There is no way for any one player to observe any 'psuedo-randomness' because the world does not revolve around you. No matter what pattern the RNG may actually possess, by the time you even made a second attempt to gather, tens if not thousands of other players have requested a RNG roll in between that time through any number of actions in this game that require a RNG roll, thus completely negating whatever pattern that may have existed. The only way to see a pattern is if you're able to gather the rolls of every single player playing FF14 at the same time. Otherwise, even if there is a pattern, no single player can ever see it because random players will take your expected roll all the time.