Capture-free proof games

In proof game problems, the objective is to find the precise sequence of moves to reach the diagram position, starting from the standard array. Because the problem position comes about directly from the full assembly of 32 pieces, the principle about economy of force in compositions doesn’t necessarily hold and the rule can even be turned on its head. In contrast to “massacre” proof games – a sub-type where the diagram positions are super-economical in terms of the number of pieces – proof game positions with most or all of the 32 units present may be viewed as more pristine or neat, exhibiting “economy of captures.” Totally capture-free play thus becomes a positive feature, or a challenging restriction, with which to accomplish a problem’s principal theme, whatever that might be.

The idea of a proof game with all pieces remaining in the final position seems especially compatible with certain themes that are pictorial in nature. The Belfort theme illustrates such a visual effect and it indicates that at least two pieces finish up on the starting squares of their opposite-coloured counterparts. In the first diagram, the four knights act as the thematic pieces, and that means two pairs of platzwechsel – exchange-of-places between two units – are additionally performed. 1.Sf3 Sc6 2.Sd4 Se5 3.Sc6 Sf6 4.d4 Se4 5.Be3 Sd2 6.Sc3 Sb1 7.Qd2 Sf3+ 8.Kd1 e5 9.Sd5 Bd6 10.Sde7 Sg1 11.Sg8 Qe7 12.Sb8. Remarkably, yet another pictorial idea is realised: the position displays a rotational symmetry between the white and black forces, while the play itself is largely non-symmetrical between the two sides.

The next problem achieves an amazing task that yields the striking diagram position: sixteen pawn double-steps are arranged. The total absence of captures not only enhances the visual aspect, but in a sense, also contributes to the intricacy of the play. Since captures are commonly used as a device in proof games to facilitate precise play, removing them means that the solution will necessitate more interesting strategic effects, such as line-opening and -closing, to attain uniqueness. Here intensive use of these effects ensures that the countless possible orders of the sixteen pawn moves are narrowed down to one. 1.d4 h5 2.Bh6 Sf6 3.f4 Se4 4.Sf3 Sd2 5.e4 a5 6.Ba6 e5 7.c4 Bb4 8.Qa4 c5 9.Qc6 b5 10.Bb7 Ra6 11.a4 Rb6 12.Sa3 Sa6 13.0-0-0 Sf1 14.Rd3 Be1 15.b4 Qh4 16.Rb3 Qf2 17.h4 Kd8 18.Rh3 d5 19.Rg3 Bh3 20.Rg6 f5 21.Rf6 g5 22.g4.

The majority of regular themes seen in proof games are feasible without employing captures, though promotion themes (ubiquitous nowadays!) represent a large group of exceptions. Weekly Problem No.690 demonstrates multiple switchbacks with no captures. A related idea is the extended round-trip, carried out by the h1-rook in the example above. Since Black has no missing unit to be captured, what could motivate the white rook to take such a trip before returning home? 1.e3 e5 2.Ba6 b5 3.Sh3 Bb7 4.0-0 Be4 5.Re1 Bf5 6.e4 Bc5 7.Re3 Bd4 8.Rg3 c5 9.Rg6 Qa5 10.Rb6 Sc6 11.Rb7 0-0-0 12.Rc7+ Kb8 13.Rb7+ Ka8 14.Rb6 Rb8 15.Bc8 Rb7 16.Kf1 Sb8 17.Rg6 Sf6 18.Rg3 Re8 19.Re3 Re6 20.Re1 Se8 21.Ke2 Rh6 22.Rh1 f6 23.Sg1 Rh3 24.Ke1. Only a rook is capable of interfering with the white bishop on a6 to allow Black to castle in time. This specific mechanism to induce a rook trek isn’t new – precursors include Caillaud’s P1000010 and Hashimoto’s non-capturing P1004020. But here the scheme is fabulously combined with another paradoxical idea: hidden white castling, i.e. both the king and rook shift back to their original squares after castling.

When we examine length records in proof games, it’s natural to consider capture-free problems as a special sub-category. Back in 1983, Michel Caillaud set a record of 38½ moves for the longest unique game without captures: P0002187. Since then another GM-composer, the late Unto Heinonen, had attempted to break this record with various settings, the longest reaching 43½ moves. Most of these problems turned out to be unsound, however – cooked by expert human solvers, as the sequences are too lengthy to unravel even by the best software of today. Here is the longest game by Unto that has withstood scrutiny, and it holds the current record of 41½ moves. 1.h4 a5 2.Rh3 Ra6 3.Rf3 Rg6 4.Sh3 Rg3 5.Sf4 Rh3 6.g3 Rh2 7.Bh3 Sh6 8.Be6 Sf5 9.Bc4 d5 10.Kf1 Rh1+ 11.Kg2 Rg1+ 12.Kh3 Kd7 13.Kg4 h5+ 14.Kg5 Rh6 15.a4 Rb6 16.Raa3 Kc6 17.Rac3 Rb3 18.Sg6 Ra3 19.b3 Ra2 20.Ba3 Qd6 21.Bc5 Sd7 22.Ba7 Sb6 23.Sh8 Kc5 24.Ba6+ Kb4 25.Rc5 g6 26.Sc3 Bg7 27.Se4 Bc3 28.Qa1 Sd4 29.Kh6 Bd7 30.Kg7 Bb5 31.Kf8 Bd3 32.Ke8 Qc6+ 33.Kd8 Sc4 34.Kc8 Ka3 35.Kb8 Bb4 36.Ka8 Qe8+ 37.Bb8 Sb6+ 38.Ka7 Sa8 39.c4 Sc2 40.Qg7 Sa1 41.Rf6 Kb2 42.Rb6+. An incredible feat of construction!

A “Holy Grail” of proof games attained

28 Feb. 2013