feat(ama): implement Milestone M12 Amazon Bow and Crossbow skills tree (#459)

src/game/engine/combat-pipeline.ts

@@ -323,6 +323,7 @@ export interface SUnitDmgPacket {
   readonly elemMin256?: number
   readonly elemMax256?: number
   readonly elemDurationFrames?: number
+  readonly slvl?: number
   readonly physToElemPct?: number // e.g. Berserk 100% magic, Magic Arrow / Fire Arrow %
   readonly concentrationBonusPct?: number // active Concentration aura %ED for Blessed Hammer (50% efficiency)
   readonly convictionPierce?: number
@@ -460,7 +461,15 @@ export function executeSUnitDmg(
   // 3. Weapon `srcdam` (128 = 100%) + Physical Damage calculation
   const hasFlatPhys = (packet.flatPhysMin256 !== undefined && packet.flatPhysMin256 > 0) || (packet.flatPhysMax256 !== undefined && packet.flatPhysMax256 > 0)
   const isSpellWithoutFlatPhys = attackKind === 'spell' && !hasFlatPhys
-  const srcDam = isSpellWithoutFlatPhys ? 0 : (packet.srcDam ?? (attackKind !== 'spell' ? 128 : 0))
+  const srcDam =
+    isSpellWithoutFlatPhys
+      ? 0
+      : (packet.srcDam ??
+        (packet.skillId === 12 || packet.skillId === 26
+          ? 96
+          : attackKind !== 'spell'
+            ? 128
+            : 0))
   let rawPhys256 = 0
   if (!isSpellWithoutFlatPhys && (srcDam > 0 || hasFlatPhys)) {
     const weapMin256 = (attacker.weaponMinPhys ?? 25) * FIXED_ONE
@@ -517,7 +526,15 @@ export function executeSUnitDmg(
 
   // 4. Physical-to-Elemental/Magic Conversion (e.g. Berserk 100% Magic, Magic Arrow, Fire Arrow, Cold Arrow)
   let rawElem256 = Math.trunc(((packet.elemMin256 ?? 0) + (packet.elemMax256 ?? 0)) / 2)
-  const convPct = Math.max(0, Math.min(100, packet.physToElemPct ?? (packet.skillId === 152 ? 100 : 0)))
+  const defaultConvPct =
+    packet.skillId === 152
+      ? 100
+      : packet.skillId === 7 || packet.skillId === 11
+        ? 80
+        : packet.skillId === 6
+          ? Math.min(100, 5 + Math.max(0, (packet.slvl ?? attacker.statList.getEffectiveSkillLevel(6) ?? 1) - 1))
+          : 0
+  const convPct = Math.max(0, Math.min(100, packet.physToElemPct ?? defaultConvPct))
   if (convPct > 0 && rawPhys256 > 0) {
     const converted256 = Math.trunc((rawPhys256 * convPct) / 100)
     rawPhys256 -= converted256
@@ -525,7 +542,14 @@ export function executeSUnitDmg(
   }
 
   // 5. Elemental Mastery & 1.13c Blessed Hammer / Venom / Static Field / Enchant rules
-  let elemType = (packet.elemType ?? (packet.skillId === 152 || packet.skillId === 112 ? 'mag' : 'fire')).toLowerCase()
+  let elemType = (
+    packet.elemType ??
+    (packet.skillId === 6 || packet.skillId === 152 || packet.skillId === 112
+      ? 'mag'
+      : packet.skillId === 11 || packet.skillId === 21 || packet.skillId === 31
+        ? 'cold'
+        : 'fire')
+  ).toLowerCase()
 
   // Added elemental damage from Paladin offensive auras (Holy Fire, Holy Freeze, Holy Shock) on physical attacks
   if (attackKind !== 'spell' && packet.skillId !== 97) {

src/game/engine/missile-engine.ts

@@ -20,6 +20,14 @@ import { getBlizzardDropOffset } from './blizzard-table.ts'
 import { METEOR_FIRE_SUBTILE_OFFSETS } from './meteor-table.ts'
 import { calculateMeteorResidualFireDamage } from '../skills.ts'
 import { compute5BandScaling, computeDiminishingReturns } from './calc-ast.ts'
+import {
+  calculateMultipleShotStats,
+  calculateStrafeStats,
+  calculateIceArrowStats,
+  calculateFreezingArrowStats,
+  generateMultipleShotAngles,
+  isMultipleShotCenterArrow,
+} from '../skills/amazon-bow.ts'
 
 export const ISO_GROUND_ASPECT_RATIO = 0.5
 
@@ -647,6 +655,8 @@ export interface ActiveMissile {
   originX?: number | undefined
   originY?: number | undefined
   spiralTheta?: number | undefined
+  readonly volleyId?: string | undefined
+  readonly canTriggerProcs?: boolean | undefined
 }
 
 export interface MissileTerrainCollision {
@@ -668,6 +678,7 @@ export class MissileEngine {
   readonly registry: D2DataRegistry
   private readonly missiles: ActiveMissile[] = []
   private readonly nextDelayExpireByTarget = new Map<string, number>()
+  private readonly volleyHits = new Set<string>()
   private uidCounter = 1
   terrain?: MissileTerrainCollision | undefined
 
@@ -704,6 +715,8 @@ export class MissileEngine {
     vx?: number
     vy?: number
     angleRad?: number
+    volleyId?: string
+    canTriggerProcs?: boolean
   }): ActiveMissile | null {
     const rec =
       typeof params.missileNameOrId === 'number'
@@ -880,8 +893,18 @@ export class MissileEngine {
       maxRangeTicks,
       nextHit: effectiveRec.nextHit,
       nextDelayFrames: effectiveRec.nextDelay,
-      canPierce: effectiveRec.pierce || !effectiveRec.collideKill || (params.pierceChancePct ?? 0) > 0 || effectiveRec.name === 'bonespear',
+      canPierce:
-      pierceChancePct: params.pierceChancePct ?? (effectiveRec.pierce || !effectiveRec.collideKill || effectiveRec.name === 'bonespear' ? 100 : 0),
+        params.sourceSkillId === 22 ||
+        effectiveRec.name.toLowerCase() === 'guidedarrow' ||
+        effectiveRec.id === 86
+          ? false
+          : effectiveRec.pierce || !effectiveRec.collideKill || (params.pierceChancePct ?? 0) > 0 || effectiveRec.name === 'bonespear',
+      pierceChancePct:
+        params.sourceSkillId === 22 ||
+        effectiveRec.name.toLowerCase() === 'guidedarrow' ||
+        effectiveRec.id === 86
+          ? 0
+          : (params.pierceChancePct ?? (effectiveRec.pierce || !effectiveRec.collideKill || effectiveRec.name === 'bonespear' ? 100 : 0)),
       pierceCount: 0,
       hitTargetIds: new Set<string>(),
       dmgPacket: params.dmgPacket,
@@ -889,6 +912,8 @@ export class MissileEngine {
       lastHitTargetId: params.lastHitTargetId,
       expired: false,
       isTurret,
+      ...(params.volleyId !== undefined ? { volleyId: params.volleyId } : {}),
+      ...(params.canTriggerProcs !== undefined ? { canTriggerProcs: params.canTriggerProcs } : {}),
       ...(params.altitude !== undefined ? { altitude: params.altitude } : {}),
       ...(params.fireCadenceTicks !== undefined
         ? { fireCadenceTicks: params.fireCadenceTicks }
@@ -1093,7 +1118,10 @@ export class MissileEngine {
         // Authentic 1.13c Homing mechanics (Bone Spirit / Guided Arrow, pSrvDoFunc = 7):
         // Continuously tracks and steers toward closest active hostile target in 2:1 isometric perspective
         if (
-          (m.name.toLowerCase() === 'bonespirit' || m.record.pSrvDoFunc === 7) &&
+          (m.name.toLowerCase() === 'bonespirit' ||
+            m.name.toLowerCase() === 'guidedarrow' ||
+            m.sourceSkillId === 22 ||
+            m.record.pSrvDoFunc === 7) &&
           !m.name.includes('explode')
         ) {
           let closestTarget: { x: number; y: number } | null = null
@@ -1115,9 +1143,17 @@ export class MissileEngine {
           if (closestTarget) {
             const speed = m.record.vel ? m.record.vel : 12
             const targetAngle = Math.atan2((closestTarget.y - m.y) / ISO_GROUND_ASPECT_RATIO, closestTarget.x - m.x)
-            m.angleRad = targetAngle
+            let diff = targetAngle - m.angleRad
-            m.vx = Math.cos(targetAngle) * speed
+            while (diff < -Math.PI) diff += Math.PI * 2
-            m.vy = Math.sin(targetAngle) * speed * ISO_GROUND_ASPECT_RATIO
+            while (diff > Math.PI) diff -= Math.PI * 2
+            const maxTurn = 0.45
+            if (Math.abs(diff) <= maxTurn) {
+              m.angleRad = targetAngle
+            } else {
+              m.angleRad += Math.sign(diff) * maxTurn
+            }
+            m.vx = Math.cos(m.angleRad) * speed
+            m.vy = Math.sin(m.angleRad) * speed * ISO_GROUND_ASPECT_RATIO
           }
         }
 
@@ -1258,6 +1294,7 @@ export class MissileEngine {
       // Check collision against alive enemy targets
       if (
         (m.name === 'meteorfire' && m.ageTicks % 5 === 0) ||
+        (m.name === 'immolationfire' && m.ageTicks % 5 === 0) ||
         m.name === 'firewall' ||
         m.name === 'blaze' ||
         m.name === 'groundfirebig' ||
@@ -1317,6 +1354,7 @@ export class MissileEngine {
         const pos = targetPositions.get(target.id) ?? { x: 0, y: 120 }
         const isGroundPatch =
           m.name === 'meteorfire' ||
+          m.name === 'immolationfire' ||
           m.name === 'firewall' ||
           m.name === 'blaze' ||
           m.name === 'groundfirebig'
@@ -1324,6 +1362,21 @@ export class MissileEngine {
           ? Math.hypot(pos.x - m.x, (pos.y - m.y) / ISO_GROUND_ASPECT_RATIO)
           : Math.hypot(pos.x - m.x, pos.y - m.y)
         if (dist <= hitRadius) {
+          // Multiple Shot volley multi-hit immunity
+          if (m.volleyId) {
+            const vKey = `${m.volleyId}:${target.id}`
+            if (this.volleyHits.has(vKey)) {
+              continue
+            }
+            this.volleyHits.add(vKey)
+          }
+
+          // Guided Arrow strict zero-pierce enforcement
+          if (m.sourceSkillId === 22 || m.name.toLowerCase() === 'guidedarrow' || m.missileId === 86) {
+            ;(m as any).canPierce = false
+            ;(m as any).pierceChancePct = 0
+          }
+
           // Enforce `NextDelay` immunity gate if `nextHit` / `nextDelayFrames > 0`
           if (m.nextDelayFrames > 0 && this.isTargetInNextDelay(target.id, currentTick)) {
             continue
@@ -1401,14 +1454,119 @@ export class MissileEngine {
             }
           }
 
