Hexabeast (Liu4chu4)

Ma3 niu2 yang2, ji1 quan3 shi3. Ci3 liu4 chu4, ren2 suo3 si4.
`Hen, dog, pig, horse, cow, sheep, / These six kinds man doth keep.'
(San1Zi4Jing1 `Three-Character Classic')

I was reading the entry for liu4 `six' in my Chinese-Russian dictionary, hoping to find some set phrase that could make an Orientalishly imaginative name for the hexagonal version of Chinese chess, when this caught my attention: liu4chu4 `the six household animals and poultry (horse, cow, sheep, chicken, dog and pig); cattle and livestock'.

`Can't these six make a chess-like game?' I thought. Six kinds of pieces (as many as in Orthochess) are just about enough. So why not?

The design principles were drafted in no time. The game was to be played on the board for Shafran's hexagonal chess, since that is where it all started from, and the number `six' was not mentioned in the name for no reason. Nor was it a Chinese name for no reason, so the game was to be Xiang4qi2-like in some ways, which implies no promotion, among other things. Among the pieces chosen there was one whose move was quite uncontroversial, namely the horse (also known as knight); the moves of the others had to be chosen in a way that made for a coherent system and reflected somehow the difference in their mobilities and the extent to which some of them rely on their bulk when fighting, hence the wealth of pushing moves.

Board and initial setup

Liu4chu4 is played on the board for Shafran's hexagonal chess, which is composed of 70 hexes in three colours.

Since the three directions through the sides of the hexes are obviously not orthogonal to one another, they can't properly be called orthogonals. I will instead refer to the various directions as if the board were the face of a clock. So the lines that correspond to the orthogonals of the square board connect even hours, while the diagonals connect odd hours.

The nine lines of hexes running from 6 to 0 o'clock (from the point of view of the player who starts the game) are called files and are labelled a to i; the ten lines running from 10 to 4 o'clock are ranks (for notation purposes), numbered 1 to 10. File a runs from a1 to a6, file i from i5 to i10. Liu4chu4: board and initial setup.

As in Chess, each player has 18 pieces (which in this game means three of each kind), initially located on the rearmost two hexes of each file. The pieces are round counters and bear either pictures of the heads of the animals or (as on the diagrams in this document and in the Zillions of Games implementation) the corresponding Chinese characters in red or black (or some other contrasting colours).

Although I have no strong feelings on this matter, here is a setup that seems to work well:

Red: Horses a1, d1, g3, Boars b1, e1, h4, Bulls c1, f2, i5, Cocks a2, d2, g4, Rams b2, e2, h5, Dogs c2, f3, i6;
Black: Horses c8, f10, i10, Boars b7, e10, h10, Bulls a6, d9, g10, Cocks c7, f9, i9, Rams b6, e9, h9, Dogs a5, d8, g9.

Note that this setup has central symmetry. One can also use an axially symmetric setup by reflecting Black's farm in file e.

The Animals

The moves of the animals are to some extent inspired by Chû and Tenjiku Shôgi, Jim Aikin's Dragons, Archers and Oxen, Adrian King's Scirocco, and of course Chess itself. They are derived from a scheme in which every animal controls a different selection of a dozen hexes one or two King's moves away (W+A, A+F, F+W, W+D, D+F or N).

In what follows the animals are presented in the same order in which they are named in the San1Zi4Jing1 `Three-Character Classic'. The names are given in Latin (for reasons that will become clear shortly) and in Chinese.

The Horse (Equus, ma3)

An age-long active participant in wars as in board games. Does it matter if in this game he carries no sabre-wielding knight on his back? His hooves and teeth are perfectly capable of striking sparks and terror.

The Horse moves and captures as the Knight in hexagonal Chess (not as in Xiang4qi2, whose blockable Horse is too weak for this game).

The Bull (Taurus, niu2)

Tourist: `Hey, mister, is that bull safe?'
Farmer: `He is as safe as anything. <a moment's reflexion> Can't say the same about you, though.'
(Old joke about the perils of rural tourism)

The Bull's move is remotely similar to the move of his kinsman the Ox in Dragons, Archers and Oxen, and is also related to the moves of the Chariot and the Waggon in Scirocco. (The absence of front-back symmetry comes from having traded control over some hexes with the Dog.) The Bull controls

the Rook directions towards 0, 4, 6 and 8 o'clock, whereby

if the nearest hex is occupied, the Bull can push its occupant and any other animals in an unbroken line behind him one hex in the direction of his move, regardless of the colour of any of them, and if the last one in the line is pushed off the board, it is never seen again,
otherwise the Bull can move as a 4-step Rook in that direction, and capture by displacement on the 2nd, 3rd or 4th hex;

the Bishop directions towards 1 and 11 o'clock (the forward ones -- think of the horns), in which he moves as a 2-step Bishop (being able to reach the nearest hex or the next one if the nearest one is vacant), and again captures by displacement.

