Firstly, just for back ground. I like the random character gen system. As a player I'm the kind of guy that doesn't always know what he wants to play and the random elements give me a good start to base a solid, balanced character on. As a GM I like when players have to form a character rather than a particular style and I'm quite generous when it comes to mixing it up if some one know's what they want to play.

But, in future I'll be loosing the random fate points roll. I'm quite happy to give players the maximum allowed for their homeworld but it's such a huge ball's up for what ever character ends up with 1 FP compared to 3 for example. If it means that for some reason, the players are particulary blessed then I'll let them have that as it just mean's I can throw what I want to at them with more confidence.

It's nice to see asscenssion reset's there FP to a base of three, gives some hope from my existing characters.

Yeah, I did that from the start, every begins with 3 fate, unless modified by backgrounds or elite advances chosen by the player.

We also rolled randomly, but everyone used the same pool of results and applied each result to the characteristic of their choise.

You could also consider "unlocking" the Cleric/Sororitas background package "Blessed Birth" for the unfortunate that rolled 1 FP. It grants an extra fate point! Or during the divination roll you could roll in secret when the player rolls and then ask them which roll they would like? Some of the results likewise grant a FP. You could also simply assume that everyone rolled a 6, 8 or even 10 on the random FP roll for their character: One of the problems with granting fixed FP is that some of the origins are balanced around granting more or less FP, so it might discourage choosing Void-Born, Mindcleansed and so on.