-          // `pSrvHitFunc = 1` or `4` or `13`: radial splash damage (`Fire Ball`, `Exploding Arrow`, `Freezing Arrow`, `Glacial Spike`)
+          // Ice Arrow (Skill 21 / missile icearrow): freezes primary target solid
+          if (m.name === 'icearrow' || m.sourceSkillId === 21) {
+            if (!dmgOut.immuneToElem && !target.statList.getAccruedStat('cannot_be_frozen')) {
+              const frzFrames = m.dmgPacket.elemDurationFrames ?? calculateIceArrowStats(m.slvl).freezeFrames
+              target.stateBus.applyState({
+                stateNameOrId: 'freeze',
+                sourceSkillId: 21,
+                slvl: m.slvl,
+                durationFrames: frzFrames,
+              })
+            }
+          }
+
+          // Freezing Arrow (Skill 31 / missile freezingarrow): freezes primary target solid
+          if (m.name === 'freezingarrow' || m.sourceSkillId === 31) {
+            if (!dmgOut.immuneToElem && !target.statList.getAccruedStat('cannot_be_frozen')) {
+              const frzFrames = m.dmgPacket.elemDurationFrames ?? calculateFreezingArrowStats(m.slvl).freezeFrames
+              target.stateBus.applyState({
+                stateNameOrId: 'freeze',
+                sourceSkillId: 31,
+                slvl: m.slvl,
+                durationFrames: frzFrames,
+              })
+            }
+          }
+
+          // Sub-missiles on hit for Amazon Bow skills (explodingarrow, icearrow, immolationarrow, freezingarrow)
+          if (m.name === 'explodingarrow' || m.sourceSkillId === 16) {
+            const expName = m.record.explosionMissile || 'explodingarrowexp'
+            this.spawnMissile({
+              missileNameOrId: expName,
+              sourceSkillId: m.sourceSkillId,
+              slvl: m.slvl,
+              owner: m.owner,
+              startX: m.x,
+              startY: m.y,
+              targetX: m.x,
+              targetY: m.y,
+              dmgPacket: m.dmgPacket,
+            })
+            subMissilesSpawned.push(expName)
+          }
+
+          if (m.name === 'immolationarrow' || m.sourceSkillId === 27) {
+            const patchName = m.record.hitSubMissile1 || 'immolationfire'
+            this.spawnMissile({
+              missileNameOrId: patchName,
+              sourceSkillId: m.sourceSkillId,
+              slvl: m.slvl,
+              owner: m.owner,
+              startX: m.x,
+              startY: m.y,
+              targetX: m.x,
+              targetY: m.y,
+              dmgPacket: m.dmgPacket,
+              maxRangeTicks: 75,
+            })
+            subMissilesSpawned.push(patchName)
+          }
+
+          if (m.name === 'freezingarrow' || m.sourceSkillId === 31) {
+            const expName = m.record.explosionMissile || 'freezingarrowexp'
+            this.spawnMissile({
+              missileNameOrId: expName,
+              sourceSkillId: m.sourceSkillId,
+              slvl: m.slvl,
+              owner: m.owner,
+              startX: m.x,
+              startY: m.y,
+              targetX: m.x,
+              targetY: m.y,
+              dmgPacket: m.dmgPacket,
+            })
+            subMissilesSpawned.push(expName)
+          }
+
+          if (m.name === 'icearrow' || m.sourceSkillId === 21) {
+            const expName = m.record.explosionMissile || 'icearrowexplode'
+            this.spawnMissile({
+              missileNameOrId: expName,
+              sourceSkillId: m.sourceSkillId,
+              slvl: m.slvl,
+              owner: m.owner,
+              startX: m.x,
+              startY: m.y,
+              targetX: m.x,
+              targetY: m.y,
+              dmgPacket: m.dmgPacket,
+            })
+            subMissilesSpawned.push(expName)
+          }
+
+          // `pSrvHitFunc = 1` or `4` or `9` or `13`: radial splash damage (`Fire Ball`, `Exploding Arrow`, `Freezing Arrow`, `Immolation Arrow`, `Glacial Spike`)
           if (
             m.record.pSrvHitFunc === 1 ||
             m.record.pSrvHitFunc === 4 ||
             m.record.pSrvHitFunc === 9 ||
-            m.record.pSrvHitFunc === 13
+            m.record.pSrvHitFunc === 13 ||
+            m.sourceSkillId === 16 ||
+            m.sourceSkillId === 27 ||
+            m.sourceSkillId === 31 ||
+            m.name === 'explodingarrow' ||
+            m.name === 'immolationarrow' ||
+            m.name === 'freezingarrow'
           ) {
-            const splashRadius = (m.record.pSrvHitFunc === 13 || m.name === 'glacialspike' || m.sourceSkillId === 55) ? 64 : 85
+            const isBowAoE =
+              m.sourceSkillId === 16 ||
+              m.sourceSkillId === 27 ||
+              m.sourceSkillId === 31 ||
+              m.name === 'explodingarrow' ||
+              m.name === 'immolationarrow' ||
+              m.name === 'freezingarrow'
+            const splashRadius = isBowAoE ? 80 : (m.record.pSrvHitFunc === 13 || m.name === 'glacialspike' || m.sourceSkillId === 55 ? 64 : 85)
             for (const other of targets) {
               if (other.id === target.id || other.statList.getHp256() <= 0) continue
               const oPos = targetPositions.get(other.id) ?? { x: 0, y: 120 }
@@ -1420,6 +1578,18 @@ export class MissileEngine {
                   damage: splashOut.totalDamage,
                   immune: splashOut.immuneToElem || splashOut.immuneToPhys,
                 })
+                // Freezing Arrow splash targets also receive solid freeze
+                if (m.name === 'freezingarrow' || m.sourceSkillId === 31) {
+                  if (!splashOut.immuneToElem && !other.statList.getAccruedStat('cannot_be_frozen')) {
+                    const frzFrames = m.dmgPacket.elemDurationFrames ?? calculateFreezingArrowStats(m.slvl).freezeFrames
+                    other.stateBus.applyState({
+                      stateNameOrId: 'freeze',
+                      sourceSkillId: 31,
+                      slvl: m.slvl,
+                      durationFrames: frzFrames,
+                    })
+                  }
+                }
                 // Glacial Spike splash targets also receive solid freeze
                 if (m.name === 'glacialspike' || m.sourceSkillId === 55 || m.record.pSrvHitFunc === 13) {
                   if (!splashOut.immuneToElem && !other.statList.getAccruedStat('cannot_be_frozen')) {
@@ -1524,6 +1694,7 @@ export class MissileEngine {
             !m.name.endsWith('explode')
           if (
             m.name === 'meteorfire' ||
+            m.name === 'immolationfire' ||
             m.name === 'firewall' ||
             m.name === 'blaze' ||
             m.name === 'groundfirebig' ||
@@ -1637,6 +1808,63 @@ export class MissileEngine {
                 dmgPacket: m.dmgPacket,
               })
               subMissilesSpawned.push(expName)
+            } else if (m.name === 'explodingarrow' || m.sourceSkillId === 16) {
+              const expName = m.record.explosionMissile || 'explodingarrowexp'
+              this.spawnMissile({
+                missileNameOrId: expName,
+                sourceSkillId: m.sourceSkillId,
+                slvl: m.slvl,
+                owner: m.owner,
+                startX: m.x,
+                startY: m.y,
+                targetX: m.x,
+                targetY: m.y,
+                dmgPacket: m.dmgPacket,
+              })
+              subMissilesSpawned.push(expName)
+            } else if (m.name === 'icearrow' || m.sourceSkillId === 21) {
+              const expName = m.record.explosionMissile || 'icearrowexplode'
+              this.spawnMissile({
+                missileNameOrId: expName,
+                sourceSkillId: m.sourceSkillId,
+                slvl: m.slvl,
+                owner: m.owner,
+                startX: m.x,
+                startY: m.y,
+                targetX: m.x,
+                targetY: m.y,
+                dmgPacket: m.dmgPacket,
+              })
+              subMissilesSpawned.push(expName)
+            } else if (m.name === 'immolationarrow' || m.sourceSkillId === 27) {
+              const patchName = m.record.hitSubMissile1 || 'immolationfire'
+              this.spawnMissile({
+                missileNameOrId: patchName,
+                sourceSkillId: m.sourceSkillId,
+                slvl: m.slvl,
+                owner: m.owner,
+                startX: m.x,
+                startY: m.y,
+                targetX: m.x,
+                targetY: m.y,
+                dmgPacket: m.dmgPacket,
+                maxRangeTicks: 75,
+              })
+              subMissilesSpawned.push(patchName)
+            } else if (m.name === 'freezingarrow' || m.sourceSkillId === 31) {
+              const expName = m.record.explosionMissile || 'freezingarrowexp'
+              this.spawnMissile({
+                missileNameOrId: expName,
+                sourceSkillId: m.sourceSkillId,
+                slvl: m.slvl,
+                owner: m.owner,
+                startX: m.x,
+                startY: m.y,
+                targetX: m.x,
+                targetY: m.y,
+                dmgPacket: m.dmgPacket,
+              })
+              subMissilesSpawned.push(expName)
             }
             m.expired = true
             break
@@ -1845,6 +2073,132 @@ export class MissileEngine {
     return spawned
   }
 
+  /**
+   * Spawns authentic 1.13c Multiple Shot volley (Skill 12):
+   * - Arrow count: min(24, 2 + slvl)
+   * - Fan arc spread (~45-50 degrees) symmetric around aim vector
+   * - 75% weapon damage (srcDam = 96)
+   * - Center 2 arrows flagged to trigger procs; outer arrows cannot
+   * - Shared volleyId enforces single-target hit immunity
+   */
+  spawnMultipleShotVolley(params: {
+    sourceSkillId?: number
+    slvl: number
+    owner: CombatUnitContext
+    startX: number
+    startY: number
+    targetX: number
+    targetY: number
+    dmgPacket: SUnitDmgPacket
+    pierceChancePct?: number
+    missileName?: string
+  }): ActiveMissile[] {
+    const stats = calculateMultipleShotStats(params.slvl)
+    const arrowCount = stats.arrowCount
+    const dx = params.targetX - params.startX
+    const dy = (params.targetY - params.startY) / ISO_GROUND_ASPECT_RATIO
+    const aimAngleRad = dx === 0 && dy === 0 ? Math.PI / 2 : Math.atan2(dy, dx)
+    const angles = generateMultipleShotAngles(aimAngleRad, arrowCount, (50 * Math.PI) / 180)
+    const volleyId = `ms-volley-${String(this.uidCounter++)}`
+    const missiles: ActiveMissile[] = []
+    const missileName = params.missileName || 'arrow'
+
+    for (let i = 0; i < arrowCount; i += 1) {
+      const angle = angles[i]!
+      const canTriggerProcs = isMultipleShotCenterArrow(i, arrowCount)
+      const m = this.spawnMissile({
+        missileNameOrId: missileName,
+        sourceSkillId: params.sourceSkillId ?? 12,
+        slvl: params.slvl,
+        owner: params.owner,
+        startX: params.startX,
+        startY: params.startY,
+        targetX: params.startX + Math.cos(angle) * 200,
+        targetY: params.startY + Math.sin(angle) * 200 * ISO_GROUND_ASPECT_RATIO,
+        angleRad: angle,
+        dmgPacket: {
+          ...params.dmgPacket,
+          srcDam: 96,
+        },
+        ...(params.pierceChancePct !== undefined ? { pierceChancePct: params.pierceChancePct } : {}),
+        volleyId,
+        canTriggerProcs,
+      })
+      if (m) missiles.push(m)
+    }
+    return missiles
+  }
+
+  /**
+   * Spawns authentic 1.13c Strafe sequence (Skill 26):
+   * - Arrow count: min(10, 4 + floor(slvl/2))
+   * - Cycles target acquisition among alive nearby enemies
+   * - 75% weapon damage (srcDam = 96) + Enhanced Damage bonus (+5%/lvl)
+   * - Locks caster in stationary state for lockInFrames
+   */
+  spawnStrafeVolley(params: {
+    sourceSkillId?: number
+    slvl: number
+    owner: CombatUnitContext
+    startX: number
+    startY: number
+    targets?: readonly CombatUnitContext[]
+    targetPositions?: ReadonlyMap<string, { x: number; y: number }>
+    targetX?: number
+    targetY?: number
+    dmgPacket: SUnitDmgPacket
+    pierceChancePct?: number
+    missileName?: string
+  }): ActiveMissile[] {
+    const stats = calculateStrafeStats(params.slvl)
+    const arrowCount = stats.arrowCount
+    const aliveTargets = params.targets ? params.targets.filter(t => t.statList.getHp256() > 0) : []
+    const missiles: ActiveMissile[] = []
+    const missileName = params.missileName || 'arrow'
+
+    // Strafe stationary lock-in state on player
+    params.owner.stateBus.applyState({
+      stateNameOrId: 'strafe_lockin',
+      sourceSkillId: 26,
+      slvl: params.slvl,
+      durationFrames: stats.lockInFrames,
+    })
+
+    for (let i = 0; i < arrowCount; i += 1) {
+      let tX = params.targetX ?? params.startX + 200
+      let tY = params.targetY ?? params.startY
+      if (aliveTargets.length > 0) {
+        const assignedTarget = aliveTargets[i % aliveTargets.length]!
+        const pos = params.targetPositions?.get(assignedTarget.id) ?? { x: tX, y: tY }
+        tX = pos.x
+        tY = pos.y
+      }
+      const dx = tX - params.startX
+      const dy = (tY - params.startY) / ISO_GROUND_ASPECT_RATIO
+      const angle = dx === 0 && dy === 0 ? 0 : Math.atan2(dy, dx)
+      const m = this.spawnMissile({
+        missileNameOrId: missileName,
+        sourceSkillId: params.sourceSkillId ?? 26,
+        slvl: params.slvl,
+        owner: params.owner,
+        startX: params.startX,
+        startY: params.startY,
+        targetX: tX,
+        targetY: tY,
+        angleRad: angle,
+        dmgPacket: {
+          ...params.dmgPacket,
+          srcDam: 96,
+          physDamagePct: (params.dmgPacket.physDamagePct ?? 0) + stats.enhancedDamagePct,
+        },
+        ...(params.pierceChancePct !== undefined ? { pierceChancePct: params.pierceChancePct } : {}),
+        canTriggerProcs: true,
+      })
+      if (m) missiles.push(m)
+    }
+    return missiles
+  }
+
   /**
    * Executes authentic 1.13c instantaneous 360° Static Field discharge with difficulty floors and LOS.
    * Cuts 25% current HP with Normal (1 HP), Nightmare (33% max HP), and Hell (50% max HP) pre-check clamps.

src/game/skills.ts

@@ -285,6 +285,54 @@ export {
   METEOR_FIRE_SUBTILE_OFFSETS,
   type MeteorFireSubtileOffset,
 } from './engine/meteor-table.ts'
+import {
+  calculateMagicArrowStats,
+  calculateFireArrowStats,
+  calculateColdArrowStats,
+  calculateMultipleShotStats,
+  calculateExplodingArrowStats,
+  calculateIceArrowStats,
+  calculateGuidedArrowStats,
+  calculateStrafeStats,
+  calculateImmolationArrowStats,
+  calculateFreezingArrowStats,
+  generateMultipleShotAngles,
+  isMultipleShotCenterArrow,
+  type MagicArrowStats,
+  type FireArrowStats,
+  type ColdArrowStats,
+  type MultipleShotStats,
+  type ExplodingArrowStats,
+  type IceArrowStats,
+  type GuidedArrowStats,
+  type StrafeStats,
+  type ImmolationArrowStats,
+  type FreezingArrowStats,
+} from './skills/amazon-bow.ts'
+export {
+  calculateMagicArrowStats,
+  calculateFireArrowStats,
+  calculateColdArrowStats,
+  calculateMultipleShotStats,
+  calculateExplodingArrowStats,
+  calculateIceArrowStats,
+  calculateGuidedArrowStats,
+  calculateStrafeStats,
+  calculateImmolationArrowStats,
+  calculateFreezingArrowStats,
+  generateMultipleShotAngles,
+  isMultipleShotCenterArrow,
+  type MagicArrowStats,
+  type FireArrowStats,
+  type ColdArrowStats,
+  type MultipleShotStats,
+  type ExplodingArrowStats,
+  type IceArrowStats,
+  type GuidedArrowStats,
+  type StrafeStats,
+  type ImmolationArrowStats,
+  type FreezingArrowStats,
+} from './skills/amazon-bow.ts'
 
 /** One castable skill, read from a table row. */
 export interface SkillDef {
@@ -5549,6 +5597,36 @@ export function isBatch1Skill(skillId: number): boolean {
  * - Resilience: Invalid / NaN / non-positive levels default to level 1.
  */
 export function getSkillManaCost(skillId: number, effectiveLevel: number): number {
+  if (skillId === 6) {
+    return calculateMagicArrowStats(effectiveLevel).manaCost
+  }
+  if (skillId === 7) {
+    return calculateFireArrowStats(effectiveLevel).manaCost
+  }
+  if (skillId === 11) {
+    return calculateColdArrowStats(effectiveLevel).manaCost
+  }
+  if (skillId === 12) {
+    return calculateMultipleShotStats(effectiveLevel).manaCost
+  }
+  if (skillId === 16) {
+    return calculateExplodingArrowStats(effectiveLevel).manaCost
+  }
+  if (skillId === 21) {
+    return calculateIceArrowStats(effectiveLevel).manaCost
+  }
+  if (skillId === 22) {
+    return calculateGuidedArrowStats(effectiveLevel).manaCost
+  }
+  if (skillId === 26) {
+    return calculateStrafeStats(effectiveLevel).manaCost
+  }
+  if (skillId === 27) {
+    return calculateImmolationArrowStats(effectiveLevel).manaCost
+  }
+  if (skillId === 31) {
+    return calculateFreezingArrowStats(effectiveLevel).manaCost
+  }
   if (skillId === 38) {
     const lvl = Number.isFinite(effectiveLevel) ? Math.max(1, Math.floor(effectiveLevel)) : 1
     // 1.13c Skills.txt: mana = 24, lvlmana = 4, manashift = 5 (factor = 0.125)
@@ -5682,6 +5760,15 @@ export function getSkillManaCost(skillId: number, effectiveLevel: number): numbe
  */
 export function getSkillCooldownTicks(skillId: number): number {
   if (
+    skillId === 6 ||
+    skillId === 7 ||
+    skillId === 11 ||
+    skillId === 12 ||
+    skillId === 16 ||
+    skillId === 21 ||
+    skillId === 22 ||
+    skillId === 26 ||
+    skillId === 31 ||
     skillId === 38 ||
     skillId === 40 ||
     skillId === 41 ||
@@ -5705,6 +5792,9 @@ export function getSkillCooldownTicks(skillId: number): number {
   ) {
     return 0
   }
+  if (skillId === 27) {
+    return 25 // Immolation Arrow: 25 frames (1.0s)
+  }
   if (skillId === 51) {
     return 35
   }
@@ -5753,6 +5843,68 @@ export function calculateSkillDamage(
   },
   weaponDamage?: { min: number; max: number }
 ): { min: number; max: number } {
+  if (skillId === 6 || skillId === '6' || skillId === 'magicarrow' || skillId === 'magic arrow') {
+    const stats = calculateMagicArrowStats(slvl)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: baseMin + stats.flatMagicDamage, max: baseMax + stats.flatMagicDamage }
+  }
+  if (skillId === 7 || skillId === '7' || skillId === 'firearrow' || skillId === 'fire arrow') {
+    const stats = calculateFireArrowStats(slvl, synergies as any)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: baseMin + stats.minDamage, max: baseMax + stats.maxDamage }
+  }
+  if (skillId === 11 || skillId === '11' || skillId === 'coldarrow' || skillId === 'cold arrow') {
+    const stats = calculateColdArrowStats(slvl, synergies as any)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: baseMin + stats.minDamage, max: baseMax + stats.maxDamage }
+  }
+  if (skillId === 12 || skillId === '12' || skillId === 'multipleshot' || skillId === 'multiple shot') {
+    const stats = calculateMultipleShotStats(slvl)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: Math.floor(baseMin * stats.damageMultiplier), max: Math.floor(baseMax * stats.damageMultiplier) }
+  }
+  if (skillId === 16 || skillId === '16' || skillId === 'explodingarrow' || skillId === 'exploding arrow') {
+    const stats = calculateExplodingArrowStats(slvl, synergies as any)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: baseMin + stats.minBlastDamage, max: baseMax + stats.maxBlastDamage }
+  }
+  if (skillId === 21 || skillId === '21' || skillId === 'icearrow' || skillId === 'ice arrow') {
+    const stats = calculateIceArrowStats(slvl, synergies as any)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: baseMin + stats.minDamage, max: baseMax + stats.maxDamage }
+  }
+  if (skillId === 22 || skillId === '22' || skillId === 'guidedarrow' || skillId === 'guided arrow') {
+    const stats = calculateGuidedArrowStats(slvl)
+    const ed = 1 + stats.enhancedDamagePct / 100
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: Math.floor(baseMin * ed), max: Math.floor(baseMax * ed) }
+  }
+  if (skillId === 26 || skillId === '26' || skillId === 'strafe') {
+    const stats = calculateStrafeStats(slvl)
+    const mult = stats.damageMultiplier * (1 + stats.enhancedDamagePct / 100)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: Math.floor(baseMin * mult), max: Math.floor(baseMax * mult) }
+  }
+  if (skillId === 27 || skillId === '27' || skillId === 'immolationarrow' || skillId === 'immolation arrow') {
+    const stats = calculateImmolationArrowStats(slvl, synergies as any)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: baseMin + stats.minExplosionDamage, max: baseMax + stats.maxExplosionDamage }
+  }
+  if (skillId === 31 || skillId === '31' || skillId === 'freezingarrow' || skillId === 'freezing arrow') {
+    const stats = calculateFreezingArrowStats(slvl, synergies as any)
+    const baseMin = weaponDamage?.min ?? 0
+    const baseMax = weaponDamage?.max ?? 0
+    return { min: baseMin + stats.minColdDamage, max: baseMax + stats.maxColdDamage }
+  }
   if (skillId === 38 || skillId === '38' || skillId === 'chargedbolt' || skillId === 'charged bolt') {
     return calculateChargedBoltDamage(slvl, synergies as any)
   }

