Even more adventures with endgame tablebases

Endgame tablebases are remarkable software that effectively plays perfect chess in any position with up to seven pieces. As such they are an invaluable analytical tool and in two previous Walkabouts (Adventures and More Adventures), I demonstrated some of their capabilities. Besides analysing existing endgames, tablebases could also assist in the creation of new positions with intriguing and even study-like play, and last time we looked at two examples of mutual zugzwang (MZ) extracted from the Syzygy tablebases. For this final part of the series, I have picked three more special cases of these paradoxical situations, again from the massive MZ files produced by Árpád Rusz. The first instance lends itself to conversion to an actual endgame study with some neat and precise variations. The other two diagrams are almost unbelievable in exemplifying double zugzwang, because in these positions both sides are able to promote a pawn safely, meaning each player would prefer it if the other side were to queen first!

In a mutual zugzwang position, each player would be worse off if given the turn, because every legal move of each side entails some exploitable weakness. The MZs presented here (unlike those in the last instalment) are not full-point ones but of the more standard type: if White is to move, Black would be able to draw, yet if Black is to move, White would have a forced win. In the analysis provided, unique drawing and winning moves, by Black and White respectively, are given with an exclamation mark. Further, the diagrams are accompanied by links to the Syzygy tablebases that will open with the positions already set up; hence you can easily follow the main variations on that site and also explore any lines not covered. Such Syzygy links have been added to the two earlier Adventures columns as well.

In the first diagram, White seems to have the advantage despite being a pawn down, because of the advanced a-pawn supported by the king. But an immediate attack with 1.Kb7? or 1.a7? only draws, largely due to the centred black king which has flexible defences. Black’s connected passed pawns are of course dangerous too and after, say, 1.Sf4? h4!, White even loses with any continuation except for the drawing 2.Kb7 or 2.a7. [Syzygy TB Link]

The correct opening 1.Sh4! places the knight in a less exposed spot and brings about the MZ position. Imagine if it’s White to move again [Syzygy TB Link], then surprisingly no win is possible: either 2.Kb7 Kc5! 3.Kxa8 (3.a7 Sb6) 3…Kb6! 4.a7 Kc7! or 2.a7 Ke5! 3.Kb7 Kd6! 4.Kxa8 Kc7! would trap the king and leave White unable to progress, as the knight is stuck holding off the black pawns. Or if White tries 2.Sf5+ then 2…Ke5! gains a vital tempo by threatening the knight, e.g. 3.Sh4 (3.Sg3? loses to 3…h4!) 3…g3 4.Kb7 Kf4! 5.Kxa8 Kg4! 6.Sg2 h4 7.Kb7 h3! draws.

With Black to play after 1.Sh4!, the king on d4 is forced by zugzwang to abandon its position where it has quick access to both c7 (via e5) and b6 (via c5), two crucial squares for defence as seen above. (1) 1…Ke5 2.Kb7! Kd6 3.Kxa8! Kc7 4.Ka7! g3 5.Sg2! h4!? By sacrificing the pawn, Black creates stalemating chances. 6.Sxh4! Kc8 7.Kb6 Kb8 8.Sg2. Not 8.a7+? Ka8 9.Sg2 =. 8…Ka8 9.Se3 (9.Sf4 is a minor dual that wins similarly.) 9…Kb8 10.a7+ Ka8 11.Sd5 g2 12.Sc7 mate. (2) 1…Kc4 2.a7! Kb4 3.Kb7! Kc5 4.Kxa8! Kb6 5.Kb8! wins. (3) 1…g3 2.Sf5+! Ke5 3.Sxg3! h4 and now a white dual follows with two “exact” ways of stopping the h-pawn: (a) 4.Se2 h3 5.Sg1! h2 6.Sf3+! or (b) 4.Sh1 h3 5.Sf2! h2 6.Sg4+! The three thematic try moves – Kb7, a7, and Sf5+ – in the MZ position suitably reappear as White’s initial moves in the three main variations.

I will finish this three-part series with two complex positions that may not be fully comprehensible, but which are fascinatingly counter-intuitive. Each setting contains five passed pawns, most of which seem free to push forward. That includes two pawns of different colours that are ready to promote, and either could do so without fear of losing the new queen to any simple tactics. Yet the outcome for each side would be better if the other were to move and could promote first. These MZ situations thus represent a sort of antithesis to the pawn race!

What’s happening here is that when the two players promote in turn, that leads to another MZ in which both queens (as well as every other piece) would prefer to stay put. The queens are already ideally placed because they control various critical squares in different directions. Now whichever queen is compelled to move first, it cannot maintain its “focus” on all of these squares, and this loss of control is immediately punished by the other side. The numerous squares that must be covered by the queens, for both offensive and defensive purposes, account for the complexity of the play. Nonetheless, in the given variations we see general principles at work that are quite understandable for such queen and pawn endings. Black, who is a pawn down, typically aims for perpetual check and sometimes draws by winning one of the two white pawns. White’s chief weapon against perpetual check is to force a queen exchange that will leave a won pawn ending. However, the deciding factor in such a simplified pawn ending is not so much White’s extra material but how advanced the remaining pawns are, and if White is not careful, Black could even win with a better placed pawn.

In the first case below, after the two promotion moves, both queens are focusing on two key squares, e8 and b4. Either queen could give a strong check on e8 if it’s left unguarded, while the white queen has another check on b4 that’s prevented by the black promotee. Another important square is c5, defended by the white queen and black king against each other.

White to play: Black forces a draw. [Syzygy TB Link] 1.f8=Q e1=Q (1) 2.Qf6. Although this queen move gives up access to b4/e8, it produces new threats on the 6th rank, besides other compensations. But let’s consider the alternatives first:

(2) 2.Qd6 Qe8+! 3.Kc7 Qf7+! 4.Kd8 Qg8+! 5.Kc7 Qf7+ perpetual check, or White could even lose if the queens are exchanged, because the c4-pawn is unhindered, e.g. 6.Qd7+? Qxd7+! 7.Kxd7 c3! 8.d6 c2! 9.Ke8 c1=Q! 10.d7 Qc6 wins.

(3) 2.Qf7 Kc5 (2…c3 also draws) 3.Qd7. This move keeps guarding d5 and e8 and threatens 4.Qc6+, but after 3…Qe4, White has to play precisely for the next five moves to avoid losing (in contrast, 3…Qe5? loses to 4.Qc6+!). 4.Qc6+!? Kd4 5.a4!? c3 6.a5!? c2 7.a6!? Qf5+ 8.Kb7!? Qxd5 9.Qxd5+ Kxd5 10.a7 c1=Q 11.a8=Q =.

(4) 2.Kb7 Qa5 (2…Qb1 also draws) 3.Qe8+ Kc5 4.Qc6+ Kd4 5.d6 c3! 6.d7 c2!! 7.Qd6+ (7.Qxc2 Qb5+! 8.Kc7 Qa5+! 9.Kc8 Qa8+ 10.Kc7 Qa7+ 11.Kd6 Qxa3+! 12.Ke6 Qe3+! 13.Kf7 Qf4+! 14.Kd8 Qe5+! 15.Kd8 Qa5+! 16.Qc7 Qa8+! 17.Ke7 Qe4+! perpetual check) 7…Ke4!! 8.Qe7+ Kf3!! 9.d8=Q Qxd8 10.Qxd8 c1=Q =. This terrific sequence – can you work out why 7…Ke4!! and 8…Kf3!! are forced? – is unfortunately devalued by the 2…Qb1 dual.

(5) 2.d6 Qe6+ (2…Qe4/Qh1 also draw) 3.Kc7 c3! 4.Qb8+ Kc4! 5.Qb4+ Kd3! 6.d7 Qe5+! 7.Kc8 Qf5! 8.Kc7 Qe5+! 9.Qd6+ Qxd6+! 10.Kxd6 c2! 11.d8=Q c1=Q! 12.Ke5+ Ke2!! =.

