USCF Home Chess Life Online 2008 August Start Solving Now: Part II
|Start Solving Now: Part II|
|By Gary Kevin Ware|
|August 29, 2008|
In the first part of Start Solving Now, Gary Kevin Ware delineates what makes a good mate in two and shows how to approach them as a solver. Here he shows what makes a good mate in three and four and discusses how much harder they really are.
Before we move on to mate in three or more move problems, I want to explain the following statement about a Jacobs mate in two I discussed in the first part of this article, "the key had the offsetting merit of permitting the white king to be checked."
Any OTB player would probably consider that statement to be insane. In, Mate in Two Moves, Brian Harley grades the value of keys in order of increasing merit as follows.
2. Flight giving
3. Self-pinning of a white man
4. Unpinning of a black man
5. Allowing a black check
A keymove may possess two or more of these characteristics, and if it does it is the more meritorious. In contrast, any apparently strong "playing" move makes a theoretically poor key. A capture key is commonly considered objectionable unless it is the capture of a black pawn by a white piece that results in a self-pin of the latter. Other poor keys include moves that restrict not only the black king but any other black piece. There is no rule that the key cannot be a checking move, but since such a move is one of the most aggressive, it is highly objectionable as a key, unless the check is part of the theme.
What is the difference between mate in two problems and mate in three problems? Kenneth S. Howard writes, "the procedure for solving three-move problems is similar in many ways to that for two-movers, however, three-movers are commonly threat problems, a waiting move three-mover being rather a rarity. Accordingly, the solver usually takes it for granted that a three-mover has a threat, unless the setting definitely suggests a block position. Since only an occasional three-mover is a block, few of them can be solved by any mechanical routine without resorting to an unnecessarily detailed analysis."
This brings to mind, something said by Sam Loyd about mate in two problems, "The difficulty of a two-move problem can be reduced to a mere mechanical analysis, depending upon the rapidity with which the solver can take up each move in succession and see if the defense has a possible reply to the few checking moves that might terminate the solution. As soon as a move is hit upon, which might possibly be one of the first looked at, which admits of no defense, the problem is solved; yet I have seen solvers baffled by a little problem where the attack had but twenty possible key moves!"
Mikhail Botvinnik, World Champion at the time, lost on first board during the 1955 Soviet-American match and said, "It shows I need to perfect my play of two-move variations." The full story and analysis of the game can be found in The Inner Game of Chess: How To Calculate and Win by Andrew Soltis. Botvinnik's quote was reminiscent of what Loyd said about two-movers, "I cannot dwell too strongly upon the importance of learning to solve a two-move problem correctly. I have devoted years of practice to this one object and am still far from perfect. No matter how many moves a solution contains, it can always be reduced to a series of steps or sequences of two moves at a time: the key move, and the second or objective move, the latter being a sequel to the first. Simple as it may appear to those who can readily boast of announcing a mate in half-a-dozen moves or more, the entire ability of a solver depends upon his powers of taking an accurate and exhaustive glance only two moves deep, and I have yet to find the solver who can infallibly do so."
Before I engage in yet more exposition, let's look at a mate in three by Sam Loyd.
Here is Loyd's analysis, "It is remarkable to see how few moves there really are to a problem. Therefore, in this position, which is a very free one, if the solver can look at each of the thirty-nine possible moves in rotation, and from that second standpoint say at a glance, in thirty-eight cases, 'No two-move mate!' he can thoroughly exhaust, analyze and solve the most difficult three-mover extant in less time than it takes to tell it."
1 Nd8 Ke4 2 Nb7 Kd3 3 Nc5#
Kxd5 3 Bf3#
Kf5 3 Nd6#
Here is analysis of the original Bristol Clearance, from Chess Problems Made Easy: How to Solve- How to Compose by Thomas Taverner.
"This is the original of what is known as the "Bristol Theme"- the movement of a piece in order that another may follow in its wake and deliver mate on one of the squares the moving piece has cleared. At the time when it created its great impression, at the British Association Tourney in 1861, the Problem Art had not made much headway. Present day ideas were largely unborn. It is with that fact in mind that this problem- really the germ of thousands of others- has now to be regarded. It will be noted that as the problem stands, Black's only move to avert mate, if it be his turn to play, is Bd7 or e8. If, on this move being made, the Q moves to b1, with a view to mating at b4, and the Black B returns and thwarts this, the Q could, but for its own R at d1, mate at g1. Rh1 is, therefore, not merely the clearing move, but that by which White throws away a move and forces Black, by moving his B, so to uncover the White N at b6, that the Q can carry out the first part of its own share in the maneuver without allowing Black to escape by Kxb6."