src/game/skills/amazon-bow.ts

@@ -0,0 +1,648 @@
+/**
+ * Diablo II: Lord of Destruction v1.13c — Amazon Bow & Crossbow Skills Tree Module
+ *
+ * Dedicated pure calculation and kinematics formulas for the 10 bow/crossbow skills:
+ * - Skill 006: Magic Arrow
+ * - Skill 007: Fire Arrow
+ * - Skill 011: Cold Arrow
+ * - Skill 012: Multiple Shot
+ * - Skill 016: Exploding Arrow
+ * - Skill 021: Ice Arrow
+ * - Skill 022: Guided Arrow
+ * - Skill 026: Strafe
+ * - Skill 027: Immolation Arrow
+ * - Skill 031: Freezing Arrow
+ *
+ * 1.13c Ground Truth:
+ * - D2Common.dll / D2Game.dll / Patch_D2.mpq: Skills.txt & Missiles.txt
+ * - Fixed-point 24.8 mana calculations
+ * - 5-band scaling across levels 1, 2..8, 9..16, 17..22, 23..28, 29+
+ * - Guided Arrow strict zero-pierce invariant (`canPierce = false`, `pierceChancePct = 0`)
+ * - Multiple Shot fan distribution, center-2 proc limitation, and single-target hit immunity
+ * - Immolation Arrow 25-frame casting cooldown and 75-frame ground fire patch
+ * - Freezing Arrow 80 sub-pixel cold splash and 50-frame freeze duration
+ */
+
+import { compute5BandScaling } from '../engine/calc-ast.ts'
+
+// --- Interfaces for Skill Calculations ---
+
+export interface MagicArrowStats {
+  readonly conversionPct: number
+  readonly flatMagicDamage: number
+  readonly minDamage: number
+  readonly maxDamage: number
+  readonly toHitBonusPct: number
+  readonly manaCost: number
+  readonly manaCost256: number
+  readonly noAmmo: boolean
+  readonly requiresAmmo: boolean
+}
+
+export interface FireArrowStats {
+  readonly minDamage: number
+  readonly maxDamage: number
+  readonly baseMinDamage: number
+  readonly baseMaxDamage: number
+  readonly physToElemPct: number
+  readonly srcDam: number
+  readonly toHitBonusPct: number
+  readonly synergyMultiplier: number
+  readonly synergyBonusPct: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface ColdArrowStats {
+  readonly minDamage: number
+  readonly maxDamage: number
+  readonly baseMinDamage: number
+  readonly baseMaxDamage: number
+  readonly durationFrames: number
+  readonly physToElemPct: number
+  readonly srcDam: number
+  readonly toHitBonusPct: number
+  readonly synergyMultiplier: number
+  readonly synergyBonusPct: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface MultipleShotStats {
+  readonly arrowCount: number
+  readonly damageMultiplier: number
+  readonly srcDam: number
+  readonly centerProcArrows: number
+  readonly onlyCenterArrowsProc: boolean
+  readonly singleTargetImmunity: boolean
+  readonly toHitBonusPct: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface ExplodingArrowStats {
+  readonly minBlastDamage: number
+  readonly maxBlastDamage: number
+  readonly baseMinBlastDamage: number
+  readonly baseMaxBlastDamage: number
+  readonly minDamage: number
+  readonly maxDamage: number
+  readonly radiusPx: number
+  readonly radiusSubtiles: number
+  readonly toHitBonusPct: number
+  readonly synergyMultiplier: number
+  readonly synergyBonusPct: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface IceArrowStats {
+  readonly minDamage: number
+  readonly maxDamage: number
+  readonly baseMinDamage: number
+  readonly baseMaxDamage: number
+  readonly freezeFrames: number
+  readonly baseFreezeFrames: number
+  readonly toHitBonusPct: number
+  readonly dmgSynergyMultiplier: number
+  readonly lenSynergyMultiplier: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface GuidedArrowStats {
+  readonly enhancedDamagePct: number
+  readonly alwaysHits: boolean
+  readonly autoHit: boolean
+  readonly canPierce: boolean
+  readonly pierceChancePct: number
+  readonly toHitBonusPct: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface StrafeStats {
+  readonly arrowCount: number
+  readonly damageMultiplier: number
+  readonly srcDam: number
+  readonly enhancedDamagePct: number
+  readonly stationaryLockIn: boolean
+  readonly lockInFrames: number
+  readonly toHitBonusPct: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface ImmolationArrowStats {
+  readonly minExplosionDamage: number
+  readonly maxExplosionDamage: number
+  readonly baseMinExplosionDamage: number
+  readonly baseMaxExplosionDamage: number
+  readonly minDamage: number
+  readonly maxDamage: number
+  readonly firePatchDurationFrames: number
+  readonly firePatchMinDamagePerSec: number
+  readonly firePatchMaxDamagePerSec: number
+  readonly cooldownFrames: number
+  readonly toHitBonusPct: number
+  readonly explosionSynergyMultiplier: number
+  readonly firePatchSynergyMultiplier: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+export interface FreezingArrowStats {
+  readonly minColdDamage: number
+  readonly maxColdDamage: number
+  readonly baseMinColdDamage: number
+  readonly baseMaxColdDamage: number
+  readonly minDamage: number
+  readonly maxDamage: number
+  readonly freezeFrames: number
+  readonly baseFreezeFrames: number
+  readonly radiusPx: number
+  readonly radiusSubtiles: number
+  readonly toHitBonusPct: number
+  readonly coldSynergyMultiplier: number
+  readonly lenSynergyMultiplier: number
+  readonly manaCost: number
+  readonly manaCost256: number
+}
+
+// --- Pure Calculation Functions ---
+
+/**
+ * Skill 006: Magic Arrow
+ * Physical-to-magic conversion `min(100, 5 + (slvl-1))%`,
+ * flat magic damage 5-band scaling (1, 1, 2, 3, 4, 5),
+ * AR bonus `+10 + 9*(slvl-1)%`,
+ * mana `max(0, 1.5 - 0.125*(slvl-1))` in 24.8 fixed point (reaches 0 at lvl 13),
+ * zero ammo consumption invariant (`noammo: 1`).
+ */
+export function calculateMagicArrowStats(slvl: number): MagicArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const conversionPct = Math.min(100, Math.max(0, 5 + (lvl - 1)))
+  const flatMagicDamage = compute5BandScaling(lvl, 1, 1, 2, 3, 4, 5)
+  const toHitBonusPct = 10 + 9 * (lvl - 1)
+  const manaCost = Math.max(0, 1.5 - 0.125 * (lvl - 1))
+  const manaCost256 = Math.max(0, 384 - 32 * (lvl - 1))
+
+  return {
+    conversionPct,
+    flatMagicDamage,
+    minDamage: flatMagicDamage,
+    maxDamage: flatMagicDamage,
+    toHitBonusPct,
+    manaCost,
+    manaCost256,
+    noAmmo: true,
+    requiresAmmo: false,
+  }
+}
+
+/**
+ * Skill 007: Fire Arrow
+ * 80% physical-to-fire conversion (`srcdam = 80`),
+ * 5-band fire damage:
+ *   Min: (1, 2, 3, 6, 12, 24)
+ *   Max: (4, 2, 3, 7, 14, 27)
+ * Exploding Arrow synergy (+12%/lvl),
+ * AR bonus `+10 + 9*(slvl-1)%`,
+ * mana `3.0 + 0.25*(slvl-1)`.
+ */
+export function calculateFireArrowStats(
+  slvl: number,
+  synergies?: number | { readonly explodingArrow?: number; readonly [key: string]: any }
+): FireArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const baseMin = compute5BandScaling(lvl, 1, 2, 3, 6, 12, 24)
+  const baseMax = compute5BandScaling(lvl, 4, 2, 3, 7, 14, 27)
+  let synergyMultiplier = 1.0
+  let synergyBonusPct = 0
+  if (typeof synergies === 'number' && Number.isFinite(synergies) && synergies > 0) {
+    synergyMultiplier = synergies
+    synergyBonusPct = Math.round((synergyMultiplier - 1.0) * 100)
+  } else if (synergies && typeof synergies === 'object') {
+    const synBlvl = Math.max(0, Math.floor(synergies?.explodingArrow ?? (synergies as any)?.['Exploding Arrow'] ?? 0))
+    synergyBonusPct = synBlvl * 12
+    synergyMultiplier = 1 + synergyBonusPct / 100
+  }
+  const minDamage = Math.floor(baseMin * synergyMultiplier)
+  const maxDamage = Math.floor(baseMax * synergyMultiplier)
+  const toHitBonusPct = 10 + 9 * (lvl - 1)
+  const manaCost = 3.0 + 0.25 * (lvl - 1)
+  const manaCost256 = Math.round(manaCost * 256)
+
+  return {
+    minDamage,
+    maxDamage,
+    baseMinDamage: baseMin,
+    baseMaxDamage: baseMax,
+    physToElemPct: 80,
+    srcDam: 80,
+    toHitBonusPct,
+    synergyMultiplier,
+    synergyBonusPct,
+    manaCost,
+    manaCost256,
+  }
+}
+
+/**
+ * Skill 011: Cold Arrow
+ * 80% physical-to-cold conversion (`srcdam = 80`),
+ * 5-band cold damage (Skills.txt: eMin=6, eMax=8 with hitShift=7 factor 0.5):
+ *   Min: (6, 4, 5, 8, 16, 42) * 0.5
+ *   Max: (8, 4, 5, 9, 17, 44) * 0.5
+ * Chill duration `50 + 10*(slvl-1)` frames,
+ * Ice Arrow synergy (+12%/lvl),
+ * AR bonus `+10 + 9*(slvl-1)%`,
+ * mana `3.5 + 0.25*(slvl-1)`.
+ */
+export function calculateColdArrowStats(
+  slvl: number,
+  synergies?: number | { readonly iceArrow?: number; readonly [key: string]: any }
+): ColdArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const baseMin = compute5BandScaling(lvl, 6, 4, 5, 8, 16, 42) * 0.5
+  const baseMax = compute5BandScaling(lvl, 8, 4, 5, 9, 17, 44) * 0.5
+  let synergyMultiplier = 1.0
+  let synergyBonusPct = 0
+  if (typeof synergies === 'number' && Number.isFinite(synergies) && synergies > 0) {
+    synergyMultiplier = synergies
+    synergyBonusPct = Math.round((synergyMultiplier - 1.0) * 100)
+  } else if (synergies && typeof synergies === 'object') {
+    const synBlvl = Math.max(0, Math.floor(synergies?.iceArrow ?? (synergies as any)?.['Ice Arrow'] ?? 0))
+    synergyBonusPct = synBlvl * 12
+    synergyMultiplier = 1 + synergyBonusPct / 100
+  }
+  const minDamage = Math.floor(baseMin * synergyMultiplier)
+  const maxDamage = Math.floor(baseMax * synergyMultiplier)
+  const durationFrames = 50 + 10 * (lvl - 1)
+  const toHitBonusPct = 10 + 9 * (lvl - 1)
+  const manaCost = 3.5 + 0.25 * (lvl - 1)
+  const manaCost256 = Math.round(manaCost * 256)
+
+  return {
+    minDamage,
+    maxDamage,
+    baseMinDamage: baseMin,
+    baseMaxDamage: baseMax,
+    durationFrames,
+    physToElemPct: 80,
+    srcDam: 80,
+    toHitBonusPct,
+    synergyMultiplier,
+    synergyBonusPct,
+    manaCost,
+    manaCost256,
+  }
+}
+
+/**
+ * Skill 012: Multiple Shot
+ * Arrow count `min(24, 2 + slvl)`,
+ * 75% weapon damage (`srcdam = 96`),
+ * center 2 arrows proc flag,
+ * single-target multi-hit immunity per volley,
+ * mana `4 + 1*(slvl-1)`.
+ */
+export function calculateMultipleShotStats(slvl: number): MultipleShotStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const arrowCount = Math.min(24, Math.max(2, 2 + lvl))
+  const manaCost = 4 + 1 * (lvl - 1)
+  const manaCost256 = manaCost * 256
+
+  return {
+    arrowCount,
+    damageMultiplier: 0.75,
+    srcDam: 96,
+    centerProcArrows: 2,
+    onlyCenterArrowsProc: true,
+    singleTargetImmunity: true,
+    toHitBonusPct: 0,
+    manaCost,
+    manaCost256,
+  }
+}
+
+/**
+ * Skill 016: Exploding Arrow
+ * 5-band blast fire damage:
+ *   Min: (2, 5, 7, 9, 12, 20)
+ *   Max: (6, 5, 8, 11, 14, 23)
+ * AoE 80 sub-pixels (5.33 yards / 2.66 tiles),
+ * Fire Arrow synergy (+12%/lvl),
+ * AR bonus `+20 + 9*(slvl-1)%`,
+ * mana `5 + 0.5*(slvl-1)`.
+ */
+export function calculateExplodingArrowStats(
+  slvl: number,
+  synergies?: number | { readonly fireArrow?: number; readonly [key: string]: any }
+): ExplodingArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const baseMin = compute5BandScaling(lvl, 2, 5, 7, 9, 12, 20)
+  const baseMax = compute5BandScaling(lvl, 6, 5, 8, 11, 14, 23)
+  let synergyMultiplier = 1.0
+  let synergyBonusPct = 0
+  if (typeof synergies === 'number' && Number.isFinite(synergies) && synergies > 0) {
+    synergyMultiplier = synergies
+    synergyBonusPct = Math.round((synergyMultiplier - 1.0) * 100)
+  } else if (synergies && typeof synergies === 'object') {
+    const synBlvl = Math.max(0, Math.floor(synergies?.fireArrow ?? (synergies as any)?.['Fire Arrow'] ?? 0))
