Ryuunosuke is Caster's Master in the Fourth Holy Grail War, though "Master" is a generous title for a serial killer with zero magical knowledge or interest in the conflict itself. He got picked by the Holy Grail basically at random to fill out the seven-Master roster, which is pretty fitting considering he has no idea what magic even is.
His summoning of Caster came down to brutal practicality: he murdered a family and used their blood for the ritual. Not exactly by-the-book magecraft, but it worked. What drives Ryuunosuke isn't ambition or desire for a wish—he's just bored and looking for entertainment. He keeps Caster around to watch her kill people in creative, interesting ways. It's all about the spectacle for him. He's essentially using the Holy Grail War as a front for his own twisted hobbies, with no real stake in who wins or what the prize actually is.
Content compiled by AnimeList.moe from publicly available sources.