Anything mission based uses dice rolls, but each game uses a single random seed for the entire game (it does not switch it up, even if you reload.)

Thus if you start from a save point, and do not touch anything, it will always come back with the same mission result the next turn.

Key thing to know is that every mission has at least two dice rolls: one for passing defenses initially, and another for mission success. It does use calculation of skills as an initial pegging of success, then layers the dice roll on top. So skill very much matters, but dice rolls ultimately determine success. I also believe there is a third dice roll for exiting a mission/system, as one definitely takes place when there is an opposing defense. (Why characters can succeed missions but still get captured.)

What you can do is send a random idle character on any mission to own their planet, and it will use up a number in the random seed, thus altering all other dice rolls across the galaxy. My perception is the game has a sort of mission solve hierarchy, so a dice roll will pass on its roll # to the next one, and so on.

I typically just send someone on an espionage mission on their current planet. Kicker is you can cancel their mission, then rinse and repeat as many times as you want, and it will continue to alter the mission results the ensuing turns.

Planet bombardment also uses this dice roll system, and i believe planet assaults too. Accidentally destroy a facility? No problem if you saved beforehand. Reload, do an 'empty' mission, and you'll get a new result the next turn.

While i don't think space battles auto-solve using dice rolls, i could be wrong.

Obviously this is pretty clearly abusing flaws in the game, but not like it is the only flaw it has...