Sena-Mukha
A Game by Ivan A Derzhanski
It all started with a word in a dictionary of one of the languages
of India, which attracted my attention, because it was glossed so:
‘a unit of an army consisting of 21 elephants, 21 chariots, 65
horses and 109 foot-soldiers’. I looked it up in the Wikipedia, and
found even more intriguing information (slightly edited here):
An akshauhini (Sanskrit: अक्षौहिणी) is a battle formation
consisting of 21,870 chariots; 21,870 elephants; 65,610 cavalry
and 109,350 infantry, as per the Mahabharata (Adi Parva 2.15-23). In each
of these large number groups, the digits add up to 18.
The count is arrived as follows:
1 elephant, 1 chariot, 3 horses and 5 foot soldiers form a patti;
3 pattis form a sena-mukha;
3 sena-mukhas make a gulma;
3 gulmas, a gana;
3 ganas, a vahini;
3 vahinis, a pruthana;
3 pruthanas, a chamu;
3 chamus, an anikini;
10 anikinis form an akshauhini.
At this point I simply had to see what this (well, some of it) would
look like on a chessboard.
Hence the idea of this game, which has the following design
features:
- Two armies, each consisting of a sena-mukha (as defined above)
and a royal piece (a King).
- Moves designed to make a Chess-like game (on which more
below). In particular, this means that the Pawn, Knight, Rook
and King, which have not changed their moves over the centuries,
should not do so on this occasion either. It also means that the
Elephant, which has done so, should do so again, in such a way
as to give the appropriate strength to itself and the army as a
whole. (Colourboundedness wouldn't be a good idea, for one
thing, since you start with an odd number of Elephants.)
- A square board of a size that makes for an initial density of
almost ½.
Board and Setup
The board is 11 by 11. The files are labelled a to k,
the ranks 1 to 11. Rank 11 is the promotion
zone for White, rank 1 for Black.
The initial setup is shown in the picture (graphics borrowed from
Christian Freeling's Dragonfly):
- White
- King f3;
Elephants g1, d3, h3;
Rooks e1, b3, j3;
Knights d1, f1, h1, a3, c3, e3, g3, i3, k3;
Pawns d2, e2, g2, h2, d4, e4, f2, g4, h4, a4, b4, c4, i4, j4,
k4.
- Black
- King f9;
Elephants d9, h9, e11;
Rooks b9, j9, g11;
Knights a9, c9, e9, g9, i9, k9, d11, f11, h11;
Pawns a8, b8, c8, i8, j8, k8, d8, e8, f10, g8, h8, d10, e10,
g10, h10.
There is nothing sacrosanct about it, but I feel that, since the
sena-mukha is composed of three pattis, the men of each patti should
stand together, and the Kings shouldn't hide in the rear, because it
is written: ‘Those kings who, seeking to slay each other in battle,
fight with the utmost exertion and do not turn back, go to heaven’ (Laws
of Manu VII:89). The arrangement of the Black army may be a
mirror or a central reflexion of the White one's.
The Units
- Pawn (Padata)
- As in OrthoChess, but without initial double move or en
passant capture (this should be a game with an ancient
feel). Promotes to Knight, Rook or Elephant.
- Knight (Ashva)
- As in OrthoChess.
- Rook (or Chariot, Ratha)
- As in OrthoChess. (No castling.)
- Elephant (Gaja)
- Wazir + Firzan + Alfil + Dabbaba; that is, 1 or 2 squares in
any ortogonal or diagonal direction, leaping over an intervening
man if necessary. (This is the move of the Pasha in Paulovits's
Game, or the eponymous elephantine beasts in Mammoth Chess
and Mastodon
Chess; the moves of the Elephants in Chaturanga/Shatranj
and in Demian Freeling's Congo
are its proper subsets.) The unit thus obtained is somewhat
Queen-like, so Queens won't be missed so much, and it is similar
to a Rook in strength, which makes sense, considering you have
an equal number of Elephants and Rooks, but thrice as many
Knights. And one more point: in Orthochess a popular estimate
has it that each side's officers are worth 9+2×5+(2+2)×3 = 31
pawns, almost 4 times more than the Pawns themselves; here the
officers in each patti work out to (1+1)×6+3×3 = 21 pawns, also
about 4 times the strength of the infantry.
- King (Raja)
- As in OrthoChess.
Victory is by checkmate.
