What are Chess Problems? Threemovers


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Written by Michael McDowell   

In the 19th century, the three-mover was considered to be the ideal length of problem by solvers. Over time the three-mover developed two main streams, one concentrating on checkmating positions, the other stressing the interplay of the pieces. For convenience these are termed model-mate problems and strategic problems. Today the latter is the dominant type.

Model-Mate Problems

Some three-movers are built around a combination of artistic mates, in the style known as Bohemian, after the school of composers who developed the principles of such problems in the late 19th century. To explain Bohemian problems, we must first consider checkmates. Problemists, unlike players, are interested in the quality of checkmating positions, and classify mates according to certain features. A pure mate is one in which the squares around the mated king are guarded or blocked in one way only and the square on which the king stands is attacked once. An economical mate is one in which all of the white pieces on the board with the possible exception of king or pawns participate. A mate that is both pure and economical is called a model mate.

In a Bohemian problem there is no main variation or variations; the composer combines a number of variations of equal value ending in diverse model mates. The white force is highly mobile, with pieces swapping the duties of delivering the mating check and guarding flight squares. Quiet continuations, that is non-checking continuations, are highly valued. Accuracy of play in non-thematic variations is considered of minor importance.

(1) C. A. L. Bull

Casopis Ceskych Sachistu, 1923


Mate in 3

The lightly-set 1 is a typical example of a Bohemian problem. The give-and-take key 1.Qa3 threatens 2.Sxe6, with 3.Qb3 to follow (if 2...Sc5 3.Rb4). Instead of actively attempting to defeat the threat, Black can co-operate in making the mate a model by capturing the e7 knight: 1...Sg6 2.Sxe6 Sxe7 3.Qb3. Such a mate is called a slaughter model. A pair of thematic variations involve the knight and rook exchanging guarding and checking functions: 1...Kd4 2.Sxe6+ Ke5 3.Re1, and 1...Sc7 2.Rb4+ Kc5 3.Se4. Finally 1...b5 leads to a mate which is almost a repeat of the threat model 1...b5 2.Rc1+ Kd4 3.Qc3.

There are two exceptions to the above definition of a model mate. A double check is considered acceptable if each check taken by itself could be countered, although the insistence on the unique guard of each flight still holds. If one of the mating pieces pins a piece which could otherwise frustrate the check the resulting mate is called a pin-model, whether or not the pinned piece occupies a square in the king's field.

(2) F. Matousek

1st Prize, Jas, 1935


Mate in 3

2 illustrates a variety of pin-models. In each variation a different piece delivers the mating check, and two black pieces are pinned, the pawn on both rank and file. The key 1.Bc5 threatens 2.Qh1+ Kxd2 3.Qc1, and gives the thematic variations 1...Sxc5 2.Qh1+ Kf2 3.Sd1, 1...Kxd2 2.Qh6+ Re3 3.Bb4 and 1...Rh8 2.Qe4 either Re8 3.Rd1. The last mate is called a sideboard model, a type considered a little inferior as there are less squares around the king to be guarded.

When two or more mates have similar arrangements of blocking and guarding pieces around the mated king the mate is referred to as an echo. Bohemian composers were particularly interested in echoed mates.

(3) J. Pospisil

Zlata Praha, 1885


Mate in 3

The flight-giving key of 3, 1.Qd1, threatens 2.Qf3+ Kd4 3.Qxd3. After 1...Kf5 2.Qf3+ leads to the model 2...Ke6 3.Sc5, a mate which is echoed after 1...Bg4 or 1...Bxg2 2.Qg4+ Kd5 3.Sb4. After 1...Kd4 or 1...Bf5 2.Qa4+ Kd5 3.Sxc7 is a model which differs slightly in that the guard and block on either side of the king have been swapped. This mate is echoed by 1...Kd5 2.Qb3+ Kc6 3.Sb8. Unusually for a Bohemian problem the play is completely accurate.

Strategic Problems

Strategic problems, where the emphasis is on the interplay between black and white pieces following the key move, have been the most popular form of three-mover for most of the last century, and improvements in constructional techniques have seen increasing complexity. Very often a type of strategy is repeated in multiple variations.

(4) I. A. Schiffmann

1st Prize, Dutch East Indies Chess Association, 1929


Mate in 3

The key of 4 is 1.g6, threatening 2.gxf7 followed by 3.Rxd8. Black can defend by moving the rook along the rank to give the queen access to h4. After 1...Rd2 White continues 2.Ka5 and 3.Sa6 mate, because the rook has prevented the possible defence 2...Qe1, pinning the knight. This idea is called anticipatory interference, and is repeated in three further variations: 1...Re2 prevents a queen check from f1, for 2.Kxb5 any 3.Sa6. 1...Rf2 cuts out Qg1 for 2.b7 and 3.Ba7, and finally 1...Rg2 is followed by 2.Bb7 and 3.Sc6, as 2...d4 no longer defends. After 1...d4 2.b7 operates again.

