## Wednesday, May 28, 2008

### Helpmates (1)

In this post, in collaboration with the International Master Harry Fougiaxis, we present another type of heterodox problems, the helpmates, where the two opponents (white and black) are working together. With the exception of the cooperation of the two opponents, every move must be legal according to the classic chess rules.

 Helpmate is a problem where black plays first and helps white to mate in a specified number of moves.

For example, in a helpmate two-mover (notation h#2), the solution consists of the first black move (the key), the first white move, the second black move, and the second white move that checkmates black: B – W – B – W.

 (Problem 95) Z. Maslar, First Prize, ”Die Schwalbe”, 1981 Black plays and helps white to mate in 8 moves h#8 (2+3) [8/8/S7/8/8/6q1/3K2k1/3b4]

The problem-95 is a more-mover helpmate, by Zdravko Maslar, awarded with first prize when published in the magazine ”Die Schwalbe” in 1981. The black King goes to a1 to become mated, while the white King tries to allow him to pass.

Let us note that in the solutions of helpmates the black move is written first, unlike what is used in other types of problems. The solution is :

Key: 1.Kf3! Kd3
2.Bb3 Kc3
3.Ke4+ Kd2 (we observe the manoeuvre of the white King, usually called King's triangle)
4.Kd4 Ke2
5.Kc3 Sb4
6.Kb2 Kd2
7.Ka1 Kc1
8.Ba2 Sc2#

During the first years of their development, in the period 1930-50, the helpmates had usually a phase of apparent play (set play) where the white plays first, and the complete solution where a black move begins the series of moves. This must be attributed to the attempt of the composers of that era to adapt on helpmates characteristics of the direct-mates. A very nice (a little posterior) example is a composition, by the Georgian Grand Master (GM) Iosif Krikheli, specialized in more-movers and in helpmates.

 (Problem 146) Iosif Krikheli First Prize, Sahovski glasnik, 1963 (There is set play). Black plays and helps white to mate in 3 moves * h#3 (5+7) [8/8/7k/7s/7s/p7/P5pR/K3BBrr]

Phase of set play (*) : 1...Bd3 2.Sf5 Bb1 3.Sg7 Bd2#
Phase of actual play : Key: 1.Sf4! Bd2 2.Kh5 Bc1 3.Sg6 Be2#

Here we have the combination of two half-pins, one black and one white. The two black Knights undertake by turns to block a flight of their King, while the white Bishops are positioned in the diagonals take care to unpin one another. The mates are chameleon, echo and model.

As the years passed by, the composers understood that the set play functioned as a limiting factor on their imagination. A specific technique is required, in order someone to construct such a problem (i.e. no black pieces should exist free to play a random first move keeping the set play intact, since this would be a "hole" in the problem), and usually the positions are heavily "loaded". The composers decided that it was clearly superior the presentation of the content in two (or more) solutions, since this facilitated the construction effort and simultaneously earned one black move.

Peculiarities of the helpmate problems

Since the two sides are cooperating, the play in the helpmates is simpler than the play in orthodox problems. In direct-mates, white plays first and attempts to checkmate black who is defending. For each white move might be many defensive answers by black, hence there are many variations. In helpmates, both black and white have unique move when it is their turn to play.

It is important to note that what has been said for the key of the direct-mates is not applicable on helpmates. Hence, the first black move can very well capture a white piece, or give check. And this is very logical. Such a move increases the strangeness of the problem : why black, who wants to help, does remove a piece or attack the white King?

Some additional rules valid for helpmates are the following :

>> In all the phases of the problem, in the final picture of mate must take part (must be necessary) all the white pieces on board. King and pawns are excluded. (Obligatory rule).

>> White must not capture black pieces, but it is tolerable to capture black pawns. (This rule is not inviolable, but a capture of piece lessens significantly the value of the problem).

>> The same moves must not be repeated in the same sequence, i.e. same second black move in both solutions. (The applicability of this rule is loose and depends, in most cases, on the number of the moves of the problem. Thus, in a h#2 such a repetition diminishes greatly the "variety" of the problem and is almost always blamable, but in helpmates of 3 or more moves might not be annoying).

For the insertion of more than one series of moves in a problem, various methods have been used. The method [the problem to have two solutions] is the most direct.
The helpmates can have more than one solutions (if this is specified), which are connected with an inner relationship, with a common theme. The solutions will somehow complement each other (homo-strategic), and they will be analogous or completely contrary.
Every solution can be considered as a different phase of play.
If more solutions exist, the composer must declare it in the stipulation. If there is not something declared there, then the problem must have only one solution.

 (Problem 96) Chris Feather, ”Schach”, 1975 Black plays and helps white to mate in 2 moves. (There are two solutions). h#2 (5+9) 2.1.1.1 [1RrB2b1/8/4s3/2s3p1/2K2b2/1p1rk3/6BR/8]

The problem-96 is a helpmate two-mover with two solutions, composed by a specialist in helpmates, Chris Feather. (The notation 2.1.1.1 in the stipulation means that there are two keys (two black first moves), but from there on all moves are unique). The two solutions are :

Key: 1.Bxb8! Bd5 2.Sc7 Bxg5#
Key: 1.Rdxd8! Bc6 2.Sd7 Rxb3#

These two series of moves are closely interconnected, because they have the same plan:
(a) First, Black captures the white piece that checkmates in the other solution (theme Zilahi), opening at the same time the line on which the mate will be given.
(b) Then, White moves a Bishop to close a line, in order the next black move not to give check.
(c) The second black move closes another line, in order not to be able to interfere when white will give check.
(d) Then White, moving in the opposite direction of the black key-move, gives checkmate.

 Theme Zilahi : black captures the white piece, which checkmates in the other solution.

See the page for helpmates, at the site of the British Chess Problem Society.

(This post in Greek language).