I assume by minning comptuer you mean ASIC. Or at least GPU rig. It depends on hashrate of coin. If noone mines that coin (rare), then you might get away only with simple pc. If coin is minned heavily you won't be profitable and will need ASIC for it. % of total hashrate you have, % of coins of total mined you are gonna have. Of course there also comes diffculty to game and bla bla.