+    synergyBonusPct = synBlvl * 12
+    synergyMultiplier = 1 + synergyBonusPct / 100
+  }
+  const minBlastDamage = Math.floor(baseMin * synergyMultiplier)
+  const maxBlastDamage = Math.floor(baseMax * synergyMultiplier)
+  const toHitBonusPct = 20 + 9 * (lvl - 1)
+  const manaCost = 5 + 0.5 * (lvl - 1)
+  const manaCost256 = Math.round(manaCost * 256)
+
+  return {
+    minBlastDamage,
+    maxBlastDamage,
+    baseMinBlastDamage: baseMin,
+    baseMaxBlastDamage: baseMax,
+    minDamage: minBlastDamage,
+    maxDamage: maxBlastDamage,
+    radiusPx: 80,
+    radiusSubtiles: 80,
+    toHitBonusPct,
+    synergyMultiplier,
+    synergyBonusPct,
+    manaCost,
+    manaCost256,
+  }
+}
+
+/**
+ * Skill 021: Ice Arrow
+ * 5-band cold damage:
+ *   Min: (6, 6, 12, 18, 26, 36)
+ *   Max: (10, 6, 13, 19, 27, 38)
+ * Freeze duration `50 + 5*(slvl-1)` frames,
+ * AR bonus `+20 + 9*(slvl-1)%`,
+ * Cold Arrow synergy (+8% damage/lvl),
+ * Freezing Arrow synergy (+5% length/lvl),
+ * mana `4 + 0.25*(slvl-1)`.
+ */
+export function calculateIceArrowStats(
+  slvl: number,
+  synergies?: number | {
+    readonly coldArrow?: number
+    readonly freezingArrow?: number
+    readonly [key: string]: any
+  }
+): IceArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const baseMin = compute5BandScaling(lvl, 6, 6, 12, 18, 26, 36)
+  const baseMax = compute5BandScaling(lvl, 10, 6, 13, 19, 27, 38)
+  let dmgSynergyMultiplier = 1.0
+  let lenSynergyMultiplier = 1.0
+
+  if (typeof synergies === 'number' && Number.isFinite(synergies) && synergies > 0) {
+    dmgSynergyMultiplier = synergies
+  } else if (synergies && typeof synergies === 'object') {
+    const caBlvl = Math.max(0, Math.floor(synergies?.coldArrow ?? (synergies as any)?.['Cold Arrow'] ?? 0))
+    const dmgSynPct = caBlvl * 8
+    dmgSynergyMultiplier = 1 + dmgSynPct / 100
+
+    const faBlvl = Math.max(0, Math.floor(synergies?.freezingArrow ?? (synergies as any)?.['Freezing Arrow'] ?? 0))
+    const lenSynPct = faBlvl * 5
+    lenSynergyMultiplier = 1 + lenSynPct / 100
+  }
+  const minDamage = Math.floor(baseMin * dmgSynergyMultiplier)
+  const maxDamage = Math.floor(baseMax * dmgSynergyMultiplier)
+
+  const baseFreezeFrames = 50 + 5 * (lvl - 1)
+  const freezeFrames = Math.floor(baseFreezeFrames * lenSynergyMultiplier)
+
+  const toHitBonusPct = 20 + 9 * (lvl - 1)
+  const manaCost = 4 + 0.25 * (lvl - 1)
+  const manaCost256 = Math.round(manaCost * 256)
+
+  return {
+    minDamage,
+    maxDamage,
+    baseMinDamage: baseMin,
+    baseMaxDamage: baseMax,
+    freezeFrames,
+    baseFreezeFrames,
+    toHitBonusPct,
+    dmgSynergyMultiplier,
+    lenSynergyMultiplier,
+    manaCost,
+    manaCost256,
+  }
+}
+
+/**
+ * Skill 022: Guided Arrow
+ * Enhanced damage `+5%*(slvl-1)`,
+ * auto-hit invariant (`alwaysHits = true`),
+ * strict `canPierce = false` and `pierceChancePct = 0` (1.13c ground truth),
+ * mana `max(1.75, 8.0 - 0.25*(slvl-1))`.
+ */
+export function calculateGuidedArrowStats(slvl: number): GuidedArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const enhancedDamagePct = 5 * (lvl - 1)
+  const manaCost = Math.max(1.75, 8.0 - 0.25 * (lvl - 1))
+  const manaCost256 = Math.round(manaCost * 256)
+
+  return {
+    enhancedDamagePct,
+    alwaysHits: true,
+    autoHit: true,
+    canPierce: false,
+    pierceChancePct: 0,
+    toHitBonusPct: 0,
+    manaCost,
+    manaCost256,
+  }
+}
+
+/**
+ * Skill 026: Strafe
+ * Arrow count `min(10, 4 + floor(slvl/2))`,
+ * 75% weapon damage (`srcdam = 96`),
+ * Enhanced damage `+5%*(slvl-1)`,
+ * stationary lock-in duration,
+ * mana fixed at 11.
+ */
+export function calculateStrafeStats(slvl: number): StrafeStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const arrowCount = Math.min(10, Math.max(4, 4 + Math.floor(lvl / 2)))
+  const enhancedDamagePct = 5 * (lvl - 1)
+  const lockInFrames = arrowCount * 2 + 4
+
+  return {
+    arrowCount,
+    damageMultiplier: 0.75,
+    srcDam: 96,
+    enhancedDamagePct,
+    stationaryLockIn: true,
+    lockInFrames,
+    toHitBonusPct: 0,
+    manaCost: 11,
+    manaCost256: 2816,
+  }
+}
+
+/**
+ * Skill 027: Immolation Arrow
+ * 5-band explosion fire damage:
+ *   Min: (12, 12, 23, 34, 36, 38)
+ *   Max: (23, 12, 23, 34, 36, 38)
+ * 75-frame ground fire patch (`immolationfire`),
+ * 25-frame casting cooldown (1.0s delay),
+ * Fire Arrow synergies (+5% explosion, +10% fire patch),
+ * AR bonus `+30 + 9*(slvl-1)%`,
+ * mana `6 + 0.5*(slvl-1)`.
+ */
+export function calculateImmolationArrowStats(
+  slvl: number,
+  synergies?: number | { readonly fireArrow?: number; readonly [key: string]: any }
+): ImmolationArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const baseMin = compute5BandScaling(lvl, 12, 12, 23, 34, 36, 38)
+  const baseMax = compute5BandScaling(lvl, 23, 12, 23, 34, 36, 38)
+  let explosionSynergyMultiplier = 1.0
+  let firePatchSynergyMultiplier = 1.0
+
+  if (typeof synergies === 'number' && Number.isFinite(synergies) && synergies > 0) {
+    explosionSynergyMultiplier = synergies
+    firePatchSynergyMultiplier = synergies
+  } else if (synergies && typeof synergies === 'object') {
+    const faBlvl = Math.max(0, Math.floor(synergies?.fireArrow ?? (synergies as any)?.['Fire Arrow'] ?? 0))
+    const expSynPct = faBlvl * 5
+    explosionSynergyMultiplier = 1 + expSynPct / 100
+    const patchSynPct = faBlvl * 10
+    firePatchSynergyMultiplier = 1 + patchSynPct / 100
+  }
+  const minExplosionDamage = Math.floor(baseMin * explosionSynergyMultiplier)
+  const maxExplosionDamage = Math.floor(baseMax * explosionSynergyMultiplier)
+
+  // 1.13c immolationfire (missile 230) base ~7-10 damage/sec scaled by synergy
+  const firePatchMinDamagePerSec = Math.floor(7 * firePatchSynergyMultiplier)
+  const firePatchMaxDamagePerSec = Math.floor(10 * firePatchSynergyMultiplier)
+
+  const toHitBonusPct = 30 + 9 * (lvl - 1)
+  const manaCost = 6 + 0.5 * (lvl - 1)
+  const manaCost256 = Math.round(manaCost * 256)
+
+  return {
+    minExplosionDamage,
+    maxExplosionDamage,
+    baseMinExplosionDamage: baseMin,
+    baseMaxExplosionDamage: baseMax,
+    minDamage: minExplosionDamage,
+    maxDamage: maxExplosionDamage,
+    firePatchDurationFrames: 75,
+    firePatchMinDamagePerSec,
+    firePatchMaxDamagePerSec,
+    cooldownFrames: 25,
+    toHitBonusPct,
+    explosionSynergyMultiplier,
+    firePatchSynergyMultiplier,
+    manaCost,
+    manaCost256,
+  }
+}
+
+/**
+ * Skill 031: Freezing Arrow
+ * 5-band frost blast cold damage:
+ *   Min: (40, 10, 15, 20, 22, 24)
+ *   Max: (50, 10, 15, 20, 22, 24)
+ * AoE 80 sub-pixels (5.33 yards / 2.66 tiles),
+ * 50-frame freeze duration,
+ * Cold Arrow synergy (+12% damage/lvl),
+ * Ice Arrow synergy (+5% length/lvl),
+ * AR bonus `+40 + 9*(slvl-1)%`,
+ * mana `9 + 0.5*(slvl-1)`.
+ */
+export function calculateFreezingArrowStats(
+  slvl: number,
+  synergies?: number | {
+    readonly coldArrow?: number
+    readonly iceArrow?: number
+    readonly [key: string]: any
+  }
+): FreezingArrowStats {
+  const lvl = Number.isFinite(slvl) ? Math.max(1, Math.floor(slvl)) : 1
+  const baseMin = compute5BandScaling(lvl, 40, 10, 15, 20, 22, 24)
+  const baseMax = compute5BandScaling(lvl, 50, 10, 15, 20, 22, 24)
+  let coldSynergyMultiplier = 1.0
+  let lenSynergyMultiplier = 1.0
+
+  if (typeof synergies === 'number' && Number.isFinite(synergies) && synergies > 0) {
+    coldSynergyMultiplier = synergies
+  } else if (synergies && typeof synergies === 'object') {
+    const caBlvl = Math.max(0, Math.floor(synergies?.coldArrow ?? (synergies as any)?.['Cold Arrow'] ?? 0))
+    const coldSynPct = caBlvl * 12
+    coldSynergyMultiplier = 1 + coldSynPct / 100
+
+    const iaBlvl = Math.max(0, Math.floor(synergies?.iceArrow ?? (synergies as any)?.['Ice Arrow'] ?? 0))
+    const lenSynPct = iaBlvl * 5
+    lenSynergyMultiplier = 1 + lenSynPct / 100
+  }
+  const minColdDamage = Math.floor(baseMin * coldSynergyMultiplier)
+  const maxColdDamage = Math.floor(baseMax * coldSynergyMultiplier)
+
+  const freezeFrames = Math.floor(50 * lenSynergyMultiplier)
+
+  const toHitBonusPct = 40 + 9 * (lvl - 1)
+  const manaCost = 9 + 0.5 * (lvl - 1)
+  const manaCost256 = Math.round(manaCost * 256)
+
+  return {
+    minColdDamage,
+    maxColdDamage,
+    baseMinColdDamage: baseMin,
+    baseMaxColdDamage: baseMax,
+    minDamage: minColdDamage,
+    maxDamage: maxColdDamage,
+    freezeFrames,
+    baseFreezeFrames: 50,
+    radiusPx: 80,
+    radiusSubtiles: 80,
+    toHitBonusPct,
+    coldSynergyMultiplier,
+    lenSynergyMultiplier,
+    manaCost,
+    manaCost256,
+  }
+}
+
+// --- Kinematics Helpers ---
+
+/**
+ * Computes symmetrical fan angles for Multiple Shot.
+ * Spreads `arrowCount` arrows across an arc centered at `aimAngleRad`.
+ */
+export function generateMultipleShotAngles(
+  aimAngleRad: number,
+  arrowCount: number,
+  arcRad: number = (45 * Math.PI) / 180
+): number[] {
+  if (arrowCount <= 1) return [aimAngleRad]
+  const angles: number[] = []
+  const halfArc = arcRad / 2
+  const step = arcRad / (arrowCount - 1)
+  for (let i = 0; i < arrowCount; i += 1) {
+    angles.push(aimAngleRad - halfArc + i * step)
+  }
+  return angles
+}
+
+/**
+ * Checks if an arrow index in a Multiple Shot volley is one of the two center arrows.
+ * Only center arrows can trigger "chance to cast on striking" procs and knockback in 1.13c.
+ */
+export function isMultipleShotCenterArrow(index: number, arrowCount: number): boolean {
+  if (arrowCount <= 2) return true
+  const mid1 = Math.floor((arrowCount - 1) / 2)
+  const mid2 = Math.ceil((arrowCount - 1) / 2)
+  return index === mid1 || index === mid2
+}

src/game/skills/impl/ama/skill-006-magic-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateMagicArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-007-fire-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateFireArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-011-cold-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateColdArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-012-multiple-shot.ts

@@ -41,4 +41,9 @@ export const skillModule: SkillModule = {
   },
 }
 
+export {
+  calculateMultipleShotStats,
+  generateMultipleShotAngles,
+  isMultipleShotCenterArrow,
+} from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-016-exploding-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateExplodingArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-021-ice-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateIceArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-022-guided-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateGuidedArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-026-strafe.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateStrafeStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-027-immolation-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateImmolationArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/impl/ama/skill-031-freezing-arrow.ts

@@ -41,4 +41,5 @@ export const skillModule: SkillModule = {
   },
 }
 
+export { calculateFreezingArrowStats } from '../../amazon-bow.ts'
 export default skillModule

src/game/skills/registry.ts

@@ -154,7 +154,16 @@ export function evaluateSkillCore113c(ctx: SkillEvalContext): SkillEvalResult {
   let elemHitShift = skill.hitShift
   let elemType = skill.eType
 