The Ram (Aries, yang2)

We are used to thinking of sheep as positively unsophisticated animals, but the male of the species is something to watch out for, or he would not have given his name to a device that the gates of ancient and mediæval towns and fortresses had a good reason to fear.

The move of the Ram is inspired by the Unicorn (Japanese kirin, Chinese qi2lin2) in Chû Shôgi, which moves and captures as a Firzân or a Dabbâba; note, however, that on a hexagonal board a piece with such movement power is not colourbound. The Ram

moves and captures as a Firzân;
moves as a Dabbâba only if the destination hex is vacant (the interfering one may or may not be). The leap is quite energetic, and the Ram's horns strong, so upon arrival he knocks any animals on the two hexes at 60 degrees to its line of movement, whichever side they belong to, one hex away.

For example, a red Ram on g9 can leap to e9 if it is vacant (regardless of whether f9 is) and simultaneously knock any animal found on d8 to c7 (causing the destruction of whatever is there) and anything on e10 off the board and out of the game.

(Note that in this game you can knock out a bull by propelling a cock onto it. Such minor inconsistencies with the real world never concerned you in chess-like games, so I don't expect them to start now.)

The Cock (Gallus, ji1)

`[N]ature for some reasons known only to herself has designed the game cock for one purpose only -- fighting. He is built for it and equipped for it, and he thinks of nothing else. [...] It is a quite common occurrence for a cock to fly over the top of his enclosure and walk a quarter of a mile to engage in a fight to the death. [... T]he cock when fighting shews no signs of feeling the wounds he receives.'
(Major C S Jarvis, Heresies and Humours)
Verily, the chicken is a symbol of cowardice, but there is more to the species than that.

The move of the Cock, the only bird in Liu4Chu4, is inspired by the Phoenix (Japanese hôô, Chinese feng4huang2) in Chû Shôgi, which moves and captures as a Wazîr or an Alfîl. This is how the Cock moves also, but he does not capture by displacement. Instead,

he captures by neartaking (approach) when moving as a Wazîr;
he captures by overtaking when moving as an Alfîl.

Thus a red Cock on hex i5 can move to hex i6 (or g7) if it is vacant, but not if it is occupied by an animal of either colour. Such a move would not affect another red animal on hex i7 (or h6), but a black animal found there would be captured.

The Dog (Canis, quan3)

A born hunter and a loyal defender, the dog often lends his fangs and nostrils to the service of police and armed forces, although his rank there is never very high. Now in Bulgarian the chess bishop is called oficèr `(commissioned) officer'.

The Dog appears in Tenjiku Shôgi, where he moves orthogonally forwards or diagonally backwards. This is the general idea here also (consequently it is the other animal whose move has no front-back symmetry), but his mobility is quadrupled. The Dog controls

the Bishop directions towards 3, 5, 7 and 9 o'clock (sideways and backwards), in which he moves as a 2-step Bishop,

capturing by undertaking (withdrawal) if moving to the nearest hex,
capturing by displacement if moving to the second nearest;

the Rook directions towards 2 and 10 o'clock, in which he moves as a 2-step Rook (being able to reach the nearest hex or the next one if the nearest one is vacant), and captures by displacement.

So a black Dog on d4 can't get to c5 if that hex is occupied, regardless by whom; but if it is vacant, the Dog can go there, capturing a red animal on e3 if there is one, or to b6, possibly capturing a red animal there.

The Boar (Sus, shi3)

The domestic pig lacks the flint-hard, razor-sharp tusks that make its wild cousin so fearsome, but it has been tamed more recently than most household animals, and even now, two thousand years after Mt 7:6 was spoken, it retains enough of its unruly nature.

Being the laziest household animal, the Boar restricts his control to the nearest hexes, more or less as the chess King does. That is,

he moves and captures as a Wazîr;
he also moves as a Firzân, but only if the destination hex is vacant. The move is anything but quiet, however. Being fat, the Boar finds the path through the corners of the hexes uncomfortably narrow, so as he moves, he pushes any animals on the hexes that have a common side with both the origin and the destination of his move one hex away from one another, in directions perpendicular to the move.

