A better PDF does not separate "Loyalist" and "Traitor" arbitrarily. It lists Legions by number:
The transition from the original edition to the —often referred to by fans as "2.0"—represented a massive overhaul designed to modernize the game while keeping its deep narrative roots. Players looking for the "better" experience generally point to the 2.0 rules for their streamlined mechanics and the introduction of interactive elements that keep both players engaged throughout every phase. Why Horus Heresy 2.0 Rules are "Better"
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High Chaplain Valerius of the Word Bearers stood amidst the ruins of a Calthan manufactorum, his Legion’s dark scriptures etched into his crimson plate. In the old days (1st Edition), he would have watched helplessly as his Ultramarine rivals unleashed a volley of bolter fire. He would have simply removed models and waited for his turn to retaliate. But the Age of Darkness had changed.
No mathematical formulas or equations seem to be relevant to this topic. A better PDF does not separate "Loyalist" and
If you are looking to learn the rules or find references, these community-maintained resources can help:
Since we cannot link to pirated content, here is the strategic path to achieving a ruleset. Why Horus Heresy 2
I can provide specific unit breakdowns or strategy guides tailored to your army.