The Allumwandlung theme in endgame studies

Promotion play, especially the surprising need for underpromotion, is a popular feature in composed problems. The Allumwandlung theme amplifies this idea and it indicates that all four types of promotion – to queen, rook, bishop, and knight – occur in a problem’s solution. The name comes from a German term meaning total or complete promotion, and it’s often abbreviated to AUW. A composition that demonstrates every kind of promotion is a fine accomplishment regardless of genre, but the theme is particularly impressive when achieved in the endgame study. Online problem databases that enable searches on themes confirm the relative rarity of such studies. Here we will look at two first-rate examples, which show the intensive promotion play with good clarity.

By early 20th century, when the chess composition field began to modernise, problemists have already rendered AUW in genres like directmates and selfmates. But the difficulty of arranging four different promotions in a study was such that many thought it was impossible to do. So when a composer named Harold Lommer pulled off the task in 1933, his work was instantly celebrated and gained a worthy first-prize. In the 1980s, however, a study by Sigurd Clausen that predates Lommer’s was rediscovered, one that produces AUW using a fairly similar mechanism. What’s more, Clausen’s setting is more economical and it isn’t flawed by a piece-capturing first move as in Lommer’s. Alas, the earlier problem was cooked – spoiled by an alternative solution. Fortunately, though, it was curable with a small and clever adjustment to the position, and this corrected version is diagrammed below.

White is in a precarious situation because of the black queen’s mating threats, and must start by giving checks. The goal is to win the queen with a discovered attack from the bishop, by promoting the f7-pawn with check (without losing the promoted piece). Once the queen is captured, however, Black has the potential to induce stalemate by sacrificing the rook. To forestall this kind of defence, White must carefully choose the right promoted piece in each variation.

White begins with 1.g7+ (not 1.e7+? which fails to 1…Kxe7 2.f8=Q+ Kxf8 3.g7+ Rxg7 4.Bxh5 Rg1+), forcing 1…Kxg7 since 1…Ke7 allows 2.f8=Q+ Kd8 3.Bxh5+. Now 2.f6+ pushes the king away from defending the promotion square, given that 2…Kf8 would lose the rook immediately to 3.e7+ Rxe7 4.fxe7+ Kxe7 5.f8=Q+ Kxf8 6.Bxh5, with a won bishop ending. The black king has five other moves, of which four generate the thematic variations by requiring White to promote to different pieces:

(1) 2…Kxf6 3.f8=Q+! Here 3.f8=R+? loses, e.g. 3…Rf7 4.Rxf7+ Ke5 5.Rf1 Qxe8. 3…Kg5 4.Bxh5 is a straightforward queen vs rook win; Black has no stalemating chances because of the mobile king. Or 3…Rf7 4.Qxf7+ Qxf7 5.Bxf7 wins.

(2) 2…Kh8 3.f8=R+! If 3.f8=Q+? Kh7, White has no more useful checks and must play 4.Bxh5, which enables 4…Rxa6+ 5.Kb1 Ra1+! 6.Kxa1 stalemate. By promoting to a rook, White gains a tempo by checking but leaves h6 unguarded for the king, so that after 3…Kh7 4.Bxh5 Rxa6+ 5.Kb1, 5…Ra1+ wouldn’t work. White wins easily on material, e.g. 5…Rxe6 6.Bd1 Kg6 7.Bxb3.

(3) 2…Kh6 3.f8=B+! If 3.f8=Q+? then 3…Kh7! transposes to the stalemating sequence. Similar to the rook-promotion variation, the promoted bishop gives a check without controlling h8, meaning there’s no stalemate defence after 3…Kh7 4.Bxh5 Rxa6+ 5.Kb1. Alternatively, Black can win a bishop with 3…Kg5 4.Bxh5 Rxa6+ 5.Kb1 Kxh5 (5…Rxe6 6.Bd1 Re1 7.Kc1 Kxf6 8.Bxb4 tablebase win), but White’s advanced pawns backed by the other bishop are too strong, e.g. 6.Bxb4 Rxe6 7.f7 Rf6 8.f8=Q Rxf8 9.Bxf8.

