Sena-Mukha

A Game by Ivan A Derzhanski

Akshauhini

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.

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 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.

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.

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–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