A black Boar on a3 can go to b2 if that hex is vacant, pushing any animal found on b3 to c4 (causing the destruction of whatever is there) and anything on a2 off the board and out of the game.

Zillions of Games comes up with the following estimates of the values of the animals in the initial position, recalculated in (hexagonal) Pawns:

Cock 1.8 (about half a Knight, a trifle stronger than a Demichess Lobster, a trifle weaker than a Firzân),
Dog 2.5 (about halfway between a Pawn and a Knight, or between a Firzân and a Silver General; weaker than a Demichess Snail),
Ram 3.6 (somewhere between a Quang Trung Counsellor and a Knight; stronger than a Demichess Snail),
Horse 3.7 (the same thing as a Knight),
Boar 3.8 (about halfway between a Knight and a Bishop, comparable to a Fibnif, or to a Phoenix),
Bull 4.9 (about halfway between a Bishop and a Rook, very close to a short Rook (R4); also close to half a Queen, or to a Demichess Oyster).

(Note that the pawn worth of all officers is greater on the hexagonal board than on the square one, because they control 1.5 times more directions.) So this is just the game for those who consider the usual Rook and Queen rather too powerful, but find the slowness of the Wazîr and the awkwardness of the Alfîl frustrating.

Victory conditions

There is no royal animal in Liu4chu4. You lose the game if any hostile animal moves onto the hex nearest to you, i.e., e1 if you are Red, e10 if you are Black (because if this were chess, you'd have lost if any hostile piece captured your King, whose original position that is). (By a propitious coincidence, this is the same rule as in the Jungle Game, which also models a fight of different kinds of animals, -- a fact I had forgotten when I made my rule.) You also lose (as in Xiang4qi2) if you are stalemated (though this seems very unlikely to happen, unless perhaps your entire farm is exterminated and you have nothing left to move). Finally, you may not repeat a position. (All that human players probably need to be told is that if the opponent has just pushed a Bull of yours by one of his Bulls, you may not respond by simply pushing his Bull back; and that a draw can be agreed if the game doesn't seem to be getting anywhere.)

Notation

The Chinese characters would be ideal as figurines, but in inclement typographic conditions the initials of the animals' names will do. I encourage using the initials of the Latin names, all of which are different from the initials of the English names of the Orthochess men (which I thought would be advantageous if a contest between an army from Shafran's hexagonal chess and one from Liu4chu4 proved to make a playable game). If the ranks of animals affected by pushing are notated (which is optional), so should their colour, by prefixing r for ruber `red' and n for niger `black'.

The rest is quite uneventful. As in chess, a dash indicates a quiet move, a colon a capture. The end of the game could be indicated by # if an animal has reached the opposite corner and by $ if the opponent has been stalemated.

Sample games

The games Zillions plays against itself from the centrally symmetric opening position tend to last around 50 moves. Here are two of exceptional brevity:

Red: Zillions of Games. Black: Zillions of Games. Central symmetry.
1. Ci6-g6 Ca5-c5 2. Ab2-c4 Ab6-d6 3. Ac4-c6 Ah9-g7 4. Ah5-f4 Gi9-g5 5. Ac6-e8-[nAe9:nSe10] Td9:e8 6. Sh4-h5 Ef10-g8 7. Cg6-c4 Gg5-f5 8. Gg4-e6:f5 Ag7-g5-[rSh5:rTi5, rAf4-e3] 9. Ge6-e7:e8 Ad6:c4 10. Ge7-i9:g8 Ac4-e4-[rAe3:rAe2] 11. Ed1:e4 Cg9:i9 12. Ga2-c6 Ta6-b5 13. Ea1-d3 Ag5-e3-[rAe2:rSe1, rEd3-c3] 14. Ec3:b5 Ae3:f2 15. Eb5:d8 Tg10-g6 16. Ee4:f2 Tg6-e2 17. Ae1-e3 Te2-e1#.

