Basilisk chess is an attempt to increase complexity in Fide-chess and
a response to the ongoing routinization of chess. It includes the
possibility to play a standard Fide-chess game, anyway, by a voting
procedure.

The Basilisk was a monster cannon used in medieval times. After having
jumped any piece, the Basilisk can slide and capture like a queen.
However, if no jump move exists it's allowable to slide like a queen,
but without capturing. Enemy pawns, however, can restrict its
movement. The Basilisk can only reach the square immediately behind
the enemy pawn, regardless of leaping direction. Its value is 4 in a
Fide-chess context. It is reminiscent of the Korean Cannon. Its
tactical capacity leads to interesting games, and an attack can
sometimes be initiated already in the opening phase.
http://hem.passagen.se/melki9/basiliskchess.htm

Mats