Sample Games
Zillions of Games—Zillions of Games 1. Na3–b5
Ne9–d7 2. Ne3–d5 Ng9–f7 3. Kf3–f4 Nh11–g9 4. Ng3–f5 Kf9–e9 5. Nd1–e3
e8–e7 6. g4–g5 Nd7–f8 7. Nf5–h6 Nf8–g6 8. Kf4–g3 Nk9–j7 9. Nk3–j5
Nj7:h6 10. Nj5:h6 Nf7:h6 11. g5:h6 Na9–b7 12. h4–h5 Ng6–f8 13. c4–c5
Ee11–c11 14. Eg1–i1 Eh9–h7 15. Ni3–g4 Ng9–f7 16. Eh3–f5 Nf11–g9 17.
Ef5:h7 Ng9:h7 18. c5–c6 Nb7–d6 19. Nb5:d6 Nf7:d6 20. e4–e5 Nd6–f7
21. Nh1–i3 Nh7–g5 22. Kg3–h4 b8–b7 23. c6:b7 Ed9:b7 24. Nf1–g3
Nc9–e8 25. Nc3–e4 Ni9–h7 26. Ne4:g5 Nf7:g5 27. Ng4–i5 Nd11–c9 28.
Ni5–g6 g10–g9 29. Re1–c1 Nc9–d7 30. Rb3–c3 Ec11–c9 31. Rc3–c6 e7–e6
32. Nd5–f4 Rb9–b11 33. Nf4–h3 Nd7–b8 34. Rc6–c5 Ng5:h3 35. g2:h3
Eb7–d7 36. Ed3–b5 Ne8–c7 37. Ng6:f8 g9:f8 38. Eb5–b3 Nb8–a6 39.
Rc5–c4 Nc7–d5 40. b4–b5 Nd5:e3 41. d2:e3 Na6–c7 42. Rc4–c6 Nc7–d5
43. Ei1–i2 Nd5–e7 44. Rc6–a6 a8–a7 45. Ei2–g4 Ke9–e8 46. Ra6:e6
i8–i7 47. Rj3–j1 c8–c7 48. h6:i7 j8:i7 49. Re6–k6 Rg11–k11 50. e5–e6
Ed7–c8 51. i4–i5 c7–c6 52. Eb3–d3 Ec9–c7 53. b5:c6 Nh7–j8 54. Rk6–k7
Rb11–b4 55. h5–h6 i7:h6 56. i5:h6 Rj9–i9 57. j4–j5 Nj8–h7 58. Rc1–c4
Rb4:c4 59. Ed3:c4 Ec8:c6 60. Eg4–e4 Ec6–d6 61. Ni3–h5 Nh7–f6 62.
Nh5:f6 Ed6:f6 63. Kh4–h5 g8–g7 64. Ng3–i4 g7:h6 65. Ni4:h6 Rk11–g11
66. Nh6–f7 Ne7–g6 67. Ee4–c6 Ke8–d9 68. Ec6–e8 Kd9:e8 69. Nf7–g9
Rg11:g9 70. Ec4–c6 Ec7:c6 71. Rk7–e7 Ng6:e7 72. Rj1–g1 Rg9:g1 73.
h3–h4 Ef6–g6×.
Zillions of Games—Zillions of Games 1. Na3–b5
Ne9–d7 2. Ne3–d5 Ng9–f7 3. Kf3–f4 Nh11–g9 4. Ng3–f5 Kf9–f8 5.
e4–e5 g8–g7 6. e5–e6 g7–g6 7. Nf5–g3 Nf11–e9 8. e6:f7 Ne9:f7 9.
Nf1–e3 c8–c7 10. Ed3–e4 Eh9–h7 11. g4–g5 Na9–c8 12. Ne3–g4 Nk9–j7
13. Nd1–e3 Ee11–c11 14. Ng4–f6 Eh7–i6 15. Eh3–g4 Nd7:f6 16. Nd5:f6
Ei6:g4 17. Ni3:g4 e8–e7 18. Nf6–d5 Ed9–e8 19. h4–h5 g6:h5 20.
g5–g6 h5:g4 21. g6:f7 Ng9:f7 22. Ee4:g4 c7–c6 23. Nk3–j5 c6:d5 24.
c4:d5 Nd11–e9 25. i4–i5 a8–a7 26. Eg1–i3 a7–a6 27. Nb5–a3 k8–k7
28. Na3–c4 Ni9–h7 29. Eg4–i6 Nf7–g9 30. Nh1–j2 Ee8–f7 31. Nj2–i4
Ef7–f6 32. Kf4–e4 Ne9–f7 33. Ei6–k8 Nf7–d6 34. Ke4–d3 Rj9–k9 35.