After 2.Qf6, White’s main threat is 3.Qc6+. 2…Qe8+! Not 2…c3? 3.Qc6+! Ka5 4.d6 c2!? 5.d7 (5.Qxc2? Qe6+ 6.d7 Qc6+ 7.Qxc6 =) 5…c1=Q 6.d8=Q mate. 3.Kc7 (3.Kb7? actually loses to 3…Qd7+! 4.Kb8 Qxd5). Now White threatens M2 with 4.Qb6+, and thanks to the queen’s placement on f6, Black is out of useful checks. However, Black still has one way to draw: 3…c3!!, a decoying sacrifice. Not 3…Qe3? 4.Qc6+! Ka5 5.Qa8+ Kb5 6.Qb7+ Kc5 7.Qb6+, or 3…Kc5? 4.Qc6+ Qxc6+ 5.dxc6 c3 6.Kb7 c2 7.c7 c1=Q 8.c8=Q+, or 3…Ka4? 4.d6! Qe3 5.d7! wins. 4.Qxc3 or 4.Qb6+ Kc4! 5.d6 c2 =, or 4.d6 Qc6+ 5.Kb8 c2 =. 4…Qe7+ 5.Kc8 Qe8+ 6.Kb7 or 6.Kc7 Qe7+ perpetual check. 6…Qd7+ 7.Qc7 Qxd5+! draws as White’s last pawn is too far back to pose a threat.

Black to play: White forces a win. [Syzygy TB Link] 1…e1=Q 2.f8=Q (1) 2…Ka4. The king aims for an escape to b3, and the queen on e1 is also allowed to maintain its focus. Other plausible moves by Black are:

(2) 2…Qa5 3.Qe8+! Kc5 4.Qc6+! Kd4 5.d6! c3 6.d7 Qf5 7.Kb7 Qf7 8.Ka6 Qf1+ 9.Ka7 Qf8 10.Qb6+ wins.

(3) 2…Qc3 3.Qe8+! Ka5 4.d6! Qf3 5.Qe5+! Ka6 (5…Ka4 6.Qc5! wins) 6.d7! Qc6+ 7.Kd8 c3 8.Ke7! c2 9.d8=Q! c1=Q 10.Qea5+! Kb7 11.Qda8 mate.

(4) 2…Qe4 3.Qb4+! Ka6 4.Kc7 Qh7+ 5.Kc6! Qg6+ 6.d6! Qe4+ 7.Kc7! (7.Kc5? Qf5+! = or 7.Kd7? Qb7+! =) 7…Qh7+ 8.d7 Qh2+ 9.Qd6+ wins.

(5) 2…c3 3.Qb4+! Ka6 4.Qa4+ Kb6 5.Qc6+ Ka5 6.d6 Qe6+ 7.Kc7 Qf7+ 8.d7 c2!? 9.Qb6+ (9.Qxc2? Qc4+! 10.Qxc4 =) 9…Ka4 10.Qb4 mate.

Black has multiple threats after 2…Ka4, including 3…Qa5 = and 3…Kb3 =, but c5 is left unguarded and b4 has become a potential mating square. 3.Qc5! Not 3.d6? c3 4.d7 c2! 5.Qf4+ Kxa3 6.d8=Q c1=Q+ =. 3…Qe8+ or 3…Kb3 4.Qb5+ Kxa3 (4…Kc3 5.Qb4+) 5.Qxc4! wins. Now White must choose carefully between 4.Kb7!! and 4.Kc7? The latter fails to 4…Qb5! 5.Qxb5+ Kxb5! 6.d6 c3! 7.d7 c2! 8.d8=Q c1=Q+! = when Black promotes with check. 4…Qb5+ or 4…Qd7+ 5.Ka6 Kb3 6.Qb4+! Ka2 7.Qxc4+ Kxa3 8.Qc5+ Ka2 9.Qa5+ Kb3 10.Qb5+, or 4…Kb3 5.Qb4+! Kc2 6.Qxc4+! wins. 5.Qxb5+! Kxb5 6.d6! c3 7.d7! c2 8.d8=Q! c1=Q and White has two neat ways to pick off the black queen. 9.Qb6+ (or 9.Qe8+ Ka5 10.Qa8+! Kb5 11.Qa6+ Kc5 12.Qc6+!) 9…Kc4 or 9…Ka4 10.Qb4 mate. 10.Qc6+ wins.

The final position is even more intricate. After both sides have promoted, the white queen guards h8 and e5, two invading points for the black queen. The latter is ironically well-placed in the corner, because it further threatens checks from the a-file when the black king moves. For instance, suppose Black is to move and plays 2…Kb6 (threatening 3…Qa8+/Qa6+), White’s only winning reply is 3.Qd8+!, taking advantage of the check to gain a tempo. But that means d8 is another key square that the white queen has to keep focusing on. If White starts instead and chooses, say, 2.Qe2+, then d8 is no longer accessible and Black draws uniquely with 2…Kb6!