(5) Vincent L. Eaton

1st Prize, American Chess Bulletin, 1950


Mate in 3

Eaton's 5 is built around the various ways in which White can unpin his own pieces. The key is 1.Bd3, which prevents Black from cutting the line connecting bishop and rook, and places Black in zugzwang. After 1...Sf2 White continues 2.Re6+, unpinning the knight, so that after 2...Sxd3+ 3.Sd2 mates. Similarly complex play features in the variation 1...Sc4 2.Sd2+ Sxd2+ 3.Re6. A trio of variations allow the king to unpin the knight and rook by vacating a2. 1...c5 allows 2.Kxa3 because the potential bishop check at d6 has been eliminated, while 1...Sb5 allows 2.Ka1 because there is no longer a check at c2. 1...Sb1 is simply met by 2.Kxb1. Any move of the e8 bishop allows 2.Rxf7+, since the bishop cannot recapture to re-establish the pin of the knight. 1...c6 prevents the e8 bishop from attacking the key piece, and is followed by 2.Bc3, threatening various rook discoveries. In this line 2…Sf2 unpins again for 3.Re1. The mop-up variations are 1...gB anywhere 2.Qe3, and 1...Bf4 2.Rxg2+ Ke1 3.Rxg1. The variety of play in this problem is quite astonishing.

(6) H. Maruta, Oey Gien Tiong & Touw Hian Bwee

1st Prize, BCF Tourney No. 133, 1972-1973


Mate in 3

Many problems successfully mix formal and strategic elements. The remarkably unified 6 features an AB-BC-CD-DA cycle of continuations and mates. The arrangement on the fifth rank is called a half-pin, since if either bishop or pawn moves off the line the remaining piece will be pinned. All of the thematic variations exploit the half-pin. The key, 1.Qh1, threatens 2.Qh3+ Sg4 3.Qxg4. 1...Rxg3 unguards f4, allowing White to drag the pawn from the half-pin line, 2.Rf4+ A exf4 3.e4 B. 1...Rg7 unguards the potential mating square d4, for 2.e4+ B Bxe4 3.Sd4 C. 1...Sc4 unguards the line b1-e4, allowing 2.Sd4+ C exd4 3.Qxf3 D (If 2...Ke4 3.Qb1). Finally 1...Sg4 shields the white king from a bishop check, leading to 2...Qxf3+ D Bxf3 3.Rf4 A. Such a superbly constructed problem makes light of the challenges facing the composer, who must not only find a matrix that allows the cyclic play, but must also arrange a threat that will be defeated by all the thematic black moves. In this case three heads were better than one!

(7) Matti Myllyniemi

1st Prize, Suomen Shakki, 1952


Mate in 3

When solving it is always worth looking for prominent set play, as the problem may be built around changed play. In 7 there are two set variations. After 1...f5 White must release the stalemate with 2.Rf3 gxf3 3.gxf3, while after 1...fxe5 2.Re2 exploits the fact that the black pawn must move on to f4 for 2...exf4 3.exf4. No pure waiting move is possible, and the key is 1.Bh6, giving the variations 1...f5 2.Re2 f4 3.exf4 and 1...fxe5 2.Rf3 gxf3 3.gxf3. The set continuations have been reversed after the key, an idea known as reciprocal change. The problem is a mutate, a type rarely seen in the three-mover compared to the two-mover.

In recent years many of the modern pattern themes which have been developed in the two-mover have been transferred to the three-mover. A number of such themes feature effects which appear paradoxical. Keller's problem illustrates one of the most popular paradox themes, the Dombrovskis theme, where black defences which defeat try threats are met by those very moves after the key.

(8) Michael Keller

1st Prize, Schweizerische Schachzeitung, 1985


Mate in 3

White's try 1.Bb6? threatening 2.Qxd4 mate is refuted by 1...Sf3!. Similarly 1.Bc7? threatening 2.Rxd6 mate is refuted by 1...Se4!. The key is 1.gxf4, threatening 2.Qxh1+ followed by capturing the knight. Black can defend by playing 1...Sf3 or 1...Se4, the two moves which defeated the try threats. After 1...Sf3 White plays 2.Qxd4+!, the move which 1...Sf3 originally defeated! This gives the continuations 2...Kxd4 3.Rxd6 and 2…Sxd4 3.Se3, which is now possible because the key removed the pawn guard on e3. 1...Se4 is followed by 2.Rxd6+ (again the move which it originally defeated) 2...Kxd6 3.Qxd4 and 2...Sxd6 3.Re5, now possible because the key put a guard on e5.

The success or otherwise of such problems lies in the ingenuity of the mechanism which allows the paradoxical effects.

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