Alright, turn 1 results are in.
As for the mechanics behind them (awful language ahead):
Also, whenever I say d[X] rolls, I mean - a (true) random number between 1 and [X], since I doubt that d3 dice exist (not that I actually did such rolls, but still).
First I did the initiative rolls. Since nobody was planning to shoot, no bonuses from weapons were applied, only the character initiatives. (D20+[initiative bonus])
Then I did two rolls for paladin's ammo crate - first to see whether or not he'd get ammo for his current weapon ie. the shotgun (d2) - if he would score 1 (which he didn't), then I would do another roll to see what kind of ammo would that be, but since we only have two ammo kinds atm it would have to be shells, but if we had more then it would be a d[amount of ammo types - 1] roll - every ammo type would be associated to one number consistent across all such rolls, but that's still for the future.
Once the ammo type is determined, I then rolled a d20 to see how much ammo would he get - in this case it was 7.
Lidku's rad roll was faster - a d8 roll which resulted in 7, therefore, 7 rads. I would add a flat number to that if he had some sort of rad gain bonus, but since that's not yet a case, I didn't do that.
As for GWG's weapon roll, I counted up a number of weapons currently in the game (7) and it turned out to be 5, which is the Slugger. Then I did another roll to see how much ammo that weapon would come with, and it turned out to be 5.
Though I plan to change that system (first roll a weapon category, then roll a weapon from that category), but right now it works the way it works.
Basically there's a lot of numbers and I still do need to document all of this better for future GMs' sake, but now is not the time.