White to play: Black forces a draw. [Syzygy TB Link] 1.e8=Q a1=Q (1) 2.Qh5. This move poses Black the most difficulties (and even defeats 2…Kb6 in a new way). Here are the alternatives:

(2) 2.Qd7 Qh8+! 3.Kc7 (or 3.Qd8 Qe5! transposes to the next line) 3…Qe5+! 4.Qd6 Qg7+ perpetual check.

(3) 2.Qd8 Qe5! 3.b5+!? Qxb5! (3…Kxb5? 4.Kb7! Qe4 5.Qb6+! Ka4 6.Kb8! f3 7.c7! Qf4 8.Qc6+ Kb3 9.Ka8! f2 10.c8=Q f1=Q 11.Qc2+ Kb4 12.Q8c5 mate) 4.c7 f3 5.Qf6+ Qb6 6.Qxf3 Qe6+! 7.Kb8 Qb6+! 8.Kc8 Qe6+! 9.Kd8 Qd6+ perpetual check.

(4) 2.Qe2+ Kb6! 3.Qf2+ Ka6! (3…Kxc6? 4.Qc5 mate) 4.Qxf4 (or 4.c7 Qh8+! =) 4…Qh8+! 5.Kd7 Qg7+ 6.Kd6 Qg6+! 7.Kd5 (7.Kc5 Qh5+! =) 7…Qd3+! 8.Qd4 (8.Kc5 Qb5+! 9.Kd6 Qb8+ 10.c7 Qb6+! 11.Kd7 Qb5+! 12.Ke7 Kb7! =) 8…Qb5+ 9.Kd6 (9.Qc5 Qd3+! perpetual check) 9…Qxc6+! 10.Kxc6 =.

(5) 2.c7 Ka7 (2…Kb6 also draws) 3.b5 Qb2! 4.Qh5 Qb4!! 5.Qf5 f3! 6.Qxf3 Qxb5! 7.Qe3+ Ka6! 8.Qa3+ Kb6! 9.Qd6+ Ka7! (9…Ka5? 10.Qe6 wins) 10.Kd8 Qg5+! perpetual check.

(6) 2.Kb8 Kb6! (threatens M2 with 3…Qa7+!) 3.Qd8+!? (unique move for White to salvage a draw) Kxc6! 4.Qc7+ Kd5! = (4…Kb5? 5.Qc5+! Ka4 6.Qa5+ wins).

In the main variation, 2.Qh5 carries these advantages: the queen maintains its defence of h8 and e5, and targets the mating square a5; further, White now threatens 3.c7/Kb8/Qh7. But Black handles all of these complications with 2…Qa4!, threatening 3…Qxc6+. Not 2…Kb6? 3.Qc5+! Ka6 4.b5+ Ka5 5.Qa7+, or 2…Qa3? 3.Qh7 Qxb4 4.Qb7+! Ka5 5.Qa7+Kb5 6.c7 Qf8+ 7.Kb7! Qf7 8.Kb8 wins. 3.Qc5 or 3.c7 Qxb4! 4.Qh6+ Ka7! 5.Kd7 Qb5+ 6.Qc6 Qf5+! perpetual check. 3…Qb5! Not 3…f3? 4.Kc7! Qb5 5.Qd4!! wins by threatening 6.Qa1+. 4.Qd6 or 4.Kc7 Qxc5! 5.bxc5 Ka7! 6.Kd7 f3! 7.c7 f2! 8.c8=Q f1=Q! 9.Qc7+ Ka8! 10.Qa5+ Kb8! (10…Kb7? 11.c6+! wins) 11.Qb6+ Ka8 12.Kc7 Qf7+ perpetual check, or 4.Qxb5+ Kxb5! 5.c7 f3! 6.Kd7 f2! 7.c8=Q f1=Q! 8.Qb7+ Ka4! = (8…Kc4? 9.Qa6+! wins). 4…f3!! Pushing the pawn is the only way to counter White’s triple threats of 5.c7+/Qd7/Kc7. Not 4…Qf5+? 5.Kb8! Qb5+ 6.Ka8! f3 7.c7+, or 4…Qb6? 5.Qd3+ Qb5 6.Qd7 f3 7.Qb7+! wins. 5.c7+ Ka7!, threatens 6…Qe8+. Not 5…Qb6? 6.Qxb6+ Kxb6 7.Kb8! f2 8.c8=Q! f1=Q 9.Qb7 mate. 6.Qd4+ or 6.Kd8 Qg5+! perpetual check. 6…Ka6! Not 6…Ka8? 7.Qa1+! wins. 7.Qe4, White guards e8 and threatens M2 with 8.Qa8+. Or 7.Qa1+ Kb6! 8.Qa5+ Qxa5! 9.bxa5+ Kxa5 10.Kd7 f2! =. 7…Ka7! 8.Qe3+ Ka6! 9.Qa3+ or 9.Kd8 Qd5+! 10.Ke7 Kb7! =. 9…Kb6! 10.Qe3+ or 10.Kb8? loses to 10…Kc6+! 10…Ka6! 11.Qe6+ Ka7! Positional draw as the white queen is tied to defending e8 and cannot dislodge the aggressively-placed black king.