-  const primaryMissileName = skill.srvMissile || skill.srvMissileA || skill.cltMissile || skill.cltMissileA
+  const primaryMissileName =
+    skill.srvMissile ||
+    skill.srvMissileA ||
+    skill.cltMissile ||
+    skill.cltMissileA ||
+    (skill.id === 22
+      ? 'guidedarrow'
+      : skill.id === 12 || skill.id === 26
+        ? 'arrow'
+        : '')
   if (baseEMin === 0 && baseEMax === 0 && primaryMissileName) {
     const msl = registry.getMissileByName(primaryMissileName)
     if (msl && (msl.eMin > 0 || msl.eMax > 0)) {
@@ -980,25 +989,59 @@ export function executeSkillCore113c(ctx: SkillExecContext): SkillExecOutcome {
     }
 
     const piercePct =
-      caster.statList.getEffectiveSkillLevel(33) > 0
+      skill.id === 22
-        ? Math.min(95, 25 + caster.statList.getEffectiveSkillLevel(33) * 3)
+        ? 0
-        : 0
+        : caster.statList.getEffectiveSkillLevel(33) > 0
+          ? Math.min(95, 25 + caster.statList.getEffectiveSkillLevel(33) * 3)
+          : 0
 
-    for (let i = 0; i < projectileCount; i += 1) {
+    if (skill.id === 12) {
-      const spreadOffset = (i - (projectileCount - 1) / 2) * 14
+      const vol = missileEngine.spawnMultipleShotVolley({
-      const m = missileEngine.spawnMissile({
+        sourceSkillId: 12,
-        missileNameOrId: evalResult.missileA,
-        sourceSkillId: skill.id,
         slvl: evalResult.slvl,
         owner: caster,
         startX: 0,
         startY: 0,
-        targetX: targetX + spreadOffset,
+        targetX,
         targetY,
         dmgPacket,
         pierceChancePct: piercePct,
+        missileName: evalResult.missileA || 'arrow',
       })
-      if (m) missilesSpawned.push(m.name)
+      missilesSpawned.push(...vol.map(m => m.name))
+    } else if (skill.id === 26) {
+      const st = missileEngine.spawnStrafeVolley({
+        sourceSkillId: 26,
+        slvl: evalResult.slvl,
+        owner: caster,
+        startX: 0,
+        startY: 0,
+        targets,
+        targetPositions: targetPositions ?? new Map(),
+        targetX,
+        targetY,
+        dmgPacket,
+        pierceChancePct: piercePct,
+        missileName: evalResult.missileA || 'arrow',
+      })
+      missilesSpawned.push(...st.map(m => m.name))
+    } else {
+      for (let i = 0; i < projectileCount; i += 1) {
+        const spreadOffset = (i - (projectileCount - 1) / 2) * 14
+        const m = missileEngine.spawnMissile({
+          missileNameOrId: evalResult.missileA,
+          sourceSkillId: skill.id,
+          slvl: evalResult.slvl,
+          owner: caster,
+          startX: 0,
+          startY: 0,
+          targetX: targetX + spreadOffset,
+          targetY,
+          dmgPacket,
+          pierceChancePct: piercePct,
+        })
+        if (m) missilesSpawned.push(m.name)
+      }
     }
 
     // Advance missile engine so immediate or close-range missiles land and record damage

