. So far we have a cycle of double threats set up by threat avoidance due to the closure of white lines. Post-key the same three bR refutations serve as defences whose weakness is line opening. 1.Sxf4! ( -2.Sd3) 1...Rxf5/Rxg4/Rg6 2.Re8/Rxb5/Bxd4. The bR has the last word in the variation 1...Kxf4 2.Qh2, for here it essentially blocks a square in the extended bK field. TC is used to bring the solution to an astonishing climax; a wonderful construction that truly deserves the label of masterpiece!

We enter the unique world of Chris Reeves with No 19. 1.S~? ( -2.Rg5) 1...Bxe5 2.fxe5 but 1...Rg8! refutes. 1.Sxe6!? ( -2.Sg7) 1...fxe6 2.Rg5 and 1...Rg8/Kxe6 2.Sxd4/f5. However, the provision for 1...Bxe5! is lost. 1.Sxe4! ( -2.Sg3) 1...Bxe4 2.Rg5 and 1...Rg8/Bxe5/Kxe4 2.Sd6/Rxe5/Bc2. This is clearly secondary threat correction doubled but Chris caused confusion by claiming a special form of TTC! It is apparent that there is no tertiary logic as applied to the various threats but the composer saw a pattern akin to that of tertiary white correction in the role of the defence 1...Bxe5 across the three phases. Equally, White’s provision for 1...Rg8 in the second and third phases demonstrates a doubling of secondary white correction. It is a delight that the continuing relevance of these defences in both the virtual and actual play help to highlight the unity. There is also great merit in the way that wBa4, wRc5 and wQf1 all play their part in controlling the extended fields of the bK. The fact that Anatoly’s twomover from Problemas 1987 stimulated Chris’s creativity is a good example of the cross fertilisation of ideas between East and West which these articles seek to stimulate. (Readers may wish to compare the various roles played by 1...Bxe5 in this problem with those played by the defence 1...dxe5 in problem No 7 of the first article. In each instance, the black move acts as a refutation and gives rise to a changed mate).

No 20 is our last diagram to demonstrate how composers attempt to generate links between the phases. Set 1...Rxe4 2.Sd3. The introductory try is 1.Sg5? ( -2.Sd3) when Black may defend by cutting the lines of wRf1, wRd6 and wBa7. 1...Bf4/Sf3/Rxf1 2.Qxf4/Sxf3/Qe3; 1...Sd6 2.Qd4 and 1...Sxa7 2.Qxc3 but 1...b6! defeats. So White corrects the primary threat by cutting the lines of these same pieces – the Caprice element is again apparent! 1.Sc5!? ( -2.Sd7) 1...Sd4 2.S1d3 but 1...cxd2!; 1.Sd6!? ( -2.Sc4) 1...exd5 2.Sd3 but Re4!; 1.Sf2! ( -2.Sg4) 1...f5/Re4 2.S1d3/S2d3.

In the first of our articles Valery outlined the contribution of Chris Reeves, who did a great service to the problem world by formulating his concept of TTC. No 21 is Chris’s first unequivocal rendering of (simple) TTC, published some 45 years after Hannelius’s pioneer but cast in a very similar mould. 1.B5~? ( -2.f6) 1...Bxd6 2.Sxc3 but 1...Sc4!; 1.Bf6!? ( -2.Se7-2.f6??) 1...Bxd6 2.Sxc3 but 1...c4!; 1.Bf4! ( -2.Sxc3-2.f6?/2.Se7?) Now Black can defend by unpinning bQb3 but at the same time blocking the flight granted by the key. 1...c4 2.f6 (2.Se7?); 1...Sc4 2.Se7 (2.f6?) and 1...Kc4 2.Sc7. The format is identical – this is simple TTC for after 1.Bf6!? the threat of 2.f6 is not so much avoided as made physically impossible. The one weakness of the key move is flight-giving, and the subsequent self-blocks with dual avoidance serve to establish the Hannelius theme. The key buries wRg4 but Chris has sought to bind the three phases together by means of the transference of 2.Sc3.