Black to play: White forces a win. [Syzygy TB Link] 1…a1=Q 2.e8=Q (1) 2…Qb2. Surprisingly this is the queen defence that requires the most precision from White, because it rules out 3.b5+, a white dual in some variations.

(2) 2…Qd4 3.c7 (3.b5+ also wins) 3…Ka7 (3…Qxb4 transposes to the main line) 4.Qa4+! Kb6 5.Qa5+ Kc6 6.Qc5+ wins.

(3) 2…Qf6 3.c7 (3.b5+/Qe2+ also win) 3…Kb6 4.Kb8 Qd6 5.Qc8 Qc6 (both queens have a potential mate on b7, and White’s next two moves are needed to avoid actually losing) 6.b5! Qd5 (6…Kxb5 7.Qb7+ wins) 7.Qa6+! Kc5 8.c8=Q+ wins.

(4) 2…Qa4 3.Qe4 (3.Kd7/Qd7 also win) 3…Qb5 4.c7 (threatens M2 with 5.Qa8+) 4…Ka7 5.Qd4+! Ka6 6.Qa1+ Kb6 7.Qa5+ Qxa5 8.bxa5+! Kxa5 9.Kd7 wins. This is almost identical to a sub-variation of the White-to-play main line above. The sole difference is the placement of the f-pawn, f3 vs f4, and for Black that’s the difference between a draw and a loss!

(5) 2…Kb6 3.Qd8+! Ka6 (3…Kxc6 4.Qd7+! Kb6 5.Qb7 mate) 4.Kb8 Qe5+ 5.Ka8! f3 6.Qc8+! Kb5 7.Qb7+ Kc4 8.c7! Qa1+ 9.Kb8 Qe5 10.Qxf3 Qb5+ 11.Qb7 Qe5 12.Ka7 Qe3+ 13.Qb6 Qe7 14.Qc5+ wins.

(6) 2…Kb5 3.Qh5+! Kxb4 4.Qf5 Qa8+ 5.Kd7! (5.Kc7? Qa5+! =) 5…Qa7+ 6.c7 Qd4+ 7.Ke8 Qe3+ (7…Qh8+ 8.Qf8+ wins) 8.Kf8 wins.

(7) 2…f3 3.c7 (3.Qh5 also wins) 3…Kb6 4.Qe3+ Ka6 (4…Kb5 5.Qc5+ Ka4 6.Qa5+) 5.Kb8 Qh8+ 6.c8=Q+ wins.

The black queen preserves its options on the long diagonal with 2…Qb2, and the move also threatens 3…Qxb4. But since the piece can no longer attack on the a-file, …Kb6 has become a weak move that doesn’t refute 3.c7! Now White threatens quick mates with 4.Qc6+/Qa4+, and the best response is still 3…Qxb4, or 3…Kb6 4.Qf8 Qe5 5.Qc5+! wins. 4.Qc6+! Not 4.Qe6+? Ka7! 5.Kd7 Qd4+ 6.Qd6 Qg7+! perpetual check. 4…Ka7 5.Kd7! Qd4+ 6.Ke6!! The intrepid white king finds a way to deal with the menacing black queen… Not 6.Qd6? Qg7+! 7.Kc6 Qc3+ 8.Qc5+ Qxc5!+ 10.Kxc5 Kb7! = or 6.Ke7? Qe5+ 7.Kf7 Qf5+ perpetual check. 6…Qe3+ 7.Kf6 Qd4+ 8.Kf7 and ironically Black’s f4-pawn has helped to create a safe haven for the white king against further checks. 8…f3 9.c8=Q! wins.