戰錘 40K 攻擊流程為連串機率事件，新手常低估「小概率事件疊加」的影響。本頁提供三張核心速查表、一台期望值計算機、與常見能力的數值修正對照，協助你評估單位戰鬥力與戰術抉擇。
40K's attack sequence is a chain of independent dice events. New players tend to underestimate how compounding probabilities erode damage output. This page provides the three core probability tables, an expected-damage calculator, and a cheat sheet for common ability modifiers.
一、攻擊流程五步驟1. The Five-Step Attack Sequence
Step 1
命中擲骰Hit Roll
擲 D6 ≥ BS/WS 命中。D6 ≥ BS/WS to hit.
Step 2
打傷擲骰Wound Roll
比較 S 對 T 查表。Compare S vs T on the chart.
Step 3
分配傷害Allocate
防守方選擇承受模型。Defender picks the model.
Step 4
豁免擲骰Save Roll
Sv − AP，或 無敵豁免。Sv − AP, or invulnerable.
Step 5
造成傷害Damage
失敗每次 −D 傷害，可 FNP。Each failed save: lose D wounds; FNP applies.
二、命中機率表2. Hit Probability (vs BS/WS)
擲 D6，≥ BS/WS 的所需點數。自然 1 永遠失敗，自然 6 永遠命中。Roll D6 ≥ BS/WS. Natural 1 always fails, natural 6 always hits.
| BS/WS | 2+ | 3+ | 4+ | 5+ | 6+ |
|---|---|---|---|---|---|
| 基礎Base | 83.3% | 66.7% | 50.0% | 33.3% | 16.7% |
| 重骰 1Re-roll 1s | 97.2% | 77.8% | 58.3% | 38.9% | 19.4% |
| 重骰失敗Re-roll Fails | 97.2% | 88.9% | 75.0% | 55.6% | 30.6% |
| +1 命中+1 to Hit | 83.3%* | 83.3% | 66.7% | 50.0% | 33.3% |
* 封頂Cap: 命中值改動最多只能達到 2+（最好）與 6+（最差），不可達 1+ 或自動命中/失敗。Modifiers cap at 2+ (best) and 6+ (worst); natural 1 still fails and natural 6 still succeeds.
三、打傷機率表3. Wound Probability (S vs T)
比較攻擊 S 與目標 T：Compare attacker's Strength (S) to target's Toughness (T):
| 比較Comparison | 所需骰數Needs | 機率Probability |
|---|---|---|
| S ≥ 2×T | 2+ | 83.3% |
| S > T | 3+ | 66.7% |
| S = T | 4+ | 50.0% |
| S < T | 5+ | 33.3% |
| 2×S ≤ T | 6+ | 16.7% |
例Ex: 爆彈槍 S=4 打 Space 陸戰隊員 T=4，需 4+ = 50%；打 終結者 T=5 則需 5+ = 33.3%；打 犀牛 T=9 則 2×S=8 < T，需 6+ = 16.7%。Bolter S=4 vs Space Marine T=4 needs 4+ (50%); vs Terminator T=5 needs 5+ (33%); vs Rhino T=9 where 2×S=8 < T, needs 6+ (17%).
四、豁免機率表4. Save Probability (Sv − AP)
豁免值被武器 AP 削減：Sv 2+、AP −1 → 3+ 豁免。AP 無法突破 無敵豁免 豁免（無敵豁免）。Sv is worsened by the weapon's AP: Sv 2+ with AP −1 becomes 3+. Invulnerable saves ignore AP.
| Sv ↓ / AP → | 0 | −1 | −2 | −3 | −4 | −5 |
|---|---|---|---|---|---|---|
| 2+ | 83.3% | 66.7% | 50.0% | 33.3% | 16.7% | 0% |
| 3+ | 66.7% | 50.0% | 33.3% | 16.7% | 0% | 0% |
| 4+ | 50.0% | 33.3% | 16.7% | 0% | 0% | 0% |
| 5+ | 33.3% | 16.7% | 0% | 0% | 0% | 0% |
| 6+ | 16.7% | 0% | 0% | 0% | 0% | 0% |
Invulnerable: 無敵豁免不受 AP 影響，但須與一般豁免擇一擲出。4++ 永遠是 50%，5++ 是 33%，6++ 是 17%。Invulnerable saves ignore AP but you may only roll one save per wound. 4++ is always 50%, 5++ is 33%, 6++ is 17%.