Goldschmeding had unveiled the possibility of complete TTC as early as 1954! 1.Sg3? ( -2.Qg5) 1...Se7(Sh6) 2.Bxf6 but 1...Bd7!/Bxe8! The dual refutation may already appear to be unfortunate but 1...Sg7!? ( -2.Re6-2.Qg5?) 1...Bxg7/Bd7 2.Qg5/Rxd5 but 1...Sc5! 1.Sxd4! (2.Qe3-2.Qg5?/2.Re6?) 1...Rxd4/dxc2/Bxe8/Sc5 2.Qg5/Re6/Rxd5/Sxc6 and 1...Kxd4 2.Qf4. The secondary try and the key both add a guard to e6 to provide for 1...Bd7/Bxe8 and the key provides for the awkward 1...Sc5. An inner harmony is created by the fact that each successive phase corrects an error in the preceding play. I find this an astonishingly mature approach for its time! It is evident that the greatest composers are quick to realise an approach to a theme that is so very satisfying to the intellect.

Much had already been achieved when I attempted to compose my first TTC. Was it remotely possible to add anything new? I noted that most examples had flight-giving keys and it was this weakness alone that prevented the primary and secondary threats from being effective. In the first article, problems No 2, 10 and 11 by Hannelius, Tikkanen and Pilchenko followed this pattern, as did problem No 21 (Reeves) in this current piece. The actual play featured self-blocks with dual avoidance so that the whole emphasis was shifted to the key phase. Correction is normally associated with the gradual accumulation of positive and negative effects. With the balance of interest shifted so much in favour of the key, a ready explanation for the delayed understanding of TTC is at hand. Perhaps a sense of correction might be encouraged if the key had two distinct weaknesses?

1.Rf5? ( -2.Sc5) 1...dxe3 2.Qxe3 but 1...Sd7!; 1.Rd5!? ( -2.Rxd4-2.Sc5?) 1...Rxd6/dxe3/Kxd5 2.Sc5/Sxc3/Qf3 but 1...Qxd6!; 1.Rxc4! ( -2.Sxc3-2.Sc5?/2.Rxd4??) 1...Rxc4/Kd5 2.Sc5/Rxd4. The weakness of 1.Rd5!? is giving the d5 flight, one that is subsequently covered after 1...Rxd6 2.Sc5. The weakness of the key lies not only in giving an escape to the bK but also in pinning the wR. Consequently Black’s defences in turn open a masked line to d5 and unpin wRc4. In this way I tried to make more evident the accumulation of effects. Hopefully the transfer of 2.Sxc3 aids cohesion.

No 24 is a most subtle problem in which the cutting of white lines is used to great effect. 1.B~? ( -2.Qc5) 1...d6/Sd3/Sb3(Bc4)/Sd4/Bb6 2.Sf6/Qxa2/Q(x)c4/Rxd4/Rd6. However, the strong 1...fxe4! defeats. 1.Bd4!? ( -2.Sc3-2.Qc5?) with 1...dxe4 2.Qc5. The defence 1...d6 now has Theme A status (2.Sf6) but 1...Se2! (2.Qxa2?) refutes. 1.Bb4! ( -2.Sf6-2.Qc5?/2.Sc3?) 1...fxe4/Bc4 2.Qc5/Sc3. As with 20, there is no flight giving nor pinning and unpinning. These devices have been replaced by a refined study in white line play. This is achieved with an excellent economy of means; in my opinion this problem was seriously under-rewarded in its tourney. For example, a lovely “grace note” is the variation 1...Bxf4 2.Ra5. Whereas the key of 21 buried wRg4 completely, here the wRa4 has an invaluable life post-key!

Gerhard Maleika has demonstrated TTC using the wK as the thematic piece! In order to do this in convincing fashion he dispensed with the idea of the primary threat being initiated by a random move dependent only upon a departure effect. His correction logic was necessarily different...

Gerhard’s sequence in No 25 begins with 1.Kf4? and the positive effect of unblocking f3 for a threat of 2.Sf3 (1...Bh6!). 1.Kg4!? unblocks f3 but carries the negative effect of unguarding e4. However, wRf5 is unpinned for a threat of 2.Rd5 (1...Sxf5!). The key is 1.Ke2! ( -2.Qa1-2.Sf3?/2.Rd5?). The correction logic is built on a series of positive and negative effects: unblock of f3 (+), unguard of e4 (-), unpin of wRf5 (+), cut of the wQ’s line of guard to c4 (-) and guard of d3 (+). bSd6 supplies the transfers – 1...Se4/Sc4 2.Sf3/Rd5 to complete the simple TTC pattern. This setting is highly original and possibly unique of its kind.

The wK is an awkward customer as the thematic piece in TTC presentations. The possibilities of the wP are limited; nevertheless John Rice has shown TTC using this unit. His various examples with the wQ have been published worldwide and readers will already be familiar with these!

