Deciphering a complex selfmate

Selfmate problems involve a curious objective: White compels Black to deliver mate, while the latter side resists doing so. Because of the counter-intuitive aim, I tend to focus on the more accessible two-move examples on this site, as in the Problem World introduction to the genre. The likewise short selfmates picked for the Weekly Problems are quite popular with regular solvers, who don’t seem troubled by them at all. Therefore I thought it’d be an interesting change to discuss a complex three-mover and describe the challenging process of solving one. Selfmates are not my forte and it was hard to wrap my head around the one I chose, composed by the great Bill Whyatt. But fortunately, I managed to crack the problem (after a couple of hours!) and it turns out to be a brilliant piece of work.

In the initial position, both kings are confined but the mobile black force suggests that White won’t be utilising zugzwang to induce the mates. As is common in selfmates, Black has a couple of batteries aimed at the white king: B + R on a light diagonal and R + P on the c-file. Hence a likely plan is to force these batteries to open and mate, by means of a deflecting queen check on d4 or e5 (not f5 because of …Bxf5). We also note that Black has a strong checking move, 1…c1=Q+, that obliges a time-wasting reply, 2.Qxc1 (by contrast, the alternative checks 1…Sxa5? and 1…Sxd6? mate immediately and so are weak moves). Consequently, we may expect the key-move to unguard c1 and thus turn 1…c1=Q? into a mate – either by shifting the queen from h6 or by interfering on its diagonal. Only the former option, however, would help to bring the piece in line with the deflection squares d4 and e5, particularly 1.Qg7 or 1.Qh8.

After either of these potential keys by the queen, White apparently threatens a random move by the f6-bishop followed by 3.Qxd4+ Rxd4/cxd4 or 3.Qe5+ Rxe5. Remarkably, though, there’s no safe landing square for the bishop to make this an effective threat. If 2.Bxd4? or 2.Bg5?, the piece would spoil the black promotion mate and turn 2…c1=Q+! into a strong defence again, forcing 3.Bc3 or 3.Bxc1. And if 2.Be7? or 2.Bd8?, the bishop would guard against a set knight mate and thus allow a similar disruptive check, respectively 2…Sxd6+! 3.Bxd6 and 2…Sxa5+! 3.Bxa5. Could 1.Qg7 or 1.Qh8 entail a different threat not starting with a bishop move? Yes, it turns out that either queen move, by unguarding e3, will threaten 2.f3+ Ke3 3.Bxd4+ Rxd4/cxd4 – a hard-to-see sequence that temporarily frees the black king.

Ignoring which queen move is correct for now, how does Black handle the threat once 1.Qg7/Qh8 is played? The most obvious defence is 1…Bxf2, removing the threat-pawn, but in doing so Black creates a flight on e3 and permits 2.Rxf2+ Ke3 3.Bxd4+ Rxd4/cxd4. This is very similar to the threat-play and hence a minor variation. More interesting is another bishop reply, 1…Bc3, preparing for 2.f3+? Ke3 3.Bxd4+ Bxd4. But this defence closes the c-file and enables White to activate the aforementioned f6-bishop with 2.Bxd4; now that 2…c1=Q no longer checks, it’s useless against the threat of 3.Qe5+ Rxe5. Only 2…Bxd4 counters but it admits 3.Qxd4+ Rxd4/cxd4 instead. Note that here White must avoid the alternative 2.Bg5? because of the strong substitute defence, 2…d3!, which thwarts 3.Qd4+/Qe5+ with 3…Bxd4/Bxe5.

Since the threat-play requires both black batteries to function, Black can also defend by dismantling one of them. Hence 1…Rcxd6 foils 2.f3+? Ke3 3.Bxd4+ with 3…cxd4. The weakness of this rook defence is that it obstructs the black knight’s checking square, thereby making it safe for the white bishop to control it. Now that 2.Be7 cannot be met by a disruptive check, Black cannot prevent 3.Qe5+ Rxe5. The c6-rook has two other defences, 1…Rb6/Rc7, where the latter places the rook under attack by the d6-pawn and so neutralises the threatened battery mate, 3…cxd4. However, both moves block the a5-d8 diagonal and allow White to play 2.Bd8 without covering the knight mate on a5, leading to an unstoppable 3.Qe5+ Rxe5.

Thus far in three thematic variations the f6-bishop has to choose its arrival squares carefully on d4, e7, and d8. Is there a fourth line that requires the bishop to go to g5? Yes, indeed! 1…Sc3 stops the threat by interfering with the e1-bishop, to create a potential flight on b4: 2.f3+? Ke3 3.Bxd4+ cxd4+. Like 1…Bc3, the knight move shields the white king from the 2…c1=Q check, such that White can now afford to control the c-file with the bishop. But here 2.Bxd4? fails to 2…cxd4+ as the white king is still released to b4, so 2.Bg5 is mandatory, followed by 3.Qe5+ Rxe5.

Back to the question of which initial queen move is correct, recall that 1…Rc7 answers the threat by allowing the rear piece of the battery to be attacked by the white pawn. In a similar way, if White starts with 1.Qh8? then Black can let the rook be attacked by the queen with 1…Rc8!, thus disabling the mate after 2.f3+ Ke3 3.Bxd4+ cxd4+; and since this rook move has no exploitable weakness, it refutes the queen try. Therefore the unique key of this first-prize problem is 1.Qg7! No less than four alternative moves by the white bishop are superbly differentiated in the main variations. A lot of the strategies motivating the play is peculiar to selfmates (such as how a black mating move becomes a strong defence only after White has defused the mate). Looking up this outstanding composition in W.A. Whyatt’s Chess Problems by Bob Meadley (No.173), I was astonished to learn that it was his first published three-move selfmate!