This paper presents a parameterized family of equilibrium strategy profiles for three-player Kuhn poker. This family illustrates an important feature of three-player equilibrium profiles that is not present in two-player equilibrium profiles - the ability of one player to transfer utility to a second player at the expense of the third player, while playing a strategy in the profile family. This family of strategy profiles was derived analytically and the proof that the members of this family are equilibrium profiles is an analytic one. In addition, the problem of selecting a robust strategy from an equilibrium profile is discussed.