Orthochess

Problems of this sort have been exhaustively dealt with for orthochess (see A Guide to Fairy Chess, p. 39, for tables of results); Haas here presents 59 positions showing his best results for all possible moves, type A.

Source: wiktionary

Avalanche chess is the same as orthochess, except that every move consists of two parts: (1) a normal legal chess move; and (2) pushing an opponent's pawn one square straight toward you. That's all there is to it really.

Source: wiktionary

In consequence, Italian domination of Progressive Chess was for many years comparable to that of Soviet domination of orthochess in times past.

Source: wiktionary