tests/skills/ama/adv-ama-bow-kinematics-stress.test.ts

@@ -0,0 +1,566 @@
+/**
+ * Diablo II: Lord of Destruction v1.13c — Amazon Bow & Crossbow Kinematics Stress Suite
+ *
+ * Comprehensive adversarial and E2E kinematics integration verification:
+ * 1. Guided Arrow homing continuous angle steering and strict zero-pierce invariant under 100% Pierce skill.
+ * 2. Multiple Shot 2..24 arrow scaling, symmetrical fan arc, center 2 proc flag, and single-target hit immunity.
+ * 3. Strafe 4..10 arrow scaling, multi-target cycling, and stationary lock-in state.
+ * 4. Immolation Arrow 25-frame casting cooldown and 75-frame ground fire patch ticking.
+ * 5. Freezing Arrow 80 sub-pixel AoE cold splash and solid freeze application.
+ * 6. Magic Arrow physical-to-magic conversion and zero-ammo requirement invariant.
+ * 7. System invariant: BATCH1_SKILLS length strictly maintained at 38; zero mocks.
+ *
+ * Ground Truth:
+ * - Blizzard v1.13c: D2Common.dll, D2Game.dll, Skills.txt, Missiles.txt
+ */
+
+import { describe, expect, it } from 'vitest'
+import {
+  BATCH1_SKILLS,
+  getSkillManaCost,
+  getSkillCooldownTicks,
+  calculateSkillDamage,
+} from '../../../src/game/skills.ts'
+import {
+  calculateMagicArrowStats,
+  calculateFireArrowStats,
+  calculateColdArrowStats,
+  calculateMultipleShotStats,
+  calculateExplodingArrowStats,
+  calculateIceArrowStats,
+  calculateGuidedArrowStats,
+  calculateStrafeStats,
+  calculateImmolationArrowStats,
+  calculateFreezingArrowStats,
+  generateMultipleShotAngles,
+  isMultipleShotCenterArrow,
+} from '../../../src/game/skills/amazon-bow.ts'
+import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts'
+import { MissileEngine, ISO_GROUND_ASPECT_RATIO } from '../../../src/game/engine/missile-engine.ts'
+import { WorldArena } from '../../../src/game/engine/world-arena.ts'
+import { UnitStatList, FIXED_ONE } from '../../../src/game/engine/stat-list.ts'
+import { StateBus } from '../../../src/game/engine/state-bus.ts'
+import type { CombatUnitContext, SUnitDmgPacket } from '../../../src/game/engine/combat-pipeline.ts'
+
+function createTestCombatUnit(
+  id: string,
+  pos: { x: number; y: number },
+  registry: any,
+  opts?: { hp?: number; cannotBeFrozen?: boolean; isBoss?: boolean }
+): CombatUnitContext {
+  const statList = new UnitStatList(registry, {
+    level: 80,
+    hitpoints: (opts?.hp ?? 10000) * FIXED_ONE,
+    maxhp: (opts?.hp ?? 10000) * FIXED_ONE,
+    armorclass: 400,
+    fireresist: 0,
+    coldresist: 0,
+    lightresist: 0,
+    poisonresist: 0,
+    damageresist: 0,
+    magicresist: 0,
+    x: pos.x,
+    y: pos.y,
+    ...(opts?.cannotBeFrozen ? { cannot_be_frozen: 1 } : {}),
+  })
+  const stateBus = new StateBus(statList, registry)
+  return {
+    id,
+    name: id,
+    statList,
+    stateBus,
+    isBoss: opts?.isBoss ?? false,
+  }
+}
+
+describe('Amazon Bow & Crossbow Kinematics Adversarial Stress Suite (1.13c Ground Truth)', () => {
+  it('enforces System Invariants: BATCH1_SKILLS length strictly equals 38 and zero mocks utilized', () => {
+    expect(Object.keys(BATCH1_SKILLS).length).toBe(38)
+    expect(BATCH1_SKILLS[6]).toBeDefined() // Magic Arrow
+    expect(BATCH1_SKILLS[7]).toBeDefined() // Fire Arrow
+    expect(BATCH1_SKILLS[11]).toBeDefined() // Cold Arrow
+  })
+
+  describe('Guided Arrow: Homing Kinematics, Continuous Steering & Strict Zero-Pierce', () => {
+    it('strictly forces canPierce = false and pierceChancePct = 0 even with 100% Pierce skill', async () => {
+      const registry = await getSharedDataRegistry()
+      const missileEngine = new MissileEngine(registry)
+
+      const owner = createTestCombatUnit('amazon-player', { x: 0, y: 0 }, registry)
+      // Simulate 100% Pierce skill from Skill 33 or Razortail
+      owner.statList.setBaseSkillLevel(33, 20)
+
+      const dmgPacket: SUnitDmgPacket = {
+        skillId: 22,
+        attackKind: 'missile',
+        srcDam: 128,
+        physDamagePct: 95, // Level 20 GA: +95% ED
+        autoHit: true,
+      }
+
+      // Spawn Guided Arrow with pierceChancePct: 100 explicitly requested
+      const missile = missileEngine.spawnMissile({
+        missileNameOrId: 'guidedarrow',
+        sourceSkillId: 22,
+        slvl: 20,
+        owner,
+        startX: 0,
+        startY: 0,
+        targetX: 100,
+        targetY: 0,
+        dmgPacket,
+        pierceChancePct: 100, // Adversarial input: 100% pierce
+      })
+
+      expect(missile).not.toBeNull()
+      // In 1.13c, Guided Arrow NEVER pierces under any circumstances
+      expect(missile!.canPierce).toBe(false)
+      expect(missile!.pierceChancePct).toBe(0)
+    })
+
+    it('continuously steers towards moving targets in 2:1 isometric space and auto-hits target defense', async () => {
+      const registry = await getSharedDataRegistry()
+      const missileEngine = new MissileEngine(registry)
+
+      const owner = createTestCombatUnit('amazon-player', { x: 0, y: 0 }, registry)
+      const targetPos = { x: 100, y: 60 }
+      const target = createTestCombatUnit('moving-target', targetPos, registry)
+      const targetPositions = new Map<string, { x: number; y: number }>()
+      targetPositions.set(target.id, targetPos)
+
+      const dmgPacket: SUnitDmgPacket = {
+        skillId: 22,
+        attackKind: 'missile',
+        srcDam: 128,
+        physDamagePct: 95,
+        autoHit: true,
+      }
+
+      // Fire in opposite direction (x: -100, y: 0)
+      const missile = missileEngine.spawnMissile({
+        missileNameOrId: 'guidedarrow',
+        sourceSkillId: 22,
+        slvl: 20,
+        owner,
+        startX: 0,
+        startY: 0,
+        targetX: -100,
+        targetY: 0,
+        dmgPacket,
+      })!
+
+      const initialAngle = missile.angleRad
+      expect(initialAngle).toBeCloseTo(Math.PI)
+
+      // Step missile engine ticks and verify steering redirects towards target
+      for (let tick = 1; tick <= 5; tick++) {
+        missileEngine.tick(tick, [target], targetPositions)
+      }
+
+      // Missile angle should have turned away from Math.PI towards positive angle
+      expect(missile.angleRad).not.toBe(initialAngle)
+      expect(missile.expired).toBe(false)
+
+      // Now move target directly in front of current missile position and step until hit
+      targetPositions.set(target.id, { x: missile.x + 20, y: missile.y })
+      const stepRes = missileEngine.tick(6, [target], targetPositions)
+
+      expect(stepRes.hits.length).toBeGreaterThanOrEqual(1)
+      expect(stepRes.hits[0]!.targetId).toBe(target.id)
+      expect(stepRes.hits[0]!.damage).toBeGreaterThan(0)
+      // Missile must expire immediately on hit (zero pierce)
+      expect(missile.expired).toBe(true)
+    })
+  })
+
+  describe('Multiple Shot: 2..24 Scaling, Fan Distribution, Center Procs & Hit Immunity', () => {
+    it('scales arrow count from 3 at level 1 to hard engine cap of 24 at level 22+', () => {
+      expect(calculateMultipleShotStats(1).arrowCount).toBe(3)
+      expect(calculateMultipleShotStats(5).arrowCount).toBe(7)
+      expect(calculateMultipleShotStats(10).arrowCount).toBe(12)
+      expect(calculateMultipleShotStats(20).arrowCount).toBe(22)
+      expect(calculateMultipleShotStats(22).arrowCount).toBe(24)
+      expect(calculateMultipleShotStats(30).arrowCount).toBe(24)
+      expect(calculateMultipleShotStats(50).arrowCount).toBe(24)
+    })
+
+    it('generates symmetric monotonic fan angles within 45-50 degree cone', () => {
+      const angles = generateMultipleShotAngles(0, 7, (50 * Math.PI) / 180)
+      expect(angles.length).toBe(7)
+      // Symmetrical about 0
+      expect(angles[3]).toBeCloseTo(0)
+      expect(angles[0]).toBeCloseTo(-angles[6]!)
+      expect(angles[1]).toBeCloseTo(-angles[5]!)
+      // Monotonic progression
+      for (let i = 0; i < angles.length - 1; i++) {
+        expect(angles[i + 1]!).toBeGreaterThan(angles[i]!)
+      }
+    })
+
+    it('flags strictly the center 2 arrows for on-striking procs; outer arrows cannot proc', () => {
+      // For a 6-arrow volley (indices 0, 1, 2, 3, 4, 5): center two are 2 and 3
+      expect(isMultipleShotCenterArrow(0, 6)).toBe(false)
+      expect(isMultipleShotCenterArrow(1, 6)).toBe(false)
+      expect(isMultipleShotCenterArrow(2, 6)).toBe(true)
+      expect(isMultipleShotCenterArrow(3, 6)).toBe(true)
+      expect(isMultipleShotCenterArrow(4, 6)).toBe(false)
+      expect(isMultipleShotCenterArrow(5, 6)).toBe(false)
+
+      // For a 24-arrow volley: center two are 11 and 12
+      expect(isMultipleShotCenterArrow(11, 24)).toBe(true)
+      expect(isMultipleShotCenterArrow(12, 24)).toBe(true)
+      expect(isMultipleShotCenterArrow(10, 24)).toBe(false)
+      expect(isMultipleShotCenterArrow(13, 24)).toBe(false)
+    })
+
+    it('enforces single-target hit immunity per Multiple Shot volley (no multi-hit shotgunning)', async () => {
+      const registry = await getSharedDataRegistry()
+      const missileEngine = new MissileEngine(registry)
+
+      const owner = createTestCombatUnit('amazon-player', { x: 0, y: 0 }, registry)
+      const target = createTestCombatUnit('boss-dummy', { x: 80, y: 0 }, registry)
+      const targetPositions = new Map<string, { x: number; y: number }>()
+      targetPositions.set(target.id, { x: 80, y: 0 })
+
+      const dmgPacket: SUnitDmgPacket = {
+        skillId: 12,
+        attackKind: 'missile',
+        srcDam: 96, // 75% weapon penalty
+        flatPhysMin256: 100 * FIXED_ONE,
+        flatPhysMax256: 100 * FIXED_ONE,
+        autoHit: true,
+      }
+
+      // Spawn a 24-arrow volley where multiple arrows pass through the target point
+      const arrows = missileEngine.spawnMultipleShotVolley({
+        sourceSkillId: 12,
+        slvl: 24,
+        owner,
+        startX: 0,
+        startY: 0,
+        targetX: 80,
+        targetY: 0,
+        dmgPacket,
+      })
+
+      expect(arrows.length).toBe(24)
+      const volleyId = arrows[0]!.volleyId
+      expect(volleyId).toBeDefined()
+      for (const a of arrows) {
+        expect(a.volleyId).toBe(volleyId)
+      }
+
+      // Step missile engine until arrows reach target at x=80
+      let totalHitsOnTarget = 0
+      for (let tick = 1; tick <= 10; tick++) {
+        const step = missileEngine.tick(tick, [target], targetPositions)
+        for (const h of step.hits) {
+          if (h.targetId === target.id) {
+            totalHitsOnTarget += 1
+          }
+        }
+      }
+
+      // Crucial 1.13c Invariant: Despite 24 arrows in the volley, a single monster receives damage exactly ONCE!
+      expect(totalHitsOnTarget).toBe(1)
+    })
+  })
+
+  describe('Strafe: Target Cycling, Rapid Burst Cadence & Stationary Lock-in', () => {
+    it('scales arrow count min(10, 4 + floor(slvl/2)) and applies 75% weapon damage + %ED', () => {
+      const s1 = calculateStrafeStats(1)
+      expect(s1.arrowCount).toBe(4)
+      expect(s1.damageMultiplier).toBe(0.75)
+      expect(s1.srcDam).toBe(96)
+      expect(s1.enhancedDamagePct).toBe(0)
+      expect(s1.manaCost).toBe(11)
+
+      const s2 = calculateStrafeStats(2)
+      expect(s2.arrowCount).toBe(5)
+
+      const s10 = calculateStrafeStats(10)
+      expect(s10.arrowCount).toBe(9)
+      expect(s10.enhancedDamagePct).toBe(45)
+
+      const s12 = calculateStrafeStats(12)
+      expect(s12.arrowCount).toBe(10)
+
+      const s20 = calculateStrafeStats(20)
+      expect(s20.arrowCount).toBe(10)
+      expect(s20.enhancedDamagePct).toBe(95)
+    })
+
+    it('distributes shots sequentially across multiple targets and applies stationary lock-in state', async () => {
+      const registry = await getSharedDataRegistry()
+      const missileEngine = new MissileEngine(registry)
+
+      const owner = createTestCombatUnit('amazon-player', { x: 0, y: 0 }, registry)
+      const t1 = createTestCombatUnit('enemy-1', { x: 100, y: 0 }, registry)
+      const t2 = createTestCombatUnit('enemy-2', { x: 0, y: 100 }, registry)
+      const t3 = createTestCombatUnit('enemy-3', { x: -100, y: 0 }, registry)
+      const targets = [t1, t2, t3]
+
+      const targetPositions = new Map<string, { x: number; y: number }>()
+      targetPositions.set(t1.id, { x: 100, y: 0 })
+      targetPositions.set(t2.id, { x: 0, y: 100 })
+      targetPositions.set(t3.id, { x: -100, y: 0 })
+
+      const dmgPacket: SUnitDmgPacket = {
+        skillId: 26,
+        attackKind: 'missile',
+        srcDam: 96,
+        autoHit: true,
+      }
+
+      const arrows = missileEngine.spawnStrafeVolley({
+        sourceSkillId: 26,
+        slvl: 20, // 10 arrows
+        owner,
+        startX: 0,
+        startY: 0,
+        targets,
+        targetPositions,
+        dmgPacket,
+      })
+
+      expect(arrows.length).toBe(10)
+      // Player is locked in stationary state
+      expect(owner.stateBus.hasState('strafe_lockin')).toBe(true)
+      const lockInState = owner.stateBus.getState('strafe_lockin')
+      expect(lockInState?.durationFrames).toBe(24) // 10 * 2 + 4
+
+      // Verify arrows target different positions cyclically
+      expect(arrows[0]!.angleRad).not.toBe(arrows[1]!.angleRad)
+      expect(arrows[1]!.angleRad).not.toBe(arrows[2]!.angleRad)
+    })
+  })
+
+  describe('Immolation Arrow: Casting Cooldown (25 frames) & Lingering Fire Patch (75 frames)', () => {
+    it('returns exact 25-frame casting cooldown and 75-frame ground fire duration', () => {
+      expect(getSkillCooldownTicks(27)).toBe(25) // 1.0 second delay in 1.13c
+      const stats = calculateImmolationArrowStats(20, { fireArrow: 20 })
+      expect(stats.cooldownFrames).toBe(25)
+      expect(stats.firePatchDurationFrames).toBe(75) // 3.0 seconds
+      expect(stats.explosionSynergyMultiplier).toBe(2.0)
+      expect(stats.firePatchSynergyMultiplier).toBe(3.0)
+    })
+
+    it('persists ground fire patch across 75 frames and ticks damage at 5-frame intervals', async () => {
+      const registry = await getSharedDataRegistry()
+      const missileEngine = new MissileEngine(registry)
+
+      const owner = createTestCombatUnit('amazon-player', { x: 0, y: 0 }, registry)
+      const target = createTestCombatUnit('standing-monster', { x: 50, y: 0 }, registry)
+      const targetPositions = new Map<string, { x: number; y: number }>()
+      targetPositions.set(target.id, { x: 50, y: 0 })
+
+      const dmgPacket: SUnitDmgPacket = {
+        skillId: 27,
+        attackKind: 'missile',
+        elemType: 'fire',
+        elemMin256: 50 * FIXED_ONE,
+        elemMax256: 50 * FIXED_ONE,
+        autoHit: true,
+      }
+
+      // Spawn primary immolation arrow
+      const mainArrow = missileEngine.spawnMissile({
+        missileNameOrId: 'immolationarrow',
+        sourceSkillId: 27,
+        slvl: 20,
+        owner,
+        startX: 0,
+        startY: 0,
+        targetX: 50,
+        targetY: 0,
+        dmgPacket,
+      })!
+
+      // Step until impact
+      let firePatchSpawned = false
+      for (let tick = 1; tick <= 5; tick++) {
+        const step = missileEngine.tick(tick, [target], targetPositions)
+        if (step.subMissilesSpawned.includes('immolationfire')) {
+          firePatchSpawned = true
+        }
+      }
+
+      expect(firePatchSpawned).toBe(true)
+
+      // Find the spawned immolationfire patch missile
+      const activeMissiles = missileEngine.getActiveMissiles()
+      const patch = activeMissiles.find(m => m.name === 'immolationfire')
+      expect(patch).toBeDefined()
+      expect(patch!.maxRangeTicks).toBe(75)
+
+      // Step through 20 ticks and count ticking damage
+      let tickHits = 0
+      for (let tick = 6; tick <= 25; tick++) {
+        const step = missileEngine.tick(tick, [target], targetPositions)
+        for (const h of step.hits) {
+          if (h.missileName === 'immolationfire') {
+            tickHits += 1
+          }
+        }
+      }
+
+      // Ground patch ticks every 5 ticks -> 20 ticks / 5 = 4 ticks
+      expect(tickHits).toBeGreaterThanOrEqual(3)
+      expect(patch!.expired).toBe(false)
+    })
+  })
+
+  describe('Freezing Arrow: 80 Sub-pixel Cold Splash & AoE Solid Freeze', () => {
+    it('splashes cold damage and applies freeze state to all enemies within 80 sub-pixels', async () => {
+      const registry = await getSharedDataRegistry()
+      const missileEngine = new MissileEngine(registry)
+
+      const owner = createTestCombatUnit('amazon-player', { x: 0, y: 0 }, registry)
+      const primary = createTestCombatUnit('primary-enemy', { x: 60, y: 0 }, registry)
+      const close1 = createTestCombatUnit('splash-enemy-1', { x: 80, y: 20 }, registry) // dist ~28px <= 80
+      const close2 = createTestCombatUnit('splash-enemy-2', { x: 40, y: -20 }, registry) // dist ~28px <= 80
+      const farEnemy = createTestCombatUnit('far-enemy', { x: 200, y: 0 }, registry) // dist 140px > 80
+
+      const allTargets = [primary, close1, close2, farEnemy]
+      const targetPositions = new Map<string, { x: number; y: number }>()
+      targetPositions.set(primary.id, { x: 60, y: 0 })
+      targetPositions.set(close1.id, { x: 80, y: 20 })
+      targetPositions.set(close2.id, { x: 40, y: -20 })
+      targetPositions.set(farEnemy.id, { x: 200, y: 0 })
+
+      const dmgPacket: SUnitDmgPacket = {
+        skillId: 31,
+        attackKind: 'missile',
+        elemType: 'cold',
+        elemMin256: 300 * FIXED_ONE,
+        elemMax256: 300 * FIXED_ONE,
+        autoHit: true,
+      }
+
+      // Spawn Freezing Arrow towards primary
+      missileEngine.spawnMissile({
+        missileNameOrId: 'freezingarrow',
+        sourceSkillId: 31,
+        slvl: 20,
+        owner,
+        startX: 0,
+        startY: 0,
+        targetX: 60,
+        targetY: 0,
+        dmgPacket,
+      })
+
+      // Step until impact and splash detonation
+      for (let tick = 1; tick <= 5; tick++) {
+        missileEngine.tick(tick, allTargets, targetPositions)
+      }
+
+      // Primary and close splash targets must receive freeze state
+      expect(primary.stateBus.hasState('freeze')).toBe(true)
+      expect(close1.stateBus.hasState('freeze')).toBe(true)
+      expect(close2.stateBus.hasState('freeze')).toBe(true)
+
+      // Far enemy outside 80 sub-pixels must NOT be frozen or damaged
+      expect(farEnemy.stateBus.hasState('freeze')).toBe(false)
+      expect(farEnemy.statList.getHp256()).toBe(farEnemy.statList.getMaxHp256())
+    })
+  })
+
+  describe('Integration with WorldArena & Central Skill Dispatchers', () => {
+    it('correctly maps calculateSkillDamage, getSkillManaCost, and getSkillCooldownTicks across all 10 bow skills', () => {
+      // Skill 6: Magic Arrow
+      expect(getSkillManaCost(6, 1)).toBe(1.5)
+      expect(getSkillManaCost(6, 13)).toBe(0.0)
+      expect(getSkillCooldownTicks(6)).toBe(0)
+      const dmg6 = calculateSkillDamage(6, 1, 1.0, { min: 20, max: 30 })
+      expect(dmg6.min).toBe(21) // 20 + 1
+      expect(dmg6.max).toBe(31) // 30 + 1
+
+      // Skill 7: Fire Arrow
+      expect(getSkillManaCost(7, 1)).toBe(3.0)
+      expect(getSkillCooldownTicks(7)).toBe(0)
+      const dmg7 = calculateSkillDamage(7, 1)
+      expect(dmg7.min).toBe(1)
+      expect(dmg7.max).toBe(4)
+
+      // Skill 11: Cold Arrow
+      expect(getSkillManaCost(11, 1)).toBe(3.5)
+      expect(getSkillCooldownTicks(11)).toBe(0)
+      const dmg11 = calculateSkillDamage(11, 1)
+      expect(dmg11.min).toBe(3)
+      expect(dmg11.max).toBe(4)
+
+      // Skill 12: Multiple Shot
+      expect(getSkillManaCost(12, 1)).toBe(4)
+      expect(getSkillCooldownTicks(12)).toBe(0)
+      const dmg12 = calculateSkillDamage(12, 1, 1.0, { min: 100, max: 200 })
+      expect(dmg12.min).toBe(75)
+      expect(dmg12.max).toBe(150)
+
+      // Skill 16: Exploding Arrow
+      expect(getSkillManaCost(16, 1)).toBe(5)
+      expect(getSkillCooldownTicks(16)).toBe(0)
+      const dmg16 = calculateSkillDamage(16, 1)
+      expect(dmg16.min).toBe(2)
+      expect(dmg16.max).toBe(6)
+
+      // Skill 21: Ice Arrow
+      expect(getSkillManaCost(21, 1)).toBe(4)
+      expect(getSkillCooldownTicks(21)).toBe(0)
+      const dmg21 = calculateSkillDamage(21, 1)
+      expect(dmg21.min).toBe(6)
+      expect(dmg21.max).toBe(10)
+
+      // Skill 22: Guided Arrow
+      expect(getSkillManaCost(22, 1)).toBe(8)
+      expect(getSkillCooldownTicks(22)).toBe(0)
+      const dmg22 = calculateSkillDamage(22, 10, 1.0, { min: 100, max: 200 })
+      expect(dmg22.min).toBe(145) // +45% ED
+      expect(dmg22.max).toBe(290)
+
+      // Skill 26: Strafe
+      expect(getSkillManaCost(26, 1)).toBe(11)
+      expect(getSkillCooldownTicks(26)).toBe(0)
+      const dmg26 = calculateSkillDamage(26, 10, 1.0, { min: 100, max: 200 })
+      expect(dmg26.min).toBe(Math.floor(100 * 0.75 * 1.45)) // 75% * 145% ED
+      expect(dmg26.max).toBe(Math.floor(200 * 0.75 * 1.45))
+
+      // Skill 27: Immolation Arrow
+      expect(getSkillManaCost(27, 1)).toBe(6)
+      expect(getSkillCooldownTicks(27)).toBe(25) // Cooldown = 25 frames
+      const dmg27 = calculateSkillDamage(27, 1)
+      expect(dmg27.min).toBe(12)
+      expect(dmg27.max).toBe(23)
+
+      // Skill 31: Freezing Arrow
+      expect(getSkillManaCost(31, 1)).toBe(9)
+      expect(getSkillCooldownTicks(31)).toBe(0)
+      const dmg31 = calculateSkillDamage(31, 1)
+      expect(dmg31.min).toBe(40)
+      expect(dmg31.max).toBe(50)
+    })
+
+    it('triggers and steps WorldArena cast cleanly across all 10 bow skills', async () => {
+      const registry = await getSharedDataRegistry()
+      const bowSkillIds = [6, 7, 11, 12, 16, 21, 22, 26, 27, 31]
+
+      for (const id of bowSkillIds) {
+        const arena = new WorldArena({
+          registry,
+          classCode: 'ama',
+          skillId: id,
+          slvl: 20,
+        })
+        const outcome = arena.triggerCast()
+        arena.stepTicks(15)
+        const dbg = arena.getDebugState()
+
+        expect(dbg.ready).toBe(true)
+        expect(dbg.skillId).toBe(id)
+        expect(dbg.castCount).toBeGreaterThanOrEqual(1)
+        expect(dbg.actionFrameTriggered).toBe(true)
+        expect(outcome?.executed).toBe(true)
+      }
+    })
+  })
+})

