This article deals with classes of antagonistic games with two players. A game is specified in terms of two "hostile" stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. The game ends when one of the players is defeated. We target the first passage time τρ of the defeat and the amount of casualties to either player upon τρ. Here we validate our claim of analytic tractability of the general formulas obtained in [1] under various transforms.