Maximummer: Black must play the geometrically longest move or may choose from among longest moves of equal length, distances being measured from the center of each square. Diagonal and oblique distances are measured from the orthogonal coordinates by using Pythagora’s theorem (take the square root of the sum of the squares of the orthogonal distances). All other orthodox chess rules apply.

Circe Equipollents: After a piece is captured, it is immediately replaced on the square which is the same distance and direction from the square of its capture, as was that square from the square upon which its captor commenced its move. (If Qf7 captures a Pawn on e7, it is reborn on d7, because d7 is a same distance and direction from e7 as e7 is from f7. Similarly, if Qg7 captures a piece on ‘e7’ its rebirth square is ‘c7’). If the rebirth square is occupied the captured piece disappears. Castling with replaced Rook is permitted. Pawns may be reborn on the 1st and 8th ranks. Pawns reborn on the 8th rank are promoted as part of rebirth and the promotion is chosen by the player who makes the capture, i.e., if White captures a black Pawn, and the black Pawn is reborn on the 8th rank, White (not Black) decides what Black’s Pawn will be promoted to. Pawns reborn on the 1st or 8th rank can make only one-square move (for example black Pc8 can play only on c7 or it can capture an enemy units on ‘b7’ or ‘d7’). During the en passant capture, the Pawn is replaced on the rank opposite of the captor. For example, if Black moves c7-c5, White Pawn on ‘b5’ captures en passant, moves to ‘c6’, while the black Pawn is reborn on ‘d6’.

Minimummer: Black must play his geometrically shortest move or may choose from among shortest moves of equal length, distances being measured from the center of each square. Diagonal and oblique distances are measured from the orthogonal coordinates by using Pythagoras’s s theorem (take the square root of the sum of the squares of the orthogonal distances). All other orthodox chess rules apply. White Minimummer: White must make moves with minimal possible length.

Marguerite (MG): Moves like all simple hoppers (eagle + grasshopper + hamster + moose + sparrow).
Grasshopper (G): Moves along Q-lines over another unit of either color to the square immediately beyond that unit. A capture may be made on arrival, but the hurdle is not affected.
Eagle (EA): A grasshopper which pivots 90 ^o (to either side) at the hurdle.
Hamster (HA): Moves like a Grasshopper but deflect 180^o on passing over the hurdle.
Moose (M): A grasshopper which pivots 45 ^o (to either side) at the hurdle.
Sparrow (SW): A grasshopper which pivots 135 ^o (to either side) at the hurdle.