This checkers variant is based on Crossings, invented by Robert Abbott and first described in Sid Sackson's A Gamut of Games. Like orthodox checkers, Neo-Crossings is played on an 8×8 board.
Each player begins with 16 checkers of his color, starting on the two ranks nearest him. White moves first, after which Black and White alternate turns.
Each player, in turn, moves either a single checker or a "phalanx" of his color. A phalanx is a line of two or more checkers of the same color, lying along a vertical, horizontal or diagonal line. Under this definition, a checker may belong to more than one phalanx.
A checker may move one space in any direction, like a king in chess. A phalanx may move, as a unit, any number of squares less than or equal to the number of checkers in the phalanx. When pieces in a phalanx move, they must all move the same distance and direction, and only along the line that defines the phalanx.
A player may "split up" a phalanx and move just part of it, as long as the checkers that move form an unbroken line, and the number of checkers moved is equal to or greater than the number of spaces moved.
A phalanx may not move over or through friendly pieces, but the "head" checker of a phalanx may land on either a single enemy piece or the first piece of a smaller phalanx. If the opposing phalanx is greater than or equal in size to the moving phalanx, the capturing move cannot be made. In determining phalanx size, the player considers only its length along the line of movement, and only those pieces that make the move are counted.
When the head of a phalanx lands on the head of an opposing phalanx, the entire opposing phalanx is captured. (This is the key rule change from Crossings. In that game, only the checker on which the player landed was captured.) Capturing moves are never compulsory.
A player wins if, at the start of his proper turn, he has more checkers on the row farthest from him than his opponent has on the row farthest from her. Stated differently, when a player gets one of his checkers to the opposite side of the board, he will win unless the opponent either captures this piece immediately or gets (or already has) one of her own pieces on the last rank. If both players have the same number of checkers on the ranks opposite them, the game continues.
If Black mimics White by making moves that are symmetrical with respect to the center point of the board (that is, a play on the left is mirrored by an opposing play in the opposite direction on the right), the game ends in a draw. The following rule will eliminate this strategy: A player may not move a piece onto the row farthest from him if the move could create a pattern of left-to-right symmetry.
Board sizes other than 8×8 will work well. The reason some players prefer a board wider than it is deep is to make the diagonals closer in value to the orthogonal lines of movement.