Now that you mention that, I'm really curious about how PPS handles a random card pick from the player.

I remember that in Marvel Avengers Alliance (a Facebook game for those who haven't played it), in some situations you had to choose between 9 possible squares to receive a random reward. Some guys from that community started to analyse the game's code and realized that the game calculates the prize you won from the random pick before you actually choose anything. Being that said, at the moment the random choice spawned, the reward was already decided, but the game simply displayed the rest of the possible rewards on the rest of the squares depending on the one you choose.

If PPS's random picks works the same way, then we're more depending on probabilities than we would on our own choices ('cause everyone tends to have a pattern when choosing).