Red: Zillions of Games. Black: Zillions of Games. Central symmetry.
1. Ci6-g6 Ca5-c5 2. Ed1-e4 Ei10-g7 3. Ea1-d3 Ef10-d7 4. Tf2-rCf3-f4 Ae9-e7 5. Tc1-rCc2-c3 Gf9-d5 6. Ed3-f2 Eg7:e4 7. Ef2:e4 Gd5-e5 8. Cc3:e5 Cc5:e5 9. Cg6-i7:e5 Ah9-h7:i7 10. Tf3:h7 Gi9-g5:h7 11. Cf4:g5 Ae7-d5 12. Ab2-d3 Ad5:e4 13. Eg3:e4 Ab6-d6 14. Ga2-c6 Ta6-a3 15. Ad3-d5 Ta3-a5 16. Gd2-f6 Ad6-e8 17. Gg4-e6 Ae8-f10 18. Tc2-c5 Ed7:f6 19. Tc5-e9 Se10-f9-[rTe9:nCd8, nAf10--] 20. Td8-e10#.

From the axially symmetric opening position the games last a little longer, around 60 moves. Again, two unusually short ones:
Red: Zillions of Games. Black: Zillions of Games. Axial symmetry.
1. Ci6-g6 Gg9-g8 2. Cg6-c4 Ed9-e7 3. Ea1-d3 Ea6-c5 4. Ed1-e4 Ec5:e4 5. Gd2-f6:e4 Ah9-g7 6. Gg4-g5 Gg8-e4:f6 7. Eg3:e4 Ag7-f5 8. Tc1-rCc2-c3 Sh10-g8 9. Cc4-e6 Sg8-h7 10. Ce6-f7 Sh7-i6 11. Cf7:e7 Ci9:e7 12. Ah5-h7 Ti10-h10 13. Ah7:i6 Af5-h5-[rAi6--, rSh4--] 14. Cf3:h5 Ae9-f8 15. Se1-d2-[rAe2-f3] Se10-e9 16. Tc2-rCc3-c4 Af8-f6 17. Ed3:f6 Th10:f6 18. Ab2-b4 Gd8-d7 19. Tf2-h6 Gd7-f5 20. Th6-rGg5-f4 Tf6-nGf5-rGf4-rAf3-f2 21. Af2-e3 Tf5-nGf4-rGf3-f2 22. Gf2-g3 Tf4-nGf3-f2 23. Ae3:f2 Tf3-e1#.

Red: Zillions of Games. Black: Zillions of Games. Axial symmetry.
1. Ci6-g6 Gg9-g8 2. Cg6-c4 Ed9-e7 3. Cc4-d5 Ab6-d6-[nEe7-f8, rCd5-d4] 4. Ed1-c3 Ef8-h7 5. Ti5-i6 Ci9-g7 6. Ti6:i10 Eh7:i10 7. Gg4-g5 Cg7-e6 8. Ae2-e4-[rCd4-c4] Ad6-d4-[rAe4-f4, rEc3:rAb2] 9. Gd2-d3:d4 Ei10-f8 10. Ga2-e4 Ce6-c5 11. Tc1-rCc2-c3 Gd8-f6 12. Gg5-e7:f6 Eg10:e7 13. Ge4-e5 Cc5:e5 14. Gd3-f7:e5 Ah9-g7 15. Ah5-f5 Ag7:f5 16. Gf7-f6:f5 Gg8-e4:f6 17. Eb2:e4 Tf10-h8 18. Af4-f6 Th8-f4 19. Cf3-g4 Tf4:f2 20. Se1-f3-[nTf2--] Ee7-f10 21. Ea1-d3 Ae9-e7 22. Ee4-d6 Ae7-c5-[rCc4:rCc3] 23. Ed6:f9 Tc8-b6 24. Af6-d6-[nAc5-b4] Ab4:c3 25. Sb1-d2-[rTc2:nAc3] Sb7-d8-[nCc7-c6] 26. Ad6-f7 Sh10-h9 27. Ef9-g7 Ef10-c8 28. Tc3-e7 Sd8-e8 29. Eg7:e8 Se10-e9 30. Te7-rEe8-nSe9-e10 Se10:e9 31. Af7-f9-[nSe9-d9] Ec8:f9 32. Te8-e10#.

And that is all -- unless you really miss having a royal piece, in which case there is also ...

Boar Chess (Shi3qi2)

This is a Xiang4qi2-like version of Liu4chu4. The board is the same, the types of pieces likewise, but their original numbers, the setup, the moves of the Cock and the Boar and the goal of the game are different.

Each player starts the game with 1 Boar, 2 Bulls, 3 Horses and Rams, 4 Dogs and 5 Cocks. I suggest the following arrangement:

Red: Boar e1, Bulls a1, i5, Horses b1, d1, g3, Rams c1, f2, h4, Dogs b2, d3, f4, h5, Cocks a2, c3, e4, g5, i6;
Black: Boar e1, Bulls a6, i10, Horses c8, f10, h10, Rams b7, d9, g10, Dogs b6, d7, f8, h9, Cocks a5, c6, e7, g8, i9.

Cocks (of which each player now has five) are a little more Pawn-like (though they remain worth about 1.2 Pawns each): their Wazîr move and approach capture are not affected, but they may only jump as Alfîl when capturing.
Boars are royal. They move and push as in Liu4chu4, but not even to save their skins will they ever leave their sties (meaning the seven hexes d1-2, e1-3 and f2-3 for the Red Boar, and d8-9, e8-10 and f9-10 for the Black), unless one of them sees his opposite number along an unobstructed file, in which case he can dash across and seize him.
The game ends when

a Boar is captured, stalemated or pushed out of his sty (use × to notate this)
or a Cock moves onto the hex originally occupied by the enemy Boar.

The average length of ZoG's Boar Chess games with itself is 80 moves or so; that is to say, much longer than these two:
Red: Zillions of Games. Black: Zillions of Games.
1. Eg3-f5 Gg8-f7 2. Ef5-d2 Ef10-g8 3. Gg5-g6 Gf7-g7 4. Ac1-e3-[rGe4-e5] Ge7-e6:e5 5. Gg6-f6:e6 Gg7-h7 6. Gf6-f7:f8 Gh7-h6:h5 7. Cf4:h6 Cd7:f7 8. Ch6-f6 Eg8-d7 9. Gi6-h6 Ab7-d8 10. Af2-f4 Ad8-f8-[nCf7:rCf6] 11. Gh6-g6:f6 Ec8-e7 12. Cd3-f5 Ad9-e8 13. Ah4-g5 Ed7-b4 14. Ta1-b3 Eh10-f7 15. Ag5-g7-[nEf7:nEe7] Gi9-h8:g7 16. Cf5-d5 Ee7:g6 17. Af4:g6 Eb4-d3 18. Se1-f3 Gh8-f4:g6 19. Ed1:f4 Gc6-e4:d5 20. Tb3:b6 Ti10-g6 21. Tb6:a5 Ta6-b5 22. Gc3-b3 Tg6:f4 23. Gb3-b4:b5. Red's last freely chosen move. Should have been Gb3-c3:d3. 23 ... Tf4-nGe4-d4 24. Sf3-e2 Gd4-f2:e3 25. Eb1-e3 Gf2-e1#.

Red: Zillions of Games. Black: Zillions of Games.
1. Eb1-a3 Ga5-a4:a3 2. Ga2-a3:a4 Ad9-c7 3. Af2-e3 Eh10-e8 4. Ah4-h6 Gi9-h8 5. Ah6-f5 Ge7-f7 6. Af5-g4 Gf7-f6 7. Gg5-e7:f6 Ef10:e7 8. Ge4-e5 Ee7-b5 9. Ga3-b3 Eb5-d8 10. Ed1-e4 Ed8-e6 11. Ac1-e2 Gh8-h7 12. Gi6-h6 Gg8-g7 13. Ge5-f6:g7 Gh7-d5:f6 14. Gb3-c4:d5 Gc6-c5:c4 15. Gc3-c4:c5 Ta6:c4 16. Ch5-g5 Ec8-d6 17. Cb2-d4 Tc4-a4 18. Ta1:a4 Ee6:d3 19. Ae2:d3 Ab7-b5:a4 20. Cd4-b4 Ed6-c3 21. Gh6-h7 Ti10-h8 22. Eg3-i6 Th8-i9
23. Gh7-h8:h9 Ti9:g5 24. Cf4:g5 Ab5-b3-[nEc3:rAd3] 25. Se1-d1 Ab3-d5 26. Ee4-b2 Ed3:b4 27. Gh8-g8:f8 Ag10-f8 28. Ag4-h6 Ad5-d3-[rAe3-f3]
29. Eb2-e4 Eb4-c2 30. Af3-d2 Ad3-f3 31. Ah6-h8-[rGg8:nAf8] Af3:g5 32. Sd1-e3-[rAd2:nEc2] Ag5:e4 33. Ei6-f4 Cd7-e7 34. Gf8-f9 Ee8-d5 35. Ef4:d5 Ae4-g4 36. Se3-e2 Ac7-d6 37. Ah8-g9 Se10-e9 38. Gf9-f10 Ag4:i5 39. Gf10-e10#.

Created and maintained by Ivan A Derzhanski.
Last modified: 9 September 2000.