You were just unlucky.
To get an accurate depiction of your chances in an 8v3 charisma encounter you would have to do at least a hundred samples, the more the better.
12 is nowhere near enough samples to deliver a verdict on the RPS system.
This is not about experimental statistics.
From what I see, Charisma only does two things:
1. gives you higher score in RPS, a minigame which I don't enjoy playing or winning at all.
2. a slight premium in selling and discount in buying from the +5 attitude per CHA point, while attitude can actually be "bought" for around 10-gold per attitude.
I believe Charisma point has no effect on the outcomes, rather it is only Intimidate/Charm/Reason that decides.
