The player with the White pieces in Leaping/Missing Bat Chess has 4 Alfils (which can reach every square on the odd-numbered ranks) and 2 Dababbas (which can reach every square on the even-numbered ranks). Reverse 'odd' and 'even' for the Black pieces. This variant makes it impossible to trade an Alfil for an Alfil (or a Dababba for a Dababba).
For another approach to covering the chessboard with colorbound pieces, see my Shatranj Kamil (64)
page. The Elephants in this variant may move like an Alfil or a noncapturing Dababbah. This results in a weaker version of the Alibaba, visiting 16 of the squares on the board. Thus the two White Elephants control the 32 light squares between them, while the White General (Ferz) controls the 32 dark squares. An Elephant is intended to have the same value as a General, so it would be reasonable to trade one for the other.
The player with the White pieces in Leaping/Missing Bat Chess has 4 Alfils (which can reach every square on the odd-numbered ranks) and 2 Dababbas (which can reach every square on the even-numbered ranks). Reverse 'odd' and 'even' for the Black pieces. This variant makes it impossible to trade an Alfil for an Alfil (or a Dababba for a Dababba).
For another approach to covering the chessboard with colorbound pieces, see my Shatranj Kamil (64) page. The Elephants in this variant may move like an Alfil or a noncapturing Dababbah. This results in a weaker version of the Alibaba, visiting 16 of the squares on the board. Thus the two White Elephants control the 32 light squares between them, while the White General (Ferz) controls the 32 dark squares. An Elephant is intended to have the same value as a General, so it would be reasonable to trade one for the other.