Chinese pieces: Pao, Vao, and Mao

Fairy problems that incorporate unorthodox pieces can bring about many intriguing special effects, and previously we’ve examined the grasshopper and the nightrider as two well-known examples. The Chinese pieces represent another popular group of fairy units, which include the pao (cannon) and mao (horse) borrowed from the game of Chinese chess. These two pieces are actually quite distinct in character; the pao is similar to a rook but, akin to a pawn, it moves and captures differently, while the mao is a kind of blockable knight. Each of these units can be generalised to form a family of related pieces, though here we will consider derivatives of the pao only, not the mao.

The pao moves on orthogonal lines like a rook, but it can capture only by hopping over another unit (of either colour) on the same line to the captive’s square of any distance beyond. In the first diagram, the white pao on g7 can move to any square on the 7th rank, as well as g6 and g5, but it does not attack the black piece on g8. By using the g4-unit as a hurdle, this pao would be able to capture any enemy placed on g3, g2, or g1, and since it checks the same way, it’s preventing the black king from reaching the g-file. The vao is the diagonal version of the pao; analogously it moves like a bishop but captures by hopping over another unit and landing on the captive’s square, all on the same diagonal line. Here the black vao on h3 has one legal move only, …VAxc8 over the g4-unit; it can’t move to g2 because it would become a hurdle that enables White’s e4-vao to check (while g4 and f1 are obstructed).

The mao moves like a knight, but only by going through an orthogonally-adjacent square, which must be empty. If such an adjacent square is occupied, the piece is blocked from moving in that direction. The black mao on g8 can move to e7, but not f6 or h6 because of the intervening unit on g7. A diagonally-adjacent piece has no effect on the mao; if a unit stood on f7, …MAe7 would remain legal.

With the king in the corner restricted by the g7-pao and d6-vao, Black has three mobile pieces and all of their moves are provided with a mating response. Either mao would open a line for the c8-pao: 1…MAc~ 2.PAcc1 and 1…MAe7 2.PAh8. The latter mate cannot be parried by shifting the black vao, since …VAg2 is illegal as mentioned. If 1.PAf3+? then 1…VAg2 blocks the check (the white vao captures/checks by hopping over one unit only); thus the remaining set variation is 1…VAxc8 2.PAf3. This mating move demonstrates an anti-battery, in which a check by a hopping fairy piece is activated by another piece that lands between it and the opposing king.

White has numerous tries that aim to preserve the zugzwang. 1.Kg3? releases the black vao, and it’s defeated by 1…MAe7! since 2.PAh8+ is answerable by various vao moves. (Subtly, this king try is not refuted by 1…VAg4 even though 2.PAf3+ then fails to 2…Kg1; rather, the vao defence is handled by 2.Kf3, which re-guards g1 with the g7-pao by using the black piece as the hurdle.) 1.PAg6? simply allows the g8-mao to check. 1.VAd5? permits 1…VAxc8! because 2.PAf3+ is countered by 2…e4. The f1-pao seems unable to move without either losing its access to f3 or abandoning its job as a potential hurdle for the c8-pao. However, 1.PAa1! (waiting) solves by crossing over the critical square b1, so that 1…VAxc8 admits a new mate, 2.VAb1. This excellent change reverses the roles of the pao-and-vao pair in executing an anti-battery mate. After 1…MAc~, the reply 2.PAcc1 is the same as before, but oddly it’s now the key-pao that’s the mating piece, and 2…VAf1 is illegal as that would activate the pao on c1. Only 1…MAe7 2.PAh8 remains unchanged from the set play. Although the maos’ powers aren’t utilised distinctively, this is a charming mutate, neatly constructed.

White has various anti-battery checks on the long diagonal, all defendable by Black, though 1.Sd4+? is quite strong in meeting 1…Qc3/Rb2 with 2.Sxf5; Black defeats this incidental try with 1…Qe5!, after which the double-check 2.Sxf5 can be defused by 2…Qxf5+. The third-pin arrangement on the 7th rank employing the pao means that when any of the three black pieces moves off the line, both remaining ones become pinned simultaneously, since each is a potential hurdle. The key 1.Kg5! controls f6 to threaten 2.Rfg8, forcing Black to shift a major piece to the top rank. Five such defences lead to different anti-battery mates that exploit the double-pin. In each case White must choose the appropriate hurdle square to prevent the defender from interposing on the diagonal. 1…Rb8 2.Sb2, 1…Qc8 2.Sc3, 1…Rd8 2.Sd4, 1…Qb8 2.Se5, and 1…Qd8+ 2.Rf6. All five variations show perfectly matching strategies.

The third problem makes intensive use of the Chinese pieces’ properties, especially the mao’s ability to act as the rear piece of a battery. The leo on c1 combines the powers of a pao and a vao and thus travels on queen-lines. The mao on e3 is blocked from attacking the black king by the knight, so White can give a discovered check by moving the latter piece. However, anywhere it goes the knight would enable a black piece to hop over it and capture the mao, e.g. 1.Sg3+? PAxe3, 1.Sd2+? LExe3. The other mao on f6 is pinning the black pawn, though this effect is discarded immediately by the key, 1.fxe6!, which forms a MA + P battery and threatens 2.e7. Black can defend by attacking that mao, such as by placing a piece on the f-file as a hurdle to activate the f1-pao. Five defences enable White to fire the MA + S battery instead in different ways. The most interesting of these variations are 1…PAhf3 2.Sg3, 1…VAf4 2.Sg5, and 1…VAd4 2.Sc5, when the knight plays to a square that’s passed over by the defender, a sort of anti-critical effect. The other thematic variations are 1…LExc6 2.Sd2 and 1…VAf2 2.Sxf2. There’s good by-play initiated by the e8-vao, which seeks to interpose on e6 but it induces more MA + P battery openings, 1…VAd7 2.exd7 and 1…VAf7 2.exf7.

The Grasshopper and the Nightrider

10 Sep. 2015