1 Rh1! Bd7 2 Qb1 Bb5 3 Qg1#
Be8 2 Qb1 Bxf7 3 Qb4#
With regards to the relative difficulty of solving chess problems, Sam Loyd said the following, "I used to think it a very good scale to say that a three-mover should be six times as difficult as a two-mover; a four-mover, four times as difficult as a three-mover; and a five-mover, five times as difficult as a four-mover, which would make it equal to 120 two-movers. This is not a very high estimate when we consider how few good five-movers have ever been composed that are up to standard." Although, if he was consistent, perhaps he should have said that a three-mover would be three times as difficult as a two-mover.
Here is another problem by Loyd with his commentary.
"There are two principal ways to set about discovering the solution of a problem. The one is by the experimental trial of moves; the other by the analytical examination of the resources of the position. In the latter method, we first study the placing of the two Kings. Is the White King in a place of safety, so that we are free to operate against the enemy? or is he so open to attack that we must commence an immediate onslaught on the adverse King, or else prepare a defense for our own? Does the White King take an active part in the fray? Is the Black King already hedged in, or has he got to be captured as well as mated? In this problem, the White King is exposed to a check that could not be allowed, as it would give the defense an opportunity of prolonging the mate beyond the required number of moves. White is, therefore, compelled to force the fight throughout or to prevent the counter attack."
1 Nxd6+ Kxd4 2 c3+
Kxd6 2 Kb5
Again quoting from Kenneth S. Howard, "When taking up a three-move problem the experienced solver judges, from the general appearance of the position, whether it has been composed to illustrate some form of strategy in the moves leading to the mates, or for the beauty of the mating position themselves. Sometimes both of these objectives are combined in one problem, but such instances are exceptional. Where the aim of the composer is centered on showing some interesting type of strategy in white's attack, in black's defense, or in both combined, the problem is termed a strategic one. In the other general class of three-move problem, the beauty of mating positions is the reason. In compositions of this kind, there will usually be two, three or more model mate positions, and so are called model mate problems. A model mate is a mate in which the square on which the black king stands and each adjoining square , is guarded or blocked only once, and every white piece on the board takes part in the mate, with the possible exception of the white king."
Now let's look at some examples of both types.
The setting suggests that it is probably a strategic problem. The black king is confined to a corner square by the white bishop and one of the rooks. The other rook is free for attacking purposes, but there is a black queen to defend the king. So the theme must be based on getting the black queen to play to some square where her guard will become ineffective. The rook can threaten an attack on both the h-file and on the eighth rank, and so the queen must parry a two-way threat. Also, a capture of the queen, without check, produces stalemate.
1 Ra2 Qc7 2 Ra8+
Qc8 2 Rh2+
To find the key to this problem, the simplest procedure is to investigate the function of each white piece. The white king is on a5 to block black's rook pawn. The white queen controls both b7 and b8. Moving the bishop off the long diagonal would allow 1...b6+ and moving the bishop along that diagonal does not lead to anything. By process of elimination, it would seem that the white rook must make the keymove. If 1 Rxg7, black plays 1...c4. 1 Rb6 increases the attack on the b-pawn but it does not threaten mate in two more moves. Other rook moves along the rank to d6, f6 or h6 are met by 1...Ne6. This leaves 1 Rc6, which seems unpromising until white's startling second-move threat is discovered. Two of the ensuing mates are pin-models. This problem is a constructive masterpiece.
1 Rc6 threatening 2 Qxb7+ Raxb7 3 Rxa6#
Rbxb7 3 Rc8#
Kxb7 3 Rxc5#
1 Rc6 bxc6 2 Qxc6+
b6+ 2 Rxb6+
Here is a mate in three move problem that can be solved thematically.
White has a seemingly unnecessarily large force, where care must be taken to avoid stalemating black. The veteran solver may recognize this as a type of problem in which one of the white pieces has to be temporarily masked, and apparently the only piece that can be masked is the king rook. This problem illustrates the Indian Theme, named after a problem composed in 1845 by the English clergyman, Reverend Henry Augustus Loveday, who was living in India (see C1, 64 Square Problem Tour.) Dr. Dobbs doubles the thematic play, which is a fine constructive feat considering that he uses but eight men. The square on which the masking occurs is known as the critical square, because the rook has to withdraw across it, the withdrawal being a critical move.
