What determines the success of Axii / Persuasion / Intimidate?

Sometimes in dialog of The Witcher 2, Geralt gets the option to try to alter the course of the conversation with persuasion, intimidate, or the axii sign.

In practice, I've had intimidation fail to work, so I'm curious as to how the chance of success is determined in the first place. Is it related to the level of the abilities gained via use of the related mechanic? E.g., Axii Sign Hex increases when you use the Axii Sign to resolve a conversation.

According to info listed on IGN Vault, you start with a 50/50 random chance of success for each one.

Each time you use one (either succeed or fail) it improves the skill (you'll see a message pop up about acquiring a new skill) thus improving your chance next time.

My person experience was that I succeeded the first/only three times I tried Axii and the first/only time I tried Persuasion, so either I'm very lucky, or it's not really 50/50...