Hi! Thanks for the interest, I'll try to answer your questions :)
A card-based mechanic sound like something for you. The card mechanic is a replacement to RNG of dice. It does not change the role-play nor the goal of the game, it is just a different resolution mechanic. You are still telling a collaborative story and fighting your way to achieve something. Therefore, I do not think it will trigger your competitive tendencies more than any other RPG. If they do trigger, you are in luck as you will fit the profile of a Kaliva believer (she is one of the Gods of FAITH), who will reward you for your achievements and for trying to be on the top.
I dislike the dice mechanic you mention of automatic failures and successes. There is not such thing in FAITH. Our system is very simple: Whenever you are confronted you must have a final action value higher than the opponent to succeed. You increase your action value by playing cards from your hand (as many as your Attribute, from 1 to 3). You achieve a decisive success by wining by 5 points and a critical by wining by 10 points if your last card was a court card (a 11, 12 or 13).
The other things to keep on mind while using cards are: - Whenever you play a card up to twice the value of your Attribute you draw a new card. Playing low cards keeps your character refreshed but it also decreases your possibilities of wining. The better you character is, the easier is for him to stay fresh. - The suits represent environments: Urban, Nature, Space and Operative System (OS). If you play a card with a matching suit to the location you are in you draw a new card. - The first card you play increases your chances of playing first during that round, but in order to achieve a critical success you should save your court cards for last. You got to choose your play style.
I would recommend you to download the Free P&P if you are interested because I believe that there are a few concepts if this game that could appeal to someone with your profile. I would also love to hear your feedback, from a mathematician and a gamer perspective. Please email us if you do at: [email protected] (this goes for everyone actually!!)
Luck management is what we want to achieve so counting cards (if you can do it) does not diminish the experience. You still have to adapt your play to the story and encounters the GM prepares for you and make big choices each time.
Sorry for the long post :S