五、傷害期望值計算機5. Expected Damage Calculator
Hits
—
Wounds
—
未豁免Unsaved
—
期望傷害Expected Damage
—
讀法Reading: 「期望傷害」為多次戰鬥的平均值。單次戰鬥實際結果可能高或低——骰運會讓 2 點期望傷害打出 0 或 5。用期望值比較武器選擇，不用它預測單回合結局。Expected damage is the long-run average. A single combat can roll much higher or lower. Use it to compare weapon choices, not to predict the outcome of one attack.
六、常見能力的數學影響6. Ability Math: How Much Do Buffs Really Help?
Lethal Hits
命中擲 6 自動打傷（跳過 致傷擲骰）。
Critical hit (natural 6) auto-wounds, skipping the wound roll.
對 T>S 目標強：6+ 命中改為自動打傷相當於把 1/6 命中轉成必中傷。Strong vs T>S targets; converts 1/6 of hits into auto-wounds regardless of S.
Sustained Hits X
命中 6 額外造成 X 次命中。
Natural 6 to hit generates X additional hits.
BS 3+ + 持續命中 1 ≈ 期望命中 +16.7%。BS 3+ with Sustained 1 ≈ +16.7% expected hits.
Devastating Wounds
打傷擲 6 造成 致命 致傷s，略過豁免。
Critical wound (natural 6) deals Mortal Wounds, bypassing saves.
對高 Sv 與高 Inv 目標效益最大（如 2+ 終結者、4++ 惡魔王子）。Best vs high-armor or high-invuln targets (2+ Terminators, 4++ Daemon Princes).
Twin-linked
重骰打傷擲骰。
Re-roll the wound roll.
4+ 打傷從 50% → 75%，S=T 的情境最有感。Turns 4+ wound (50%) into 75%; most impactful when S equals T.
+1 to Wound
打傷 +1 修正。
+1 modifier to the wound roll.
4+ → 3+（50% → 67%），S<T 場合把 5+ 變 4+ 更關鍵。4+ → 3+ (50% → 67%); crucial when S<T, turning 5+ into 4+.
Anti-Vehicle 4+
對載具擲 ≥4 為 致命致傷（配 致命/毀滅 威力大增）。
Against Vehicle, wound rolls of 4+ count as critical (powerful with Lethal/Devastating).
本身不自動打傷，需搭配 致命命中 或 毀滅傷害 才發揮。Doesn't auto-wound by itself; shines with Lethal Hits or Devastating Wounds.
七、實用估算原則7. Rules of Thumb
三步複利Compounding Three
命中 × 打傷 × 失敗豁免：0.67 × 0.5 × 0.33 ≈ 0.11。每次攻擊平均只有 11% 成功。Hit × Wound × Failed-save. A typical 3+/S=T/3+Sv chain ≈ 0.67 × 0.5 × 0.33 ≈ 11% per attack.
想殺 1 隻 陸戰隊員 平均需 9~10 次攻擊。Killing a single 2W Marine needs ~9–10 attacks.
傷害期望 = DExpected D for D-dice
D3 期望 2，D6 期望 3.5，D6+1 期望 4.5。D3 averages 2; D6 averages 3.5; D6+1 averages 4.5.
但多點高傷害 = 高變異，容易「過量傷害」浪費。High variance → overkill waste on low-wound targets.
武器配對目標Match Weapon to Target
多次低傷武器打小兵；少次高傷武器打大怪或載具。Many low-D attacks for chaff; few high-D shots for monsters/vehicles.
爆彈槍 不該打 騎士，雷射加農砲 不該打 教徒暴民。Don't fire bolters at Knights or lascannons at cultists.
重骰的邊際效益Re-roll Diminishing Returns
BS 越好，重骰 1 的邊際收益越低；BS 5+/6+ 重骰全失敗骰效益最大。Better BS = lower marginal gain from re-rolling 1s; worst-BS benefits most from "re-roll all fails."
誓言時刻 因此對命中 4+/5+ 的武器特別有價值。Oath of Moment is disproportionately strong on BS 4+/5+ weapons.
進階工具Advanced Tools: 想模擬更複雜情境（Sustained + Crit Mods + FNP 堆疊），推薦外部免費工具如 UnitCrunch 或 Wahapedia 的機率專欄。For complex stacking (Sustained + crit mods + FNP layers), external free tools like UnitCrunch or Wahapedia's math section are excellent.