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Midgard Chess

Introduction

Midgard Chess uses the General (Bishop + Wazir), the War Elephant (moves up to two steps like a Ferz) and the War Machine (Greg Strong's shortrange leaper).

Setup

Pieces

  8 Pawns 
  3 valuable pieces: King, General, Rook
  2 colorbound pieces: War Elephants
  4 color alternating leapers: Knights and War Machines

King -k- This is the royal piece. As in Shatranj, it moves 1 square in any direction. It may not move into or remain in check.

General -G- This piece slides any distance along a diagonal like the modern bishop. It also moves 1 square orthogonally like a Wazir. It is called a dragon horse in Shogi.

Rook -r- As in Shatranj, this piece slides any distance orthogonally.

War Elephant -L- This colorbound piece slides 1 or 2 squares like a ferz. It may change direction during its move. It may not jump. It may not make a null move (move off and then back onto its starting square). A capture immediately ends its move, no piece in this game is allowed to capture twice. I have used this piece in other chess variants. In the diagram below, a red "X" marks every square reached by a War Elephant placed in the center.

Knight -n- This piece leaps 2 squares like the Shatranj knight. In the diagram below, a Knight placed in the center moves to the 8 closest squares not reached by the War Elephant or the War Machine.

War Machine -H- This piece moves 1 square orthogonally or leaps 3 squares orthogonally. In the diagram below, a red hollow square marks every square reached by a War Machine placed in the center. Greg Strong introduced this piece, calling it a Scout, in Brouhaha and Hubbub.

Pawn -p- As in Shatranj, this piece moves 1 square orthogonally forward and captures 1 square diagonally forward. It promotes to a General of the same color on the player's eighth rank.

Roberto Lavieri's elegant "Galactic Graphics" are used for the pieces on this page and in the Game Courier preset. The War Elephant is represented by a capital "L" for the White piece and a lowercase "l" for the Black piece. "L" stands for Lion in his "Galactic Symmetron" graphics.

Adding a Ferz move to a (3,0) leaper will also result in a compound piece that visits every square on the board. That piece is called a Frog by George Jelliss in his "A Guide to Variant Chess: All the King's Men". I have seen a few invented pieces that combine the move of this Frog with my War Machine. In Mark Hedden's Ganymede Chess, a Pawn promotes to a Frog = W + F + (3,0) leaper. In Adrian King's Scirocco, the complex promotion sequence of the Pawn ends in his Frog = W + F + (3,0) leaper + (3,3) leaper.

Rules

No castling rules in this game. They are not needed, as a War Machine can leap out of the corner at any time. Pawns move only one square at a time and promote to a General of the same color on the last rank. Promotion is not limited in any other way, a player may have up to nine Generals on the board. Victory conditions are the same as for modern chess. In particular, checkmate is a win and stalemate is a draw. It is not hard to verify that King and General can force mate against a lone King. A pair of War Machines should also be able to force mate - note that War Machines on (d2) and (e2) attack every square on the second rank. They even defend each other.

These two short games illustrate how the pieces move:

1.h1-h4 b7-d7 2.h4-e4 d6-d5 3.e4-e5 mate.

1.d2-d3 g8-f6 2.g1-e2 f6-d5 3.b1-d2 d5xe3 mate.

Notes

How did I choose the pieces and setup for this game? First, placing four Cannons in the corners of MIR CHESS 32 and two Rooks on g2 and b7 is an old idea. But there is a problem with Cannons attacking undefended Pawns. Second, I have toyed with the idea of allowing the Cannon to also capture like a Wazir. Such a piece would still be useful late in the endgame. Now add some (debatable) translations of the Grande Acedrex, in which the Lion piece leaps 3 squares orthogonally. I was suddenly struck by the thought that the (almost completely useless) Lion had a vague similarity to the Cannon. So I combined the Wazir with this 3-leaper, called it a War Machine, and substituted it for the Cannon in my first game idea. A week later I remembered that Greg Strong had already used this piece! Midgard Chess shows a strong Shogi influence in the way pieces are set up at each player's right hand. Also there is one (promoted) Shogi Bishop on each side, but it has been pushed back to the first rank. The Pawns are set up to give the board rotational symmetry, in a pattern related to the one used in BURMESE CHESS.

SHATRANJ KAMIL X: 56 empty squares, 44 pieces, 9 piece types. Attack Density is [2.50], the same as classic Shatranj. Attack Density is calculated by adding up the number of adjacent squares each "nonpawn piece" attacks and then dividing by the number of nonpawn pieces. The Cannons cannot capture on adjacent squares, so they count for zero attacks. The large board and wide selection of weak pieces help to make this is my favorite "Western" chess variant using Cannons.

MIDGARD CHESS: 30 empty squares, 34 pieces, 7 piece types. Attack Density is [4.00], the same as modern chess. Since Cannons are not used here, the pieces in this game can be stronger than those in Shatranj or Shatranj Kamil X. These two chess variants have empty squares behind the lines of Pawns. I am going to try a new way of looking at piece density here. In Midgard Chess, the two players are competing to occupy and control the 24 empty squares placed between the two armies. Compare this number with 32 for modern chess and 40 for Shatranj Kamil X.

Pawn = 100, Knight = 300, War Elephant=325, Rook = 500, General = 600 in this game. If anyone is curious, I value a Bishop halfway between a Knight and a War Elephant. The War Machine falls somewhere between 250 and 325, playtesting will be required for a better estimate. In the endgame K+R+R+Pawns versus K+Q+Pawns, we know that two Rooks can easily be traded for a Pawn and a Queen. So it would be unreasonable to value a pair of Rooks lower than a Pawn and a Queen. This raises the interesting question: how often can one player force the trade of two War Machines for a Pawn and a Rook?

"There is some relationship between the geometric length of a piece's longest move and the size of the board, such that a piece can suffer from having too short a range, from being too slow. On the 8x8 board, the Knight is on the cusp. Situations often arise in which the shortness of its move is a disadvantage, but most of the time its move is long enough; in comparison, the WD suffers more notably from shortness (but has other advantages in compensation)." - Ralph Betza.

Adding to Betza's statement, I wish to point out that moving from (b2) to (h8) takes: [3] moves for a War Elephant, [4] moves for a Knight or a War Machine and [6] moves for a King or a WD (Wazir+Dabbabah).



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By David Paulowich.
Web page created: 2007-05-12. Web page last updated: 2007-05-12