Solidity check — the 10% rule, corrected

Are you protected from your troop-triangle counter? The required defence surplus is 10 points on day one and ~25 at endgame stacks (Algorithm A3, Theorems 4–6).

Combat math

Economy & progression

Solidity check — the 10% rule, corrected

Are you protected from your troop-triangle counter? The required defence surplus is 10 points on day one and ~25 at endgame stacks (Algorithm A3, Theorems 4–6).

Attacker’s summed attack

their whole attack stack: tech + skills + talents + gear + buffs

Your summed defence

your whole defence stack, same categories

Worked example — compendium D.8 / Figure 14

Field	Example	Where it comes from
Attacker’s attack	150%	a typical spender endgame stack
Your defence	160%	your stack — a 10-point surplus, the old field rule
κ	1.10	5% base triangle bonus, ~doubled by troop-tree talents

Result: R ≈ 1.058 — the 10-point cushion no longer protects you at endgame stacks; you need 25 points (s* = (κ−1)(1+a)).

Counter coefficient κ (troop-triangle bonus)

The “10% rule”, corrected

The required surplus is s* = (κ−1)(1+a): exactly 10 points on day one (a = 0), but it inflates linearly with the meta’s attack stacks — ~25 points once attackers sit at +150%. A fixed 10-point cushion stops protecting you mid-game.

Solidity ratio R

1.100×

R > 1 — the counter-type attacker still hits you harder than a same-type one.

Required surplus s*

10.0 pts

defence points above the attacker’s 0% needed for exact parity

Your current surplus

0.0 pts

10.0 more points of defence close the gap

Damage mitigation from surplus

−0.0%

a defence surplus is a reverse shred: it scales ALL incoming damage down by s/(1+a+s) — Theorem 6