tests/skills/ama/skill-006-magic-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-006-magic-arrow.ts'
+import { calculateMagicArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #006] Magic Arrow (AMA) — 1.13c Parity (Issue #160)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,60 @@ describe('[Skill #006] Magic Arrow (AMA) — 1.13c Parity (Issue #160)', () => {
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateMagicArrowStats pure calculations and boundary invariants', () => {
+    // Level 1: 5% magic conversion, 1 flat magic dmg, +10% AR, 1.5 mana (384 fixed-point), noAmmo: true
+    const s1 = calculateMagicArrowStats(1)
+    expect(s1.conversionPct).toBe(5)
+    expect(s1.flatMagicDamage).toBe(1)
+    expect(s1.toHitBonusPct).toBe(10)
+    expect(s1.manaCost).toBe(1.5)
+    expect(s1.manaCost256).toBe(384)
+    expect(s1.noAmmo).toBe(true)
+    expect(s1.requiresAmmo).toBe(false)
+
+    // Level 10: 14% conversion, 12 flat magic dmg, +91% AR, 0.375 mana (96 units)
+    const s10 = calculateMagicArrowStats(10)
+    expect(s10.conversionPct).toBe(14)
+    expect(s10.flatMagicDamage).toBe(12)
+    expect(s10.toHitBonusPct).toBe(91)
+    expect(s10.manaCost).toBe(0.375)
+    expect(s10.manaCost256).toBe(96)
+
+    // Level 20: 24% conversion, 36 flat magic dmg, +181% AR, 0 mana
+    const s20 = calculateMagicArrowStats(20)
+    expect(s20.conversionPct).toBe(24)
+    expect(s20.flatMagicDamage).toBe(36)
+    expect(s20.toHitBonusPct).toBe(181)
+    expect(s20.manaCost).toBe(0)
+    expect(s20.manaCost256).toBe(0)
+
+    // Level 96+: capped at 100% conversion
+    const s96 = calculateMagicArrowStats(96)
+    expect(s96.conversionPct).toBe(100)
+
+    // Monotonicity checks
+    for (let lvl = 1; lvl < 30; lvl++) {
+      const cur = calculateMagicArrowStats(lvl)
+      const nxt = calculateMagicArrowStats(lvl + 1)
+      expect(nxt.conversionPct).toBeGreaterThanOrEqual(cur.conversionPct)
+      expect(nxt.flatMagicDamage).toBeGreaterThanOrEqual(cur.flatMagicDamage)
+      expect(nxt.toHitBonusPct).toBeGreaterThan(cur.toHitBonusPct)
+      expect(nxt.manaCost).toBeLessThanOrEqual(cur.manaCost)
+    }
+
+    // Boundary resilience: 0, negative, NaN, fractional
+    const sZero = calculateMagicArrowStats(0)
+    expect(sZero.conversionPct).toBe(5)
+    expect(sZero.manaCost).toBe(1.5)
+
+    const sNeg = calculateMagicArrowStats(-10)
+    expect(sNeg.conversionPct).toBe(5)
+
+    const sNan = calculateMagicArrowStats(NaN)
+    expect(sNan.conversionPct).toBe(5)
+
+    const sFrac = calculateMagicArrowStats(5.7)
+    expect(sFrac.conversionPct).toBe(9)
+  })
 })

tests/skills/ama/skill-007-fire-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-007-fire-arrow.ts'
+import { calculateFireArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #007] Fire Arrow (AMA) — 1.13c Parity (Issue #161)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,60 @@ describe('[Skill #007] Fire Arrow (AMA) — 1.13c Parity (Issue #161)', () => {
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateFireArrowStats pure calculations and boundary invariants', () => {
+    // Level 1: 80% conversion, 1-4 fire dmg, +10% AR, 3.0 mana
+    const s1 = calculateFireArrowStats(1)
+    expect(s1.physToElemPct).toBe(80)
+    expect(s1.srcDam).toBe(80)
+    expect(s1.minDamage).toBe(1)
+    expect(s1.maxDamage).toBe(4)
+    expect(s1.toHitBonusPct).toBe(10)
+    expect(s1.manaCost).toBe(3.0)
+
+    // Level 10: 21-24 fire dmg, +91% AR, 5.25 mana
+    const s10 = calculateFireArrowStats(10)
+    expect(s10.minDamage).toBe(21)
+    expect(s10.maxDamage).toBe(24)
+    expect(s10.toHitBonusPct).toBe(91)
+    expect(s10.manaCost).toBe(5.25)
+
+    // Level 20: 63-70 fire dmg, +181% AR, 7.75 mana
+    const s20 = calculateFireArrowStats(20)
+    expect(s20.minDamage).toBe(63)
+    expect(s20.maxDamage).toBe(70)
+    expect(s20.toHitBonusPct).toBe(181)
+    expect(s20.manaCost).toBe(7.75)
+
+    // Synergy test: Exploding Arrow +12%/level
+    const s20Syn = calculateFireArrowStats(20, { explodingArrow: 20 })
+    expect(s20Syn.synergyBonusPct).toBe(240)
+    expect(s20Syn.synergyMultiplier).toBe(3.4)
+    expect(s20Syn.minDamage).toBe(Math.floor(63 * 3.4))
+    expect(s20Syn.maxDamage).toBe(Math.floor(70 * 3.4))
+
+    // Monotonicity checks
+    for (let lvl = 1; lvl < 30; lvl++) {
+      const cur = calculateFireArrowStats(lvl)
+      const nxt = calculateFireArrowStats(lvl + 1)
+      expect(nxt.minDamage).toBeGreaterThanOrEqual(cur.minDamage)
+      expect(nxt.maxDamage).toBeGreaterThanOrEqual(cur.maxDamage)
+      expect(nxt.toHitBonusPct).toBeGreaterThan(cur.toHitBonusPct)
+      expect(nxt.manaCost).toBeGreaterThan(cur.manaCost)
+    }
+
+    // Boundary resilience
+    const sZero = calculateFireArrowStats(0)
+    expect(sZero.minDamage).toBe(1)
+    expect(sZero.manaCost).toBe(3.0)
+
+    const sNeg = calculateFireArrowStats(-5)
+    expect(sNeg.minDamage).toBe(1)
+
+    const sNan = calculateFireArrowStats(NaN)
+    expect(sNan.minDamage).toBe(1)
+
+    const sFrac = calculateFireArrowStats(4.8)
+    expect(sFrac.minDamage).toBe(calculateFireArrowStats(4).minDamage)
+  })
 })

tests/skills/ama/skill-011-cold-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-011-cold-arrow.ts'
+import { calculateColdArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #011] Cold Arrow (AMA) — 1.13c Parity (Issue #165)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,64 @@ describe('[Skill #011] Cold Arrow (AMA) — 1.13c Parity (Issue #165)', () => {
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateColdArrowStats pure calculations and boundary invariants', () => {
+    // Level 1: 80% conversion, 3-4 cold dmg, 50 frames chill duration, +10% AR, 3.5 mana
+    const s1 = calculateColdArrowStats(1)
+    expect(s1.physToElemPct).toBe(80)
+    expect(s1.srcDam).toBe(80)
+    expect(s1.minDamage).toBe(3)
+    expect(s1.maxDamage).toBe(4)
+    expect(s1.durationFrames).toBe(50)
+    expect(s1.toHitBonusPct).toBe(10)
+    expect(s1.manaCost).toBe(3.5)
+
+    // Level 10: 22-23 cold dmg, 140 frames chill duration, +91% AR, 5.75 mana
+    const s10 = calculateColdArrowStats(10)
+    expect(s10.minDamage).toBe(22)
+    expect(s10.maxDamage).toBe(23)
+    expect(s10.durationFrames).toBe(140)
+    expect(s10.toHitBonusPct).toBe(91)
+    expect(s10.manaCost).toBe(5.75)
+
+    // Level 20: 53-56 cold dmg, 240 frames chill duration, +181% AR, 8.25 mana
+    const s20 = calculateColdArrowStats(20)
+    expect(s20.minDamage).toBe(53)
+    expect(s20.maxDamage).toBe(56)
+    expect(s20.durationFrames).toBe(240)
+    expect(s20.toHitBonusPct).toBe(181)
+    expect(s20.manaCost).toBe(8.25)
+
+    // Synergy test: Ice Arrow +12%/level
+    const s20Syn = calculateColdArrowStats(20, { iceArrow: 20 })
+    expect(s20Syn.synergyBonusPct).toBe(240)
+    expect(s20Syn.synergyMultiplier).toBe(3.4)
+    expect(s20Syn.minDamage).toBe(Math.floor(53 * 3.4))
+    expect(s20Syn.maxDamage).toBe(Math.floor(56 * 3.4))
+
+    // Monotonicity checks
+    for (let lvl = 1; lvl < 30; lvl++) {
+      const cur = calculateColdArrowStats(lvl)
+      const nxt = calculateColdArrowStats(lvl + 1)
+      expect(nxt.minDamage).toBeGreaterThanOrEqual(cur.minDamage)
+      expect(nxt.maxDamage).toBeGreaterThanOrEqual(cur.maxDamage)
+      expect(nxt.durationFrames).toBeGreaterThan(cur.durationFrames)
+      expect(nxt.toHitBonusPct).toBeGreaterThan(cur.toHitBonusPct)
+      expect(nxt.manaCost).toBeGreaterThan(cur.manaCost)
+    }
+
+    // Boundary resilience
+    const sZero = calculateColdArrowStats(0)
+    expect(sZero.minDamage).toBe(3)
+    expect(sZero.manaCost).toBe(3.5)
+
+    const sNeg = calculateColdArrowStats(-1)
+    expect(sNeg.minDamage).toBe(3)
+
+    const sNan = calculateColdArrowStats(NaN)
+    expect(sNan.minDamage).toBe(3)
+
+    const sFrac = calculateColdArrowStats(7.2)
+    expect(sFrac.minDamage).toBe(calculateColdArrowStats(7).minDamage)
+  })
 })

tests/skills/ama/skill-012-multiple-shot.test.ts

@@ -7,6 +7,11 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-012-multiple-shot.ts'
+import {
+  calculateMultipleShotStats,
+  generateMultipleShotAngles,
+  isMultipleShotCenterArrow,
+} from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #012] Multiple Shot (AMA) — 1.13c Parity (Issue #166)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +111,60 @@ describe('[Skill #012] Multiple Shot (AMA) — 1.13c Parity (Issue #166)', () =>
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateMultipleShotStats pure calculations and kinematics invariants', () => {
+    // Level 1: 3 arrows, 75% weapon damage (srcdam=96), 4 mana
+    const s1 = calculateMultipleShotStats(1)
+    expect(s1.arrowCount).toBe(3)
+    expect(s1.damageMultiplier).toBe(0.75)
+    expect(s1.srcDam).toBe(96)
+    expect(s1.centerProcArrows).toBe(2)
+    expect(s1.onlyCenterArrowsProc).toBe(true)
+    expect(s1.singleTargetImmunity).toBe(true)
+    expect(s1.manaCost).toBe(4)
+
+    // Level 10: 12 arrows, 13 mana
+    const s10 = calculateMultipleShotStats(10)
+    expect(s10.arrowCount).toBe(12)
+    expect(s10.manaCost).toBe(13)
+
+    // Level 20: 22 arrows, 23 mana
+    const s20 = calculateMultipleShotStats(20)
+    expect(s20.arrowCount).toBe(22)
+    expect(s20.manaCost).toBe(23)
+
+    // Level 22+: capped at 24 arrows
+    const s22 = calculateMultipleShotStats(22)
+    expect(s22.arrowCount).toBe(24)
+    const s30 = calculateMultipleShotStats(30)
+    expect(s30.arrowCount).toBe(24)
+
+    // Proc flag: only center 2 arrows proc
+    // For 4 arrows (0, 1, 2, 3): mid1=1, mid2=2
+    expect(isMultipleShotCenterArrow(0, 4)).toBe(false)
+    expect(isMultipleShotCenterArrow(1, 4)).toBe(true)
+    expect(isMultipleShotCenterArrow(2, 4)).toBe(true)
+    expect(isMultipleShotCenterArrow(3, 4)).toBe(false)
+
+    // Symmetrical fan angles test
+    const angles = generateMultipleShotAngles(0, 5, Math.PI / 4)
+    expect(angles.length).toBe(5)
+    expect(angles[0]).toBeCloseTo(-Math.PI / 8)
+    expect(angles[2]).toBeCloseTo(0)
+    expect(angles[4]).toBeCloseTo(Math.PI / 8)
+
+    // Boundary resilience
+    const sZero = calculateMultipleShotStats(0)
+    expect(sZero.arrowCount).toBe(3)
+    expect(sZero.manaCost).toBe(4)
+
+    const sNeg = calculateMultipleShotStats(-5)
+    expect(sNeg.arrowCount).toBe(3)
+
+    const sNan = calculateMultipleShotStats(NaN)
+    expect(sNan.arrowCount).toBe(3)
+
+    const sFrac = calculateMultipleShotStats(3.9)
+    expect(sFrac.arrowCount).toBe(5)
+  })
 })

tests/skills/ama/skill-016-exploding-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-016-exploding-arrow.ts'
+import { calculateExplodingArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #016] Exploding Arrow (AMA) — 1.13c Parity (Issue #170)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,59 @@ describe('[Skill #016] Exploding Arrow (AMA) — 1.13c Parity (Issue #170)', ()
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateExplodingArrowStats pure calculations and AoE invariants', () => {
+    // Level 1: 2-6 blast fire dmg, 80 sub-pixel AoE, +20% AR, 5.0 mana
+    const s1 = calculateExplodingArrowStats(1)
+    expect(s1.minBlastDamage).toBe(2)
+    expect(s1.maxBlastDamage).toBe(6)
+    expect(s1.radiusPx).toBe(80)
+    expect(s1.toHitBonusPct).toBe(20)
+    expect(s1.manaCost).toBe(5.0)
+
+    // Level 10: 51-57 blast fire dmg, +101% AR, 9.5 mana
+    const s10 = calculateExplodingArrowStats(10)
+    expect(s10.minBlastDamage).toBe(51)
+    expect(s10.maxBlastDamage).toBe(57)
+    expect(s10.toHitBonusPct).toBe(101)
+    expect(s10.manaCost).toBe(9.5)
+
+    // Level 20: 129-149 blast fire dmg, +191% AR, 14.5 mana
+    const s20 = calculateExplodingArrowStats(20)
+    expect(s20.minBlastDamage).toBe(129)
+    expect(s20.maxBlastDamage).toBe(149)
+    expect(s20.toHitBonusPct).toBe(191)
+    expect(s20.manaCost).toBe(14.5)
+
+    // Synergy test: Fire Arrow +12%/level
+    const s20Syn = calculateExplodingArrowStats(20, { fireArrow: 20 })
+    expect(s20Syn.synergyBonusPct).toBe(240)
+    expect(s20Syn.synergyMultiplier).toBe(3.4)
+    expect(s20Syn.minBlastDamage).toBe(Math.floor(129 * 3.4))
+    expect(s20Syn.maxBlastDamage).toBe(Math.floor(149 * 3.4))
+
+    // Monotonicity checks
+    for (let lvl = 1; lvl < 30; lvl++) {
+      const cur = calculateExplodingArrowStats(lvl)
+      const nxt = calculateExplodingArrowStats(lvl + 1)
+      expect(nxt.minBlastDamage).toBeGreaterThanOrEqual(cur.minBlastDamage)
+      expect(nxt.maxBlastDamage).toBeGreaterThanOrEqual(cur.maxBlastDamage)
+      expect(nxt.toHitBonusPct).toBeGreaterThan(cur.toHitBonusPct)
+      expect(nxt.manaCost).toBeGreaterThan(cur.manaCost)
+    }
+
+    // Boundary resilience
+    const sZero = calculateExplodingArrowStats(0)
+    expect(sZero.minBlastDamage).toBe(2)
+    expect(sZero.manaCost).toBe(5.0)
+
+    const sNeg = calculateExplodingArrowStats(-3)
+    expect(sNeg.minBlastDamage).toBe(2)
+
+    const sNan = calculateExplodingArrowStats(NaN)
+    expect(sNan.minBlastDamage).toBe(2)
+
+    const sFrac = calculateExplodingArrowStats(8.6)
+    expect(sFrac.minBlastDamage).toBe(calculateExplodingArrowStats(8).minBlastDamage)
+  })
 })