(4) 2…Kh7 3.f8=S+! Another essential check to prevent the queen mate. As in the bishop-promotion line, Black can capture the light-squared bishop but that won’t halt the white pawns, e.g. 3…Kh6 4.Bxh5 Rxa6+ 5.Kb1 Kxh5 6.e7 Ra8 7.f7. Or 3…Kg8 4.Bxh5 Rxa6+ 5.Kb1 Ra5 6.Sd7 Rxh5 7.f7+ Kh7 (7…Kg7 8.f8=Q+) 8.Sf6+ wins.

The remaining king move, 2…Kg6, is subsidiary although it prompts another underpromotion, 3.f8=R+ (3.f8=Q+? Kh7! as before), e.g. 3…Kg5 4.Bxh5 Rxa6+ 5.Kb1 Rxe6 6.Bd1 wins.

In this study, a single white pawn executes the AUW in separate lines of play (consistently promoting on the second move). The thematic promotions thus occur in parallel, resulting in four variations of equal importance. Another way of presenting AUW involves multiple pawns that promote sequentially in one principal variation, as illustrated in the next problem.

Black has numerous mating threats, the most pressing of which are …Qf6+/Qxg7+. Also dangerous is …Ka3 preparing for …Sb3, a scheme that manages to refute 1.Sc1+? with a forced mate, thus 1…Ka3 2.f8=Q+ Qd6 3.Qxd6+ cxd6 4.Se4 Bf6+ 5.Sxf6 Sb3+ 6.Sxb3 Kxb3 and 7…c1=Q mate is unstoppable. The key 1.f8=Q! defuses such threats while aiming for 2.Qb4 mate. With the white queen observing a3, Black can’t afford to play 1…Be1 2.Sc1+ Kc4 or 1…c1=Q+ 2.Sxc1+ Kc4, which would release the white king and leave Black hopelessly down in material. Strongest is 1…Qd6, which maintains the attack even after the queen exchange, 2.Qxd6 cxd6, because a3 is accessible again, not to mention the black bishop’s ability to threaten mate on the long diagonal.

To deal with the main threat of 3…Ka3 4.Sc1 Sb3+ 5.Sxb3 Kxb3 and 6…c1=Q, White has to eliminate the a5-knight. However, 3.a8=Q? runs into 3…Bxg5 4.g8=S Bf6+ 5.Sxf6 Ka3 6.Qxa5 (6.Sc1? still loses to 6…Sb3+) c1=Q+ 7.Sxc1 stalemate! Correct is 3.a8=R! Bxg5 4.g8=S! (Notice a subtlety of this white move which, besides holding f6, also opens the long diagonal for a later promoted piece on h8. Hence not 4.Rf8? Be3 and White can’t prevent 5…Bd4+ 6.Sc3 Bxc3 mate.) Now that 4…Bf6+ 5.Sxf6 Ka3 6.Rxa5 c1=Q+ 7.Sxc1 fails to stalemate, with 7…Kb4 available, Black tries 4…Ka3 5.Rxa5 Be3. The threat of 6…Bd4+ 7.Sc3 Bxc3 can only be parried by promoting the h-pawn, but 6.h8=Q? Bd4+ 7.Qxd4 c1=Q+ 8.Sxc1 forces another stalemate. Therefore White chooses 6.h8=B!, thwarting 6…Bd4+ 7.Bxd4 c1=Q+ 8.Sxc1 by again leaving b4 unguarded, and Black has no more counterplay.

Even among the few studies that bring about white AUW, this is a remarkably compact example. The main variation goes for only six moves, of which obviously four are taken up by the white promotions, leaving just two “extraneous” moves. Black’s resourceful defence is also noteworthy; the stalemating plans entail three sacrifices in the line 3.a8=Q? Bxg5 4.g8=S Bf6+ 5.Sxf6 Ka3 6.Qxa5 c1=Q+ 7.Sxc1, and two in 6.h8=Q? Bd4+ 7.Qxd4 c1=Q+ 8.Sxc1 – all of which underline the foresight of White’s underpromotion play.