Finally No 26 strikes me as a most beautiful and economical presentation of complete TTC. 1.Sc~? ( -2.Rc4) 1...Qxc7/Qc6/Qc5 2.Qxc7/Rxc6/Rxc5 but 1...b5! 1.Se5!? ( -2.g3-2.Rc4?) 1...Qxe5/Qd4 2.Rc4/Sg6 but 1...Qd3! 1.Sd4!! ( -2.Se2-2.Rc4?/2.g3?) with 1...Qxd4/Qe5 2.Rc4/g3 and 1...Ke5/Qa6/Qe6/Qe7 2.Rxf5/Rc6/Sxe6/Rxe7. The wQ functions only as a third wB but everything else works wonderfully. In particular the precise control exercised over the bQ in the post-key play is a joy. The set 1...Qe5 2.Bxe5 is also an important detail but the great unity is conferred by a separate factor – much of the relevant play is generated by the masked battery. Frequently with many TTCs various constructional devices are required to realise the theme, but here just the one mechanism suffices! Mere words are woefully inadequate to do justice to this fine work; fortunately it speaks eloquently (and economically!) for itself.

So where should we travel after TTC? Chris Reeves developed the concept of Tertiary Arrival Threat Correction and a theme tourney held in 2010 showed that his idea held much potential! No 27 was a co-winner. Let us see how this works in practice. 1.Rc4? ( -2.Bf4) represents a random arrival on c4. 1...Sd4 2.cxd4 but 1...Be4! refutes. 1.c4!? ( -2.Sc6-2.Bf4?) 1...S~/Sd4 2.Bc3/Bf4 when 1...Qa8! refutes. 1.Bc4! ( -2.Qxe6-2.Bf4?/2.Sc6?) 1...B~/Be4/Bf5 2.Sd3/Bf4/Sc6. The author has sought to combine the theme of arrival threat correction on c4 with that of black correction involving bSb5 and bBg6. This BC is of the “error avoidance” type but this is a most ambitious enterprise. Do note that this is the complete form of TATC; not only do the primary and secondary threats recur through transference post-key but 2.Bf4# also reappears in the second phase.

No 28 is a great classic of black correction, one to be found in all the anthologies. 1.Qd7! ( -2.Qf5) 1...Sce7 pins bSd5 to permit 2.Qxe7. 1...Sd4 corrects but blocks d4 for 2.Sxg5 (2.Qe7?). Now comes Casa’s conjuring trick! A random move by bSd5 defends against the primary threat by opening a line of defence to f5. bSc6 is now pinned but 2.Qe7 does not mate. A white line to d4 has been opened but neither will 2.Sxg5 mate since the line of bRa5 extends beyond f5 to g5! However, the line of the wQ also extends beyond d4... So 1...Sd~ 2.Qd3 (2.Qe7?/2.Sxg5?) Finally 1...Se3 2.Sd2 (2.Qe7?/Sxg5?/Qd3?) and 1...Sf4 2.Re3 (2.Qe7?/Sxg5?/Qd3?/Sd2?) extend the black correction to the 5th degree! (1...Sdb4 2.Qd4) Here we witness not BC by a unique black piece but correction by a system of half-pinned bSs. You may wonder what relevance this has to our present discussion. If we are looking for higher degrees of white (threat) correction the equivalent arrangement would be a half-battery with the masking pieces operating in similar fashion to Casa’s bSs.

In No 29 1.Sc~? opens the line of wRa4 to d4 to introduce a threat of 2.Rxe3 when 1...Bb4! refutes. 1.Sxe3!? blocks the square needed for the primary threat but establishes a guard over d5 for the secondary threat of 2.Qd5. However, there is no answer to 1...Sc3! Now things become complicated! 1.Sd~? places extra guards on both d4 and d5. 2.Rxe3 is no threat since the line of bBc5 has been opened. Likewise 2.Qd5 will not mate because White has lost control over f5. Instead the threat is double check and mate. 1.Sd~!!? ( -2.Sd6-2.Rxe3?/2.Qd5?) but after 1...f2! there is no way to cover the f3 flight. White must grant the flight immediately – Caprice! 1.Sxf3!!! ( -2.Sxg5-2.Rxe3?/2.Qd5?/2.Sd6?) Yes, this is quaternary threat correction! 1...Be7/Rf5/Rxf3 2.Rxe3/Qd5/Sd6 and 1...Kxf3/Rg7 2.Qg4. Doukhan’s powers of mystery and invention never cease to impress me. With this wonderful exposition of our art this second article must come to an end.