Ek8–i6 Ef6–f4 36. Ei3–h4 Ef4:h4 37. Nj5:h4 Nh7–f6 38. Nh4–g6
Kf8–f9 39. Ni4–h6 Nj7:h6 40. Ng6:h8 Kf9–e8 41. Ei6:h6 j8–j7 42.
Nc4:d6 Nc8:d6 43. Kd3–c2 Nc9–d7 44. Eh6–i7 Rk9–k11 45. Kc2–b1
Ec11–c10 46. Nh8–j9 Rk11–k10 47. Ei7–h8 h10–h9 48. Eh8:f10
Rg11–f11 49. Ef10–h8 Nf6–g8 50. Nc3–e4 Nd6:e4 51. Ng3:e4 Ng9–f7
52. Eh8–j8 Nf7–d6 53. Ne4:d6 e7:d6 54. Ne3–c4 Rf11:f2 55. Nc4:d6
Ke8–e7 56. Nd6–b7 Ec10–c8 57. Rb3–e3 Ke7–f8 58. Ej8–h8 Kf8–f9 59.
Re3–f3 Rf2:f3 60. Rj3:f3 Nd7–f6 61. Nb7–c5 Kf9–e8 62. Rf3:f6
Ng8:f6 63. Eh8:f6 Rb9–f9 64. Ef6–g6 Ke8–e7 65. Nj9–h8 Rf9–f2 66.
Nc5–e4 Rf2–f11 67. Re1–c1 Ec8–d9 68. Eg6–g7 Ke7–d7 69. Ne4–f6
Rf11:f6 70. Eg7:f6 Kd7–e8 71. Ef6–g6 Ke8–f8 72. Rc1–f1 Kf8–g9 73.
Eg6–g7 Kg9–h10 74. Eg7–f8 Kh10–i11 75. Ef8–g9 Ki11–h11 76. Eg9–i9
g10–g9 77. Ei9:h9 Kh11–g11 78. Eh9:g9 Kg11–h11 79. Eg9–h9 Kh11–g11
80. Eh9–i9 Kg11–h11 81. Ei9–j9 Kh11–h10 82. Ej9:k10 Kh10–h9 83.
Ek10–i10 Kh9:h8 84. Rf1–f8 Kh8–g9 85. Ei10–g8 Kg9–h10 86. Rf8–f10
Kh10–i9 87. Rf10–i10 Ki9–j9 88. Eg8:i8 Kj9–k9 89. Ri10–k10×.
Zillions of Games—Zillions of Games 1. Na3–b5
Ne9–d7 2. Ne3–d5 Ng9–f7 3. Kf3–f4 Nh11–g9 4. Ng3–f5 Kf9–e9 5.
Nd1–e3 e8–e7 6. g4–g5 Nd7–f8 7. Nf5–h6 Nf8–g6 8. Kf4–g3 Nk9–j7 9.
Nk3–j5 Nj7:h6 10. Nj5:h6 Nf7:h6 11. g5:h6 Eh9–f7 12. Ed3–f5 e7–e6
13. Ef5:f7 Ed9:f7 14. Nd5–f4 Ng6:f4 15. Kg3:f4 Ef7–f6 16. Kf4–g4
Ef6–g6 17. Kg4–f3 Eg6:h6 18. Ne3–g4 Eh6–i6 19. Nf1–e3 Ke9–f8 20.
Eh3–h5 Ei6:h5 21. Ni3:h5 Nd11–e9 22. Nh1–g3 Ee11–c11 23. Nh5–f4
d8–d7 24. Eg1–i3 Ne9–f7 25. Nf4–g6 Kf8–f9 26. Nb5–d6 Nf11–e9 27.
Ng6–e7 Kf9–f8 28. Ne7–g6 Kf8–f9 29. Ng6–e7 Kf9–f8 30. Ne7–g6
Kf8–f9=. White loses a Knight by making any other move, and Black
loses the game (30. … Kf8–g7 31. Ei3–i5 Kg7:g6 32. h4–h5 Kg6–h7
33. Ng4–f6×).
Zillions of Games
The implementation is here.
Created: 13 March 2016.