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Hesse: Threats of the nth degree2/5/2016 – Averbakh called them "threats of the 1st degree" – moves which directly and bluntly threaten to bringabout a concrete mate or the win of material. 2nd degree threats are moves which are intended to enable threatsof the 1st degree. And so it continues, recursively. In his wonderfully entertaining book Joys of Chess Prof.Christian Hesse goes all the way to threats of the 5th degree.

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Threats of the nth degree

By Prof. Christian Hesse

The success of a threat or of a counter-measure is based almost exclusively on a correct evaluation of theother person’s concept of reality. That means on my correct estimation of what he will do about it, because heworks out what I might do about it, because I have considered... etc. – Paul Watzlawick: Wie wirklich ist dieWirklichkeit (How real is real?)

We humans can in principle soar to rather complex degrees: I assume that you are wondering if I realise howdifficult it is for you to be sure that you understand if I intend to say that you could recognise that I believe youwould like me to explain that most of us can only manage as far as the fifth or sixth step. – Daniel Dennett:Intentional Systems

There are moves which directly and bluntly threaten to bring about a concrete threat – perhaps mate or the win ofmaterial. In his book Chess tactics for advanced players Averbakh described these as threats of the 1st degree.2nd degree threats are moves which are intended to enable threats of the 1st degree. And so it continuesrecursively. Threats of the 3rd degree are those moves which are intended to enable threats of the 2nd degree,etc.

As a simple primer, let us enjoy the following position, which is the starting point for threats of various degrees. Itis a snapshot from the game B. Katalymov-E. Mnatsakanian, USSR 1959:

From a purely visual point of view, Black’s king appears to be in some sort of danger. But White has to transformthis instinctive feeling into a tangible plan. There exists in 1.Qf8+ a simple threat of the 1st degree. But the f6 rookis protecting the square on the back rank and thus preventing this check. The threat of the 2nd degree consists of1.Bh6 and carrying it out activates the threat of the 1st degree, because after ...Rxh6 the f8-square is no longerunder the surveillance of the rook.

But the 1st degree threat is not yet convincing, because Black has in his hands the defence ...Bg8, which willprevent it being carried out. A further enhancement is required: a threat of the 3rd degree, which is the nowdecisive 1.Rd7!! Carrying it out makes possible the carrying out of the threat of the 2nd degree, which in its turnenables the threat of the 1st degree and finally wins the game: 1...Bxd7, and the bishop can no longer interposeitself on g8. Then comes 2.Bh6!!, which makes the threat of the first degree playable, since either 2...Rxh63.Qf8# or 2...gxh6 3.Qxf6+ Kg8 4.Qf7+ Kh8 5.Qf8# must happen. 1-0. A combination with a preface. And with apreface to the preface.

Let us now turn to the realms of chess art.

S. Eisert & H. Rehm, 1995

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White to move and mate in 6 movesThis problem has as a pretty motif a threat of the 3rd degree.

The primary threat consists of 1.Nxd5, which, when combined with 2.Nxe7# or with 2.N3b4+ Rxb4 3.Nxb4# wouldin each case force mate. 1...Rxd5 cannot serve as a defence, since 2.Rf8 and 3.Rc8# lead to mate. But 1.Nxd5 failsto 1...b4!. The secondary threat seeks to prevent this with the knight sacrifice 1.Nb4+, but after 1...Rxb4 the mainthreat 2.Nxd5? is now refuted by 2...Re4!. So to get rid of this new obstacle, a threat of the third degree isrequired, to first of all push away the influential black rook: 1.h3!! Ra4 2.Rf4 d4, and we have reached thefollowing position:

And White has achieved his goal of the 3rd degree. Now the threats involved in degrees 1 and 2 can take effectaccording to plan: 3.Nb4+ Rxb4 4.Nd5 Rxd5 5.Rf8 and then 6.Rc8#.

[Event "?"] [Site "?"] [Date "1995.??.??"] [Round "?"] [White "Eisert/Rehm, S/H."] [Black "Mate in six"] [Result "1-0"] [SetUp "1"] [FEN "1K4B1/B1Npp3/P1kp2pn/1p1p2r1/6r1/2pN4/5R1P/8 w - - 0 1"] [PlyCount "11"] [EventDate"1995.??.??"] [SourceDate "2016.02.05"] 1. h3 $3 (1. Nxd5 b4 $1 (1... Rxd5 2. Nb4+ (2. Rf8 b4) 2... Rxb4 3. Rf8Nxg8 4. Rc8#)) (1. Nb4+ Rxb4 2. Nxd5 Re4 $1) 1... Ra4 2. Rf4 d4 3. Nb4+ Rxb4 4. Nd5 Rxd5 5. Rf8 Nxg8 6. Rc8#1-0

Our next position shows an artistically orchestrated masterpiece in which White, in order to meet continually freshobstacles, has to find more and more threats, going as far as the 5th degree:

H. Grasemann, 1961

White to move and mate in 11 moves

The main threat 1.Bxf2# is quite obviously blocked by the pawn on e2. If the latter moves away with 1.e4?? (2nddegree threat), the result is a common-or-garden stalemate. So a threat of the 3rd degree is needed: 1.e3!? couldbe considered and after 1...Re2 the planned 2.e4+ Rf2 3.Bxf2# would follow. But unfortunately after 1.e3!? theprosaic 1...Rxd2 provides Black with another defence. White gets rid of this counter by arranging (4th degreethreat) for the white rook to first move away and then come back, while keeping a close eye on possible moves forBlack so as to avoid stalemate. This works along the following lines: 1.d4!! Rg2 2.d5+ Rf2 3.Rd4 Rg2 4.Rc4+ Rf2.And now the variation 5.e3 Rg2 6.e4+ takes into account all the defensive lines which have so far appeared forBlack and White mates with 6...Rf2 7.Rd4 Rg2 8.Rd2+ Rf2 9.Bxf2#.

But once more there is an obstacle for White in the series of exchanges: after 5.e3 Black does not only have at hisdisposal the move 5...Ra2!, which means that 6.e4+ no longer works, but he also has 5...Rxf3! and then 6.e4+ Rf27.Rd4 Rxf4+. So White requires an even more deeply hidden move generating a two-pronged threat (a threat ofthe 5th degree), which takes into account these latest two complications and at the same time nullifies both ofBlack’s resources. That is achieved by 4.Rb4+ (instead of 4.Rc4+?).

This maps out the further course of events: 4...Rf2 5.Rb6! Rg2 6.Ra6+!. This liquidates one of the two defensivelines. 6...Rf2 7.e3 Rxf3 8.e4+ Rf2 9.Rb6 Rxf4+.

Now 10.Rf6+ can neutralise the other of Black’s two defensive possibilities. Mate is in sight.To sum up we have the following main line: 1.d4!! Rg2 2.d5+ Rf2 3.Rd4 Rg2 4.Rb4+ Rf2 5.Rb6 Rg2 6.Ra6+Rf2 7.e3 Rxf3 8.e4+ Rf2 9.Rb6 Rxf4+ 10.Rf6+ Rf2 11.Bxf2#, and that’s that!

Elegant to the very end, complex and positively breathtaking. A web of intricate rook manœuvres which is markedby white threats, black parries, white counter-threats, black ripostes to the counter-threats, etc., until the f4-rook,which has to shoulder all the defensive work in this chain of cause and effect, finally runs out of breath. But in thefinal analysis, it is the latter’s king who has to pay the price.

[Event "?"] [Site "?"] [Date "1961.??.??"] [Round "?"] [White "Grasemann, H."] [Black "Mate in 11"] [Result "*"][SetUp "1"] [FEN "5K2/B7/8/8/5P1P/3P1PN1/3RPr1p/4N1kr w - - 0 1"] [PlyCount "21"] [EventDate "1961.??.??"][SourceDate "2016.02.05"] 1. d4 $3 (1. e4 $4 {stalemate.}) (1. e3 $5 Rxd2 (1... Re2 2. e4+ Rf2 3. Bxf2#)) 1...Rg2 2. d5+ Rf2 3. Rd4 Rg2 4. Rb4+ (4. Rc4+ Rf2 5. e3 Ra2 $1 (5... Rg2 6. e4+ Rf2 7. Rd4 Rg2 8. Rd2+ Rf2 9.Bxf2#) (5... Rxf3 6. e4+ Rf2 7. Rd4 Rxf4+) 6. e4+ Rxa7) 4... Rf2 5. Rb6 Rg2 6. Ra6+ Rf2 7. e3 Rxf3 8. e4+ Rf2 9.Rb6 Rxf4+ 10. Rf6+ Rf2 11. Bxf2# *

