Square Strategy

All chess moves involve two basic effects: the departure from a square, and the arrival on a square. These concrete effects of a move underlie most of what problemists would call strategic ideas, such as line opening and closing (that is, a piece’s departure from/arrival on a square opens/closes a line controlled by another piece). Strategy in this problem sense also includes, besides the various forms of line play, some motifs that specifically relate to squares. The main examples of the latter are (1) square-vacation, in which a piece’s departure from a square enables a friendly piece to occupy it, and (2) square-obstruction, in which a piece’s arrival on a square prevents a friendly piece from occupying it. Such strategic effects are sometimes developed as a problem’s theme, meaning they recur in an interesting way across multiple variations.

The oft-seen device of self-block, where the occupation of a flight by a black piece prevents the black king’s escape to that square, is a special case of square-obstruction. In Problem 103, one of the most celebrated two-movers, eight self-blocks are achieved, a record number of such variations. The key 1.Rc8! waits for Black to commit the errors: 1…dxc6 2.Rd8, 1…d6 2.e6, 1…e6 2.Qe4, 1…fxe5 2.Qxd7, 1…Sxc6 Sc7, 1…Sc5 2.Sxb4, 1…Sd4 2.Sf4, and 1…Rd4 2.Sc3. The non-blocking black moves lead to good by-play, 1…S4-else 2.e6, 1…S3-else 2.Ra5, 1…R-else 2.Be4, and 1…c3 2.Bxb3. This problem is in fact a mutate, with set mates provided for all of Black’s moves in the diagram; two of these set variations have been changed by the key: 1…dxc6 2.Rd7, and 1…Sxc6 2.Rxd7. Self-blocks are the only type of black square-obstruction that can be obtained in a two-mover, because of its short length of play.

In the more-mover 104, White seeks to give a battery mate on the h-file by moving the rook to an unguarded square, but careless attempts to do so would fail due to the harassing black knights, e.g. 1.Rh3? Sg5! 2.Rh4 Sg6, or 1.Rh4? Sg6! 2.Rh5 Sh4/Sg5. To mate in four moves, White must manipulate the black pawn into obstructing the squares needed by the knights. 1.Rh5! g6 2.Rh4 – now correct since 2…Sg6 is no longer an option, 2…g5 3.Rh3 – similarly playable now that 3…Sg5 is precluded, 3…g4 4.Sxg4.

Problem 105 demonstrates square-obstruction by both White and Black. White has two natural ways to start, 1.Bd8 to threaten 2.Bxf6, and 1.Sd8 to threaten 2.Sf7. Black’s only defences to these moves are, respectively, 1…Sd5 to cover f6, and 1…Bd5 to cover f7. Both of these defences occur on d5, so the two black pieces will hinder each other when either plays to that square. However, after 1.Bd8? Sd5!, White cannot exploit the disabling of …Bd5, because the try move itself has blocked the vital square of d8, ruling out the continuation 2.Sd8. Similarly, 1.Sd8? is refuted by 1…Bd5!, when White cannot proceed with 2.Bd8 to take advantage of the impeded …Sd5. Therefore the problem shows a mutual obstruction between a pair of white minor pieces, as a weakness that allows a similar mutual obstruction between Black’s minor pieces to occur, with impunity. The solution is 1.Rg6!, which threatens 2.Rxf6 and 3.Rf8. The thematic defences work against the threat, but now their obstruction errors are exploited: 1…Bd5 2.Bd8 and 3.Bxf6, and 1…Sd5 2.Sd8 and 3.Sf7.

Problem 106 features multiple square-vacations by White, coupled with queen sacrifices. The key 1.Sb6! aims for a knight mate on d5 after the queen has left that square. White is required to give a forcing queen check on the second move, one that doesn’t allow Black to reply with either a check or a guard on d5. Initially only one such queen move qualifies, making it the threat: 2.Qe5+ Sxe5 3.Sd5. The black rook defends by opening the long diagonal for the bishop – 2.Qe5+? Bxe5+!, and depending on where the rook goes, four more square-vacating sacrifices follow. A ‘random’ rook move that relinquishes control of d2, such as 1…Rb3, permits 2.Qd2+ Sxd2 3.Sd5. Black ‘corrects’ the error of unguarding d2 by moving the rook on the rank, but new errors arise when the rook interferes with the second black bishop or the queen, 1…Rc2 2.Qe4+ fxe4 3.Sd5, 1…Re2 2.Qd3+ Bxd3 3.Sd5, and 1…Rf2 2.Qxf3+ Rxf3 3.Sd5. Two secondary variations are 1…Qxe1 2.Qxf3+ Kd2 3.Qc3, and 1…Qxc4 2.Sxc4+ Kf4 3.Qxf3. (Also, 1…Be4 2.Qxe4+, and 1…Qd3 2.Qxd3+.)

Intensive square strategy is brought about in Problem 107, particularly Black’s play which illustrates how a single move can incorporate both vacating and obstructing effects. In this example of the logical style of more-movers, White has a course of action, called the mainplan, that fails to a certain black defence. Here the plan is 1.Kg7 and 2.Sh6 mate, and if played immediately it is refuted by a discovered check, 1…Sxc4+. White accordingly begins with a preparatory manoeuvre designed to neutralise that defence, before proceeding with the mainplan. 1.Bb7! threatens 2.Bxe4 and compels 1…Rxc4 (1…Bf3? 2.h3 leads to a quicker mate), which blocks the square needed by the knight. However, 2.Kg7? is still premature because Black’s rook move has also vacated a square for the knight – 2…Sa4+! (3.Kf7 Bg7 4.Kxg7 a1=Q+!). Instead White continues with 2.Bc8 to threaten 3.Bxd7, inducing 2…Ba4, which obstructs the a4-square. Now 3.Kg7? is too early still because of 3…Sd1+!, using the square vacated by the bishop. Correct is 3.h3, which threatens 4.hxg4 (3…gxh3? 4.Rxg5), and this forces 3…d1=Q, an obstruction that finally incarcerates the knight, and allows 4.Kg7 and 5.Sh6.