This is something to assist in solo campaigns or as a tool for random encounters, not yet usable with Tyranids or Genestealer Cults:
Step -1: Faction
Before randomly generating the army composition, the faction to which the army belongs has to be determined. This should usually be a direct result of game events or be informed by another random tool (such as one to generate faction active on a planet).
Step 0: Total Strength
The total strength of the army in points is determined by rolling a number of D6 and multiplying the result by 100. The number of dice to be rolled could be random itself, be informed by game events, or derived from other factors (e.g., see the way Mighty Empires determines initial strength based on controlled area and settlements therein).
Step 1: Army Core
Out of all the company cards which cost less than the total strength, one is randomly determined. This is the first company card of the army. The points still availabe are now equal to total strength less the cost of the company card.
Step 2: Determination of Additional Troops
Step 2a: Card Type
D6: 1-3 support card; 4-5 company card; 6 special card
If the type of card determined does not fit within the army, because the maximum allowed number of cards has already been reached, the roll is repeated.
If within the type of card determined, there are no cards whose points value is equal or lower to the available points, the roll is repeated.
Step 2b: Card
Within the card type, one card with cost equal or lower to the available points is randomly determined. This is added to the army.
If an support or special card, it is randomly assigned to a company that still has room to attach such a card.
The points still availabe are reduced by the cost of the company card.
Step 2 and its substeps are repeated until the total strength is matched (0 available points) or until there are no cards left that could be attached to the army without going over the total strength (in which case any leftover available points are discarded).
Demonstration, using the terrible Saharduin:
Total strength: 5W6*100 points; 5, 5, 6, 2, 5; 2300 points
1st Card: Saharduin War School, 550 points; available points: 1750 points (as the War School is the only Saharduin company card, no randomisation is needed)
2nd Card: 5: Company card; Saharduin War School, 550 points; available points: 1200 points
3rd Card: 6: Special card; 1: Piscean Mega, 50 points; available points: 1150 points (used D6 to randomise between the two Saharduin special cards)
3: attached to the 1st company card (also randomised using D6)
4th Card: 5: Company card; Saharduin War School, 550 points; available points: 600 points
5th Card: 1: Support card; 1: Piscean Warrior Shiver, 150 points; available points: 450 points (used D6 to randomise between the five Saharduin support cards)
2: attached to the 1st company (again D6 for randomisation)
6th Card: 3: Support card; 5: Steel Urchin Shoal, 100 points; available points: 350 points
3: attached to the 2nd company card (as there are now three company cards rather than two, the 3 now means attachment to 2nd company rather than 1st)
7th Card: 5: as the available points are no longer sufficient for another War School, the card type is rerolled, 2: Support card; 3: Sea Tank Shoal, 200 points; available points: 150 points
5: attached to the 3rd company card
8th Card: 4: rerolled, 6: Special Card; 6: Saharduin Siren, 100 points; available points: 50 points
5: attached to the 3rd company card
9th Card: Piscean Mega, 50 points; 0 points available
attached to the 2nd company card (neither card not attachment were randomised as for both there was only one legal option – the Piscean Mega is the only Saharduin card with a points value of 50 points and as the 1st and 3rd companies both already have special cards attached, this special card has to go to 2nd company)
Endresult is a Saharduin force consisting of
War School with Piscean Mega and one additional Shiver of Piscean Warriors
War School with Piscean Mega and one Steel Urchin Shoal
Wat School with Saharduin Siren and one Sea Tank Shoal