Talking about chess variants is more complicated than playing them! Back on [2006-04-03] Joost Brugh commented on this page that there is no forced mate, in general, with Wildebeest + King against lone King. But I suspect that such endgames usually lead to a stalemate victory in Wildebeest Chess.
Falcon Chess has the opposite problem: I have not seen anyone state that King and Falcon can force a lone King into a corner. But consider the following endgame position, which could arise after Black has promoted a Pawn to a Rook, or perhaps captured with his Rook:
White K(b2) and Black K(a4), R(a1), F(h7). After
1.Kxa1 Kb3 2.Kb1, the Falcon moves h7-e6-g3-d4-c1-f2-c4 checkmate.
Talking about chess variants is more complicated than playing them! Back on [2006-04-03] Joost Brugh commented on this page that there is no forced mate, in general, with Wildebeest + King against lone King. But I suspect that such endgames usually lead to a stalemate victory in Wildebeest Chess.
Falcon Chess has the opposite problem: I have not seen anyone state that King and Falcon can force a lone King into a corner. But consider the following endgame position, which could arise after Black has promoted a Pawn to a Rook, or perhaps captured with his Rook: