Mining for Bits

GUESS WHO STARTED LOOKING STRAIGHT INTO THE COMBAT CODE.

Me, of course. I need a place to write down my observations.

tl;dr: It uses a weighed table based on each servant's personal criticalWeight and 3 random cards are given 50, 20 and 20 extra criticalWeight.

FIRST OFF.
There's a concept of 'critical weight'. It's called that because it's used for a weighed table. Tally up all the results and you get 100%, and each value is a fraction of the pie. So [20 30 50] adds up to 100 and thus the chances become [20% 30% 50%]. If it's [10 5 7 3] then it adds up to 25 and the chances are [40% 20% 28% 12%].

Alright. HOW DOES IT WORK.
First, the game assigns base weights to three of the five cards. 50, 20 and 20.. The cards are then shuffled.
Second, it adds the card's servant's criticalWeight, multiplied by their critical focus factor (This is what Gil's Collector EX does and whatnot), to each card.
What are these criticalWeights? These:

Spoiler:

servant	criticalWeight
Mashu Kyrielite	99
Artoria Pendragon	102
Artoria Pendragon (Alter)	99
Artoria Pendragon (Lily)	102
Nero Claudius	102
Siegfried	97
Gaius Julius Caesar	99
Altera	102
Gilles de Rais	98
Chevalier d'Eon	102
Emiya	145
Gilgamesh	153
Robin Hood	150
Atalanta	148
Euryale	156
Arash	147
Cu Chulainn	87
Elizabeth Bathory	90
Musashibou Benkei	89
Cu Chulainn (Prototype)	88
Leonidas I	89
Romulus	90
Medusa	194
Saint George	205
Edward Teach	198
Boudica	196
Ushiwakamaru	204
Alexander	205
Marie Antoinette	201
Saint Martha	205
Medea	50
Gilles de Rais	48
Hans Christian Andersen	48
William Shakespeare	50
Mephistopheles	50
Wolfgang Amadeus Mozart	49
Zhuge Kongming (El-Melloi II)	50
Cu Chulainn	49
Sasaki Koujirou	102
Hassan of the Cursed Arm	97
Stheno	104
Jing Ke	98
Charles-Henri Sanson	102
Phantom of the Opera	98
Mata Hari	98
Carmilla	98
Heracles	10
Lancelot	10
Lu Bu Feng Xian	9
Spartacus	9
Sakata Kintoki	9
Vlad III	9
Asterion	9
Caligula	9
Darius III	9
Kiyohime	9
Eirik Bloodaxe	9
Tamamo Cat	10
Jeanne d'Arc	99

Yes, Riders and Archers will attract the most stars (plus minus the skew caused by those base weights I mentioned before. Also RNG)
And Gil? Well he'll prolly get ALL THE STARS. The bling extends to his gameplay.

Anyways.
Third, the game tallies up the total weight. Like I said, weighed table.
Fourth, it goes one by one with each star you got. It will roll a random number between 0 and [totalWeight]. Whichever slot corresponds to the number will get the crit star. Imagine it as dividing a dartboard into 5 sections in proportion of each card's criticalWeight and then throwing a dart. Wherever the dart hits, that card gets +X (where X is 11% as of this writing) crit chance.
Fairly simple, really. But now you know why Berserkers never get crits. Unless they luck out and get that base 20 or 50 criticalWeight, their slice of the pie is literally zero almost zero.

Interestingly the devs have a system so cards would get X bonus crit rate for every Y stars they get, but the parameters that control it are both set to 0. I guess they realized it'd go nuts too quickly.