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、攻擊流程四步驟1. The Four-Step Attack Sequence
Step 1
命中擲骰Hit Roll
擲 D6 ≥ BS/WS 命中。D6 ≥ BS/WS to hit.
Step 2
致傷擲骰Wound Roll
比較 S 對 T 查表。Compare S vs T on the chart.
Step 3
豁免擲骰Save Rolls
防守方分組並宣告分配順序後，每個致傷擲一顆豁免骰。Defender groups models, declares allocation order, then rolls one save per wound.
Step 4
造成傷害Inflict Damage
由最低結果開始選模型結算；豁免失敗 −D 傷害，可 FNP。Resolve lowest results first; each failed save loses 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% |
| 重擲 1Re-roll 1s | 97.2% | 77.8% | 58.3% | 38.9% | 19.4% |
| 重擲失敗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: 未修改的 1 永遠失敗、未修改的 6 永遠命中（暴擊命中），因此修正無法讓 2+ 打得更準、也無法讓 6+ 完全打不中。An unmodified 1 always fails and an unmodified 6 always hits (critical hit), so modifiers can't push past the 2+ / 6+ values.
三、致傷機率表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 打星際戰士 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 無法影響無敵豁免。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: 11e 每個致傷只擲一顆豁免骰，同一結果同時對照無敵豁免（不受 AP 修正）與甲救（受 AP 修正），任一達標即豁免成功。4++ 保底永遠是 50%，5++ 是 33%，6++ 是 17%。In 11e you roll one save per wound and check the result against both the invulnerable save (unmodified by AP) and the armour save (modified by AP); either passing blocks the wound. A 4++ floor is always 50%, 5++ 33%, 6++ 17%.
五、傷害期望值計算機5. Expected Damage Calculator
Hits
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Wounds
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未豁免Unsaved
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期望傷害Expected Damage
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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（暴擊命中）時可選擇自動致傷（跳過致傷擲骰）。11e 改為可選。
On a critical hit (natural 6) you may choose to auto-wound, skipping the wound roll. Optional in 11e.
對 T>S 目標強：6+ 命中改為自動致傷相當於把 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+ + 連擊 1 ≈ 期望命中 +16.7%。BS 3+ with Sustained 1 ≈ +16.7% expected hits.
Devastating Wounds
致傷擲 6 造成 致命傷，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++ 惡魔親王）。Best vs high-armor or high-invuln targets (2+ Terminators, 4++ Daemon Princes).
Twin-linked
重擲致傷擲骰。
Re-roll the wound roll.
4+ 致傷從 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
致傷 +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+
對載具而言，未修改致傷擲骰 ≥4 即為 暴擊致傷。
Against Vehicle, an unmodified wound roll of 4+ is a critical wound.
暴擊致傷本身就是成功致傷──無論 S/T 差多少，對載具至少 50% 致傷；再搭配 毀滅傷害 威力大增。A critical wound is still a wound — at least 50% to wound a Vehicle regardless of S vs T; devastating with Devastating Wounds.
七、實用估算原則7. Rules of Thumb
三步複利Compounding Three
命中 × 致傷 × 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.
1 點傷害的武器想殺 1 隻 2W 星際戰士，平均需 18 次攻擊。With Damage 1, killing a single 2W Marine needs ~18 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.
重擲的邊際效益Re-roll Diminishing Returns
BS 越好，重擲 1 的邊際收益越低；BS 5+/6+ 重擲全失敗骰效益最大。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。For complex stacking (Sustained + crit mods + FNP layers), external free tools like UnitCrunch are excellent.