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Armour cannot create negative damage

Part E · L19 · Prerequisite: L18 · One modelling idea

Situation, question, and prediction

Cairn 2e subtracts armour from damage. For a d8 hit against armour 2, how often does no damage get through? Predict what should happen when the raw roll is 1.

Build

Subtract armour first. .clamp(0, 8) floors negative values at zero and puts a ceiling of 8 on the result. The ceiling here is deliberately at the original die maximum, so it cannot reduce any legitimate post-armour result. Probabilities of all floored results collect at zero.

armour = 2
raw = d(8)
damage = (raw - armour).clamp(0, 8)
output("Damage after armour", damage)
output("No damage gets through", damage.pmf(0))

Damage after armour · DieRoll · mean 2.625

No damage gets through · Prob

Run, read, and check

Raw 1 and 2 both become zero: probability 2/8 = 1/4. The remaining values 1–6 each have probability 1/8. The mean is (1+2+3+4+5+6)/8 = 21/8, not raw mean 4.5 minus 2: flooring changes the calculation.

Change one thing

Use armour 3, within Cairn’s cap. No damage becomes 3/8 and mean damage 15/8.

Try it yourself

Apply armour 2 to the mixed-weapon maximum from L16. Answer: join dice, select maximum, subtract, then clamp. Chance of no damage is (2/6)(2/8) = 1/12. Do not armour each weapon and add the results.

Rules and model notes

Cairn second edition, core rules, Armor and Attack Modifiers. Only this damage component; no HP, STR, scars, impairment, or enhancement unless explicitly stated. Armour inputs here are integers 0–3.

What you now know / where next

Armour cannot create negative damage is the reusable idea. Follow the generated previous/next links below, or return to the course index. For a complete self-contained application, see cairn-armour.

Content ID: L19 · Review status: pilot

Prerequisites: L18