Why can't I take a point in Game of Thrones: Dragonfire?

Because a full point or defender doesn't fall to one army, and that's arithmetic, not bad luck.

The measured numbers: against a full defender (around 14,250 troops), a single one of your armies melts 1,000–2,000 troops per round over 10 rounds and leaves it at roughly 2,500–3,300 — still standing. Result: a stalemate, no capture.

The key is attrition: the defender never heals, not between rounds and not between waves. So:

1. Chain the waves on the same point. Each wave picks up where the last one left off.
2. Once the defender is softened (2,000 or below), one wave finishes it in 1 or 2 rounds.
3. If you have an ally, have them soften the point first — it changes everything.

So the right strategy isn't "one perfect army", it's several waves grinding down a defender that doesn't recover.