tests/skills/ama/skill-021-ice-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-021-ice-arrow.ts'
+import { calculateIceArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #021] Ice Arrow (AMA) — 1.13c Parity (Issue #175)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,63 @@ describe('[Skill #021] Ice Arrow (AMA) — 1.13c Parity (Issue #175)', () => {
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateIceArrowStats pure calculations and freeze invariants', () => {
+    // Level 1: 6-10 cold dmg, 50 frames freeze duration, +20% AR, 4.0 mana
+    const s1 = calculateIceArrowStats(1)
+    expect(s1.minDamage).toBe(6)
+    expect(s1.maxDamage).toBe(10)
+    expect(s1.freezeFrames).toBe(50)
+    expect(s1.toHitBonusPct).toBe(20)
+    expect(s1.manaCost).toBe(4.0)
+
+    // Level 10: 72-78 cold dmg, 95 frames freeze duration, +101% AR, 6.25 mana
+    const s10 = calculateIceArrowStats(10)
+    expect(s10.minDamage).toBe(72)
+    expect(s10.maxDamage).toBe(78)
+    expect(s10.freezeFrames).toBe(95)
+    expect(s10.toHitBonusPct).toBe(101)
+    expect(s10.manaCost).toBe(6.25)
+
+    // Level 20: 216-232 cold dmg, 145 frames freeze duration, +191% AR, 8.75 mana
+    const s20 = calculateIceArrowStats(20)
+    expect(s20.minDamage).toBe(216)
+    expect(s20.maxDamage).toBe(232)
+    expect(s20.freezeFrames).toBe(145)
+    expect(s20.toHitBonusPct).toBe(191)
+    expect(s20.manaCost).toBe(8.75)
+
+    // Synergies test: Cold Arrow +8% damage/lvl, Freezing Arrow +5% freeze length/lvl
+    const s20Syn = calculateIceArrowStats(20, { coldArrow: 20, freezingArrow: 20 })
+    expect(s20Syn.dmgSynergyMultiplier).toBe(2.6) // 1 + 20 * 0.08
+    expect(s20Syn.lenSynergyMultiplier).toBe(2.0) // 1 + 20 * 0.05
+    expect(s20Syn.minDamage).toBe(Math.floor(216 * 2.6))
+    expect(s20Syn.maxDamage).toBe(Math.floor(232 * 2.6))
+    expect(s20Syn.freezeFrames).toBe(Math.floor(145 * 2.0))
+
+    // Monotonicity checks
+    for (let lvl = 1; lvl < 30; lvl++) {
+      const cur = calculateIceArrowStats(lvl)
+      const nxt = calculateIceArrowStats(lvl + 1)
+      expect(nxt.minDamage).toBeGreaterThanOrEqual(cur.minDamage)
+      expect(nxt.maxDamage).toBeGreaterThanOrEqual(cur.maxDamage)
+      expect(nxt.freezeFrames).toBeGreaterThan(cur.freezeFrames)
+      expect(nxt.toHitBonusPct).toBeGreaterThan(cur.toHitBonusPct)
+      expect(nxt.manaCost).toBeGreaterThan(cur.manaCost)
+    }
+
+    // Boundary resilience
+    const sZero = calculateIceArrowStats(0)
+    expect(sZero.minDamage).toBe(6)
+    expect(sZero.manaCost).toBe(4.0)
+
+    const sNeg = calculateIceArrowStats(-2)
+    expect(sNeg.minDamage).toBe(6)
+
+    const sNan = calculateIceArrowStats(NaN)
+    expect(sNan.minDamage).toBe(6)
+
+    const sFrac = calculateIceArrowStats(9.4)
+    expect(sFrac.minDamage).toBe(calculateIceArrowStats(9).minDamage)
+  })
 })

tests/skills/ama/skill-022-guided-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-022-guided-arrow.ts'
+import { calculateGuidedArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #022] Guided Arrow (AMA) — 1.13c Parity (Issue #176)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,57 @@ describe('[Skill #022] Guided Arrow (AMA) — 1.13c Parity (Issue #176)', () =>
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateGuidedArrowStats pure calculations and zero-pierce invariant', () => {
+    // Level 1: +0% ED, alwaysHits = true, canPierce = false, pierceChancePct = 0, 8.0 mana
+    const s1 = calculateGuidedArrowStats(1)
+    expect(s1.enhancedDamagePct).toBe(0)
+    expect(s1.alwaysHits).toBe(true)
+    expect(s1.autoHit).toBe(true)
+    expect(s1.canPierce).toBe(false)
+    expect(s1.pierceChancePct).toBe(0)
+    expect(s1.manaCost).toBe(8.0)
+
+    // Level 10: +45% ED, 5.75 mana
+    const s10 = calculateGuidedArrowStats(10)
+    expect(s10.enhancedDamagePct).toBe(45)
+    expect(s10.alwaysHits).toBe(true)
+    expect(s10.canPierce).toBe(false)
+    expect(s10.manaCost).toBe(5.75)
+
+    // Level 20: +95% ED, 3.25 mana
+    const s20 = calculateGuidedArrowStats(20)
+    expect(s20.enhancedDamagePct).toBe(95)
+    expect(s20.alwaysHits).toBe(true)
+    expect(s20.canPierce).toBe(false)
+    expect(s20.manaCost).toBe(3.25)
+
+    // High level clamp: mana floor is 1.75
+    const s30 = calculateGuidedArrowStats(30)
+    expect(s30.manaCost).toBe(1.75)
+    const s50 = calculateGuidedArrowStats(50)
+    expect(s50.manaCost).toBe(1.75)
+
+    // Strict zero-pierce invariant at all levels
+    for (let lvl = 1; lvl <= 40; lvl++) {
+      const s = calculateGuidedArrowStats(lvl)
+      expect(s.canPierce).toBe(false)
+      expect(s.pierceChancePct).toBe(0)
+      expect(s.alwaysHits).toBe(true)
+    }
+
+    // Boundary resilience
+    const sZero = calculateGuidedArrowStats(0)
+    expect(sZero.enhancedDamagePct).toBe(0)
+    expect(sZero.manaCost).toBe(8.0)
+
+    const sNeg = calculateGuidedArrowStats(-10)
+    expect(sNeg.enhancedDamagePct).toBe(0)
+
+    const sNan = calculateGuidedArrowStats(NaN)
+    expect(sNan.enhancedDamagePct).toBe(0)
+
+    const sFrac = calculateGuidedArrowStats(6.5)
+    expect(sFrac.enhancedDamagePct).toBe(calculateGuidedArrowStats(6).enhancedDamagePct)
+  })
 })

tests/skills/ama/skill-026-strafe.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-026-strafe.ts'
+import { calculateStrafeStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #026] Strafe (AMA) — 1.13c Parity (Issue #180)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,53 @@ describe('[Skill #026] Strafe (AMA) — 1.13c Parity (Issue #180)', () => {
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateStrafeStats pure calculations and burst invariants', () => {
+    // Level 1: 4 arrows, 75% weapon damage (srcdam=96), +0% ED, stationary lock-in, 11 mana
+    const s1 = calculateStrafeStats(1)
+    expect(s1.arrowCount).toBe(4)
+    expect(s1.damageMultiplier).toBe(0.75)
+    expect(s1.srcDam).toBe(96)
+    expect(s1.enhancedDamagePct).toBe(0)
+    expect(s1.stationaryLockIn).toBe(true)
+    expect(s1.lockInFrames).toBe(12) // 4 * 2 + 4
+    expect(s1.manaCost).toBe(11)
+
+    // Level 2: 5 arrows
+    const s2 = calculateStrafeStats(2)
+    expect(s2.arrowCount).toBe(5)
+
+    // Level 10: 9 arrows, +45% ED, 11 mana
+    const s10 = calculateStrafeStats(10)
+    expect(s10.arrowCount).toBe(9)
+    expect(s10.enhancedDamagePct).toBe(45)
+    expect(s10.manaCost).toBe(11)
+
+    // Level 12+: capped at 10 arrows
+    const s12 = calculateStrafeStats(12)
+    expect(s12.arrowCount).toBe(10)
+    const s20 = calculateStrafeStats(20)
+    expect(s20.arrowCount).toBe(10)
+    expect(s20.enhancedDamagePct).toBe(95)
+    expect(s20.manaCost).toBe(11)
+
+    // Fixed mana cost invariant
+    for (let lvl = 1; lvl <= 30; lvl++) {
+      expect(calculateStrafeStats(lvl).manaCost).toBe(11)
+    }
+
+    // Boundary resilience
+    const sZero = calculateStrafeStats(0)
+    expect(sZero.arrowCount).toBe(4)
+    expect(sZero.manaCost).toBe(11)
+
+    const sNeg = calculateStrafeStats(-5)
+    expect(sNeg.arrowCount).toBe(4)
+
+    const sNan = calculateStrafeStats(NaN)
+    expect(sNan.arrowCount).toBe(4)
+
+    const sFrac = calculateStrafeStats(7.9)
+    expect(sFrac.arrowCount).toBe(calculateStrafeStats(7).arrowCount)
+  })
 })

tests/skills/ama/skill-027-immolation-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-027-immolation-arrow.ts'
+import { calculateImmolationArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #027] Immolation Arrow (AMA) — 1.13c Parity (Issue #181)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,66 @@ describe('[Skill #027] Immolation Arrow (AMA) — 1.13c Parity (Issue #181)', ()
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateImmolationArrowStats pure calculations, cooldown, and fire patch invariants', () => {
+    // Level 1: 12-23 explosion fire dmg, 75 frames ground fire, 25 frames delay, +30% AR, 6.0 mana
+    const s1 = calculateImmolationArrowStats(1)
+    expect(s1.minExplosionDamage).toBe(12)
+    expect(s1.maxExplosionDamage).toBe(23)
+    expect(s1.firePatchDurationFrames).toBe(75)
+    expect(s1.cooldownFrames).toBe(25)
+    expect(s1.toHitBonusPct).toBe(30)
+    expect(s1.manaCost).toBe(6.0)
+
+    // Level 10: 142-153 explosion fire dmg, +111% AR, 10.5 mana
+    const s10 = calculateImmolationArrowStats(10)
+    expect(s10.minExplosionDamage).toBe(142)
+    expect(s10.maxExplosionDamage).toBe(153)
+    expect(s10.firePatchDurationFrames).toBe(75)
+    expect(s10.cooldownFrames).toBe(25)
+    expect(s10.toHitBonusPct).toBe(111)
+    expect(s10.manaCost).toBe(10.5)
+
+    // Level 20: 416-427 explosion fire dmg, +201% AR, 15.5 mana
+    const s20 = calculateImmolationArrowStats(20)
+    expect(s20.minExplosionDamage).toBe(416)
+    expect(s20.maxExplosionDamage).toBe(427)
+    expect(s20.firePatchDurationFrames).toBe(75)
+    expect(s20.cooldownFrames).toBe(25)
+    expect(s20.toHitBonusPct).toBe(201)
+    expect(s20.manaCost).toBe(15.5)
+
+    // Synergies: Fire Arrow (+5% explosion dmg, +10% patch dmg per level)
+    const s20Syn = calculateImmolationArrowStats(20, { fireArrow: 20 })
+    expect(s20Syn.explosionSynergyMultiplier).toBe(2.0) // 1 + 20 * 0.05
+    expect(s20Syn.firePatchSynergyMultiplier).toBe(3.0) // 1 + 20 * 0.10
+    expect(s20Syn.minExplosionDamage).toBe(Math.floor(416 * 2.0))
+    expect(s20Syn.maxExplosionDamage).toBe(Math.floor(427 * 2.0))
+
+    // Monotonicity checks
+    for (let lvl = 1; lvl < 30; lvl++) {
+      const cur = calculateImmolationArrowStats(lvl)
+      const nxt = calculateImmolationArrowStats(lvl + 1)
+      expect(nxt.minExplosionDamage).toBeGreaterThanOrEqual(cur.minExplosionDamage)
+      expect(nxt.maxExplosionDamage).toBeGreaterThanOrEqual(cur.maxExplosionDamage)
+      expect(nxt.toHitBonusPct).toBeGreaterThan(cur.toHitBonusPct)
+      expect(nxt.manaCost).toBeGreaterThan(cur.manaCost)
+      expect(nxt.cooldownFrames).toBe(25)
+      expect(nxt.firePatchDurationFrames).toBe(75)
+    }
+
+    // Boundary resilience
+    const sZero = calculateImmolationArrowStats(0)
+    expect(sZero.minExplosionDamage).toBe(12)
+    expect(sZero.manaCost).toBe(6.0)
+
+    const sNeg = calculateImmolationArrowStats(-4)
+    expect(sNeg.minExplosionDamage).toBe(12)
+
+    const sNan = calculateImmolationArrowStats(NaN)
+    expect(sNan.minExplosionDamage).toBe(12)
+
+    const sFrac = calculateImmolationArrowStats(11.3)
+    expect(sFrac.minExplosionDamage).toBe(calculateImmolationArrowStats(11).minExplosionDamage)
+  })
 })

tests/skills/ama/skill-031-freezing-arrow.test.ts

@@ -7,6 +7,7 @@ import { getSharedDataRegistry } from '../../../src/game/engine/data-registry.ts
 import { UnitStatList } from '../../../src/game/engine/stat-list.ts'
 import { WorldArena } from '../../../src/game/engine/world-arena.ts'
 import { skillModule } from '../../../src/game/skills/impl/ama/skill-031-freezing-arrow.ts'
+import { calculateFreezingArrowStats } from '../../../src/game/skills/amazon-bow.ts'
 
 describe('[Skill #031] Freezing Arrow (AMA) — 1.13c Parity (Issue #185)', () => {
   it('evaluates exact 1.13c Skills.txt / Missiles.txt formulas at slvl 1, 10, and 20', async () => {
@@ -106,4 +107,64 @@ describe('[Skill #031] Freezing Arrow (AMA) — 1.13c Parity (Issue #185)', () =
     expect(dbg.actionFrameTriggered).toBe(true)
     expect(outcome?.executed).toBe(true)
   })
+
+  it('validates 1.13c calculateFreezingArrowStats pure calculations, splash, and freeze invariants', () => {
+    // Level 1: 40-50 cold dmg, 80 sub-pixel AoE, 50 frames freeze duration, +40% AR, 9.0 mana
+    const s1 = calculateFreezingArrowStats(1)
+    expect(s1.minColdDamage).toBe(40)
+    expect(s1.maxColdDamage).toBe(50)
+    expect(s1.radiusPx).toBe(80)
+    expect(s1.freezeFrames).toBe(50)
+    expect(s1.toHitBonusPct).toBe(40)
+    expect(s1.manaCost).toBe(9.0)
+
+    // Level 10: 140-150 cold dmg, +121% AR, 13.5 mana
+    const s10 = calculateFreezingArrowStats(10)
+    expect(s10.minColdDamage).toBe(140)
+    expect(s10.maxColdDamage).toBe(150)
+    expect(s10.freezeFrames).toBe(50)
+    expect(s10.toHitBonusPct).toBe(121)
+    expect(s10.manaCost).toBe(13.5)
+
+    // Level 20: 310-320 cold dmg, +211% AR, 18.5 mana
+    const s20 = calculateFreezingArrowStats(20)
+    expect(s20.minColdDamage).toBe(310)
+    expect(s20.maxColdDamage).toBe(320)
+    expect(s20.freezeFrames).toBe(50)
+    expect(s20.toHitBonusPct).toBe(211)
+    expect(s20.manaCost).toBe(18.5)
+
+    // Synergies: Cold Arrow (+12% cold damage/lvl), Ice Arrow (+5% freeze length/lvl)
+    const s20Syn = calculateFreezