Parachess

Locations on a hexagon-shaped, 72-rhombus Parachess board can be identified by “transposed” algebraic notation, with rows indicated by the letters a (White's end) through k (Black's end) and positions within rows numbered from White's left.

Three types of single-space moves on a Parachess board are

Longer straight-line movement (similar to a Rook’s or a Bishop’s move in standard chess) can be defined as a series of single-space moves:

Two-step leapers -- similar to a standard chess Knight -- can be developed by combining two different types of one-step moves, with the second step “continuing away” from the starting space: if the first step is edgewise the second step would continue across the opposite edge or the acute angle corner adjacent to the opposite edge (as appropriate), while if the first step is diagonal or arcwise, the second step would continue through the opposite corner or an edge adjacent to the opposite corner.  

A piece analogous to a “Knight”, for example, would shift either one step diagonally followed by one step edgewise or one step edgewise followed by one step diagonally to reach its destination.  A different type of two-step leaper is the “Archer”, which moves by shifting either one space arcwise followed by one space diagonally or one space diagonally followed by one space arcwise. From a central space (such as e5, as shown in the diagram below) a Knight or Archer each has eight possible leaps (the maximum number for each piece), always to a rhombus of a different color not linked to its starting space by an Edge-path, Diagonal-path or Wave-path:

A significant collection of unusual chessmen can be developed from the basic line movements and the variations on the two-step leap patterns sketched above, but a relatively simple variant that bears some resemblance to standard chess involves the following chess pieces:

The Parachess pawn (with four possible moves and up to two captures from any space not on the board’s edge) is more mobile than the standard chess pawn,.   A rough guess at the relative values of the pieces (on a scale where pawns = 1) would be Rook = 3, Bishop = 3, Sorcerer (combination of Knight + Archer) = 3.5 (i.e., between 3 and 4) and Queen = 6. The initial placement of the chessman is illustrated below.

In this variant castling is not permitted. A player wins by either checkmating the opposing King or by stalemating the opponent.

A “Zillions of Games” program for this variant (“Parachess - Queen-SRB Variant”) also includes a number of other variants involving different sets of Parachess pieces. You can download it here: parachess.zip.