I just expect hentai that flows way too slow to get to the hentai, and I don't really have the tension for this to really be interesting as a death game (and anyways most/almost all death game stuff usually is pretty stupidly setup or doesn't pay out well to begin with).
That aside. She is indeed an idiot. The goal is to please the pervert prince and ultimately your value will be as an object of lust, clearly. Displeasing him is obviously the thing that leads you faster to death. If anything, the saint is probably closest to winning a jewel.
The fine line to figure out here is what turns him off and what he is displeased by. I expect eventually one of them will try to buddy up to the prince and be overly flirtatious and incidentally do something that he dislikes. The real game is figuring out what turns this ugly bastard on and play up to it to his taste. And if his taste is you being unwilling to play to his game but ending up playing his game, then that's what you gotta do, a fine line.