1 Rh1 Kg4 2 Kh2 Kh5 3 Kg3#
g4 2 Nh2 Kh4 3 Nf1
Here is a detailed analysis by Brian Harley in solving a mate in three problem with a model mate theme. "When most of the squares in the Black K's field (or a little outside it, assuming that he may move out) are controlled in only one way, model mates are reasonably likely. A solver should then search for play which will purify the remaining squares, remembering that sacrifice is frequently used to economize the White force."
"The position has a model-mate look; six of the squares adjoining the Black K are only once controlled; no other theme seems likely, from the lay-out of the pieces, which show little possibility of Black strategy. A well-known type of model is seen to arise, if the White R, abandoning his control (doubled by a White P) on c2, can mate on the fourth rank, provided that the Q's control of d5 can be abolished. The try 1 Re3 is soon given up, for 2 Re4, while it shuts off the Q's control of d5, is by no means a pure mate, the B and N holding squares controlled by the R. We come to the Q; how can we abolish her? It is soon seen that Qh4+ achieves our aim, and this may be taken to be the second-move threat. The key must be 1 Rf3, with a model mate after the Q sacrifice, by Rf4. The White P on a4 confirms a R key, for its purpose must be the guard of b5, when the K moves out."
1 Rf3 threatening 2 Qh4+ gxh4 3 Rf4#
1 Rf3 Bxc4 2 c3+ Kxd5 3 Rf6#
Nxc4 2 Rd3+ Bxd3 3 c3#
Bxf3 2 Qa1+ Kxc4 3 Ne3#
Kxc4 2 Rf4+ gxf4 3 Qe4#
Sam Loyd's views on the relative difficulty of four-move problems conflict with Kenneth S. Howard's and John Nunn's views.
Howard: "The usual four-move problem is often easier to solve than a complex three-mover. Because of the great constructional difficulties involved, only a few outstanding composers have the technical skill and patience to construct elaborate four-movers with several complex variations. So ordinarily the four-move problem is either a dainty miniature or a strategic composition designed to illustrate some strikingly thematic line of play."
Nunn: "It might be thought that the difficulty of a problem increases in proportion to its length, but fortunately this isn't so. Few long problems are as difficult as a tricky three-mover and the great majority are much simpler. The reason is that the composer must ensure the problem is sound, so in many long problems, Black has an enormous material advantage. This compels White to keep making one-move threats to prevent Black's extra material coming into play. Consequently, the solver can often narrow the search down to a few moves with no more than a glance at the position."
In general, the same methods of solving used for three-movers may be applied to four-movers.
This is a brilliant example of a four-mover with a single thematic line. The solver will see that black can check on his second move with rook or bishop, if not forced to give immediate attention to some threat by white. Then the isolated position of the white queen suggests that she must find some way to get into play. This limits the choice of possible white moves to consider. Once the correct keymove is tried, the continuations will be relatively easy to find. Ordinarily, a threat of mate in less moves than the stipulated number is regarded as a defect. But here the threat of immediate mate that occurs after both white's first and second move is not such a defect, since the threats are an inherent part of the theme.
1 Bf6 (threatening 2 c3#) 1...Kg6 2 Be5 (threat 3 c3#) 2...Kf5 3 Bd4 Ke4 4 c3#
For our last problem, we will look at an 'unorthodox' problem by Raymond Smullyan, with the analysis being by John Nunn from his book, Solving in Style.
Where is White's king? In the course of play, White's king was accidentally knocked off the board. What is its correct square? We cannot assume that it is White's move. If it were White's move, his king would have to be on b3, or else Black's king would be in check, but then Black has no previous move, since he cannot lift both checks with a single retraction. So it is Black to move, what has White just played? Since the bishop could not have moved to a4, it must have been Kb3-? or Kb3x?. The only way to give double check without moving one of the checking pieces is by means of an en passant capture. So Black must have played b4xc3 en passant in reply to c2-c4 by White. So the last move was Kb3xPc3 and the king stands at c3 in the diagram.
I hope that both novice solvers and more experienced solvers have learned something from my article. In my next article, I will be taking a similar approach, distilling the wisdom of great composers, to now learn how to compose chess problems. Meanwhile, I am still hoping to revive the solving ladder. The missing data for the Solving Ladder is from the tenure of Dr. Steven Dowd. If you still have your original e-mails, you can send them to me at firstname.lastname@example.org for scoring, and/or you can send me an honest estimate or calculation of your score during that period. That would include not only Dr. Dowd's CLO columns but also any of his Problem of the Week postings at www.chessproblem.net. That is where I will be hosting the problems that will be used for scoring purposes.