Christian Hesse holds a Ph.D. from Harvard University and was on the faculty of the University of California atBerkeley until 1991. Since then he is Professor of Mathematics at the University of Stuttgart (Germany).Subsequently he has been a visiting researcher and invited lecturer at universities around the world, ranging fromthe Australian National University, Canberra, to the University of Concepcion, Chile. Recently he authored“Expeditionen in die Schachwelt” (English translation: The Joys of Chess, ISBN 978-90-5691-355-7), a collection ofabout 100 essays that the Viennese newspaper Der Standard called “one of the most intellectually scintillating andrecommendable books on chess ever written.”

Christian Hesse (photo above by Ivo Kljuce) is married and has a 13-year-old daughter and an 11-year-old son. Helives in Mannheim and likes Voltaire's reply to the complaint: ”Life is hard” – “Compared to what?”.

The Joys of Chess is an unforgettable intellectual expedition to theremotest corners of the Royal Game. En route, intriguing thoughtexperiments, strange insights and hilarious jokes will offer vistas youhave never seen before.

The beauty, the struggle, the culture, the fun, the art and the heroismof chess – you will find them all in this sparkling book that will give youmany hours of intense joy.

Christian Hesse is a Harvard-trained professor of Mathematics who hastaught at the University of California, Berkeley (USA), and since 1991 atthe University of Stuttgart. He has written a textbook called'Angewandte Wahrscheinlichkeitstheorie'.

Chess and literature are his main hobbies, and he also likes fitness andboxing. His heroes are the ones who fall to the bottom and rise again,fall and rise again…

From the foreword by Ex-World Champion Vishy Anand: "A richcompendium of spectacular highlights and defining moments fromchess history: fantastic moves, beautiful combinations, historicalblunders, captivating stories, and all this embedded into a plentitude ofquick-witted ideas and contemplations as food for thought."

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Joys of Chess – Castling12/13/2013 – Did you know that until the 17th century castling in chess was twoseparate moves? Or that today there is a chess magazine devoted entirely to castling?Professor Christian Hesse has devoted a section of his book The Joys of Chess tospectacular instances of castling, including rare positions in which the castling movedeserves two or even three exclamation marks. [Discuss]

Nabokov: Poems and problems10/23/2014 – "Chess problems demand from the composer the same virtues thatcharacterize all worthwhile art," said Vladimir Nabokov, one of the greatest novelists ofour time. He was also an avid chess player and composer of chess problems. One of hisnovels, Luzhin’s Defence, became a popular movie. Prof. Christian Hesse tells us thestory of the greatest chess lover among writers, and vice versa. [Discuss]

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No word about the cat?

What is Hesse's response to documented theft of material from Winter and Crabbe?

"His heroes are the ones who fall to the bottom and rise again, fall and rise again…"

It is apt that Vishy has written the forward :-)

Well, T J, really, difficult to come to terms with statements such as "With the atrociousChristian Hesse, chess knowledge moves backwards." I wonder what the response may be,indeed. :)

Why is ChessBase promoting the work of a known plagiarist? seehttp://www.chesshistory.com/winter/extra/copying.html

The accusation of plagiarism is untrue. Prof. Christian Hesse On a light-hearted note: On occasion, I enjoy introducing a tiny, but inconsequential inaccuracyinto my chess stories, just to have a little fun with the self-appointed chess historians. So far, theyhave not found every single one of them, but I hope they will keep looking for and writing about

them.

Threats of nth degree?It is fifth,see the title of the article and change it ;)

After consulting Chess Notes, it becomes clear Hesse's plagiarisms. I second psilocybin coomentand ask CB to avoid further promotion of Hesse's books. To answer simply this is "untrue" doesnothing to reverse copies documented by Winter. Even worse is to write "[I] enjoy introducing atiny, but inconsequential inaccuracy into my chess stories, just to have a little fun". Does anybodywould believe in such foolish affirmation?

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