If a pawn could “promote” to a pawn… – Part 2

In the Walkabout of 17 Dec. 2017, I presented two endgame studies that utilise an unorthodox promotion rule – namely, a pawn is allowed to remain as a pawn upon reaching the eighth rank. The problems demonstrate the paradoxical idea of such a non-promotion move being the best, i.e. the only move to force a draw or a win. As mentioned at the end of that blog, when my positions were posted on the Mat Plus forum, they sparked an interesting discussion, where problemists referenced precursors or shared their own renditions of the theme. Since that time, a lot of activities have occurred in this area, so here I wish to provide an update and show four new studies, all of which effect the non-promotion move (P=P) with great economy.

A special mention goes to James Malcom and Andrew Buchanan, whose tremendous research has uncovered many fascinating historic problems that feature this type of non-promotion play, known as “dummy pawn” in the literature. As active composers, they have also produced their own versions of the theme in a variety of problem genres. You can check out their discoveries, both of the old and the new, in the Schwalbe problem database; search for the keyword, “dummy pawn”. One particularly notable entry in the database is a study composed by John Beasley. This “White to play and win” problem, published in 1996, means that my own Win study wasn’t the first to accomplish the difficult task (which is distinct from directmates). In fact, John’s version has better construction and play – it contains three deflection variations – though mine does avoid the drastic measure of starting with White in check.

A Draw study that is solved by a P=P key is easier to arrange, obviously because the move facilitates self-stalemate. However, an interesting challenge then is to create the most economical setting of the theme. The minimum number of units required for this seems to be six, but before looking into such positions, I want to revisit the idea of using only pawns. With the assistance of endgame tablebases, can we improve on the eight-unit setting that was seen in the earlier blog? The answer is yes, although the miniature necessitates a second white pawn.

The thematic try 1.f8=Q? fails to 1…d1=Q!, which threatens 2…Ke2 and 2…Qd5+ 3.Qf3 Qxf3. White cannot handle the double-threat without allowing an immediate mate: 2.Qd6 Qf3 (not 2…Ke2+? 3.Qxd1+ Kxd1=), or 2.Qxf2+ Kxf2. Only 1.f8=P! draws as Black cannot stave off stalemate. The try play is simple, but what’s surprising about this setting is that it’s the only sound one possible for the matrix, and hence the problem could be a unique pawns-only miniature. Here’s the Syzygy link for the position, indicating that White loses with any orthodox promotion. Now consider alternative settings for the matrix, such as shifting the f7-pawn to other squares on its rank and likewise for the d2-pawn, and these options can be further combined with placing the h2/h3 pair of pawns on g2/g3. In every case, White can still force stalemate with P=P but that’s rendered pointless because a queen promotion would also draw.

The Draw task has been achieved in various problems with six units, which as mentioned is apparently the fewest possible. The economy record is hence focused on reducing the ranks of the six units deployed. The next two problems, which involve very different schemes, represent the best efforts along these lines.

After 1.h8=Q?, the tempting battery set-up 1…Bf3? allows White to escape with 2.Qa8! (2…Sh4+ 3.Qxf3+ Sxf3=, or 2…Kf2 3.Qa2+). Only 1…Sf4! wins; it shields the king from checks on the f-file while threatening both 2…Bf3 and 2…g2+ 3.Kh2 g1=Q. For example, 2.Qa8 g2+ 3.Qxg2+ Sxg2, or 2.Qh3+ g2+! 3.Kh2 Sxh3 4.Kxh3 g1=Q. White must aim for stalemate with 1.h8=P! Unlike other economical studies showing the theme, here Black is able to release White with 1…Ke2/Ke1; yet White still manages to draw: 2.Kxg2 ~ 3.Kxg3. The post-key play accentuates the paradox: an active white queen would face defeat but the lone white king saves the day.

Andrew’s position contains terrific try play. 1.g8=Q? g1=Q! – Black sacrifices both major pieces – 2.Qxg1 Rf8+! 3.Qg8 Rxg8+ 4.Kxg8 Kg6!, or 2.Qxf7 Qd4+ 3.Kg8 Qd8+ 4.Qf8+ Qxf8+! 5.Kxf8 and the h-pawn carries the day. Black is also unfazed by five white queen checks, in contrast to most miniature settings of P=P where Black aims to preclude such defences. Here Black meets each check with either an immediate mate or a capture that avoids stalemate: 2.Qf8+ Rxf8, 2.Qg7+ Qxg7, 2.Qxh7+ Rxh7, 2.Qg5+ Kxg5, or 2.Qg6+ Kxg6/hxg6. There’s no such stalemate avoidance though after 1.g8=P!

In the above setting, the unpromoted pawn on g8 conveniently helps to lock up the white king. I sought to exploit this device and came up with another six-unit study: Syzygy link. It uses exactly the same material as my second problem, and while the matrix is new, the play is not as clear-cut. However, this arrangement is amenable for doubling the theme: by adding just two more units, we create a position that is solved by consecutive P=P moves. The eight-unit diagram takes us out of tablebase territory, but it’s more-or-less confirmed sound by the Stockfish engine. (A Draw study by T. R. Dawson features three P=P moves in a much heavier position.)

The try 1.g8=Q? threatens 2.Qg6+/Qg5+, inducing stalemate; thus 1…b1=Q? is ineffective. Black’s only winning move is 1…Sf4! (Stockfish flags it as a mate-in-31, and views 1…Sxg8 as the one viable alternative but the engine doesn’t know about the P=P rejoinder.) Now that 2.Qg6+ is countered by a knight mate, and 2.Qg5+ Kxg5 isn’t stalemate, White cannot stop Black from winning on material, e.g. 2.Qg7+ Kh5 3.Qxf6 b1=Q 4.Kg7 Qb7+ 5.Qf7+ Qxf7+ 6.Kxf7 Bxh7, or 2.Qf8+ Kg5 3.Qh6+ Kg4! 4.Qh1 b1=Q. The key 1.g8=P! threatens stalemate, which must be relieved by 1…Sxg8. This capture sets up a tablebase position that’s equivalent to the six-unit one linked above. Remarkably, 2.hxg8=Q? is not defeated by 2…b1=Q?, because 3.Qxe6+! Bxe6 prompts another stalemate (also 2…Sd4? 3.Qg7+ Kh5 4.Qxd4). Instead, the unique 2…Kh5! uncages the white king and neutralises the queen’s sacrificial threat. The white queen is left incapable of picking off either minor piece or the unprotected pawn, e.g. 3.Qe8+ Kg4 4.Qa4+ Kg5! 5.Qb4 b1=Q, or 3.Qf7+ Kg4 4.Qg8+ Kh4 5.Qg1 b1=Q and Black wins. Only 2.hxg8=P! salvages the draw. This matrix does permit other sound settings but they lack the surprising 2…Kh5! refutation, relying on black queening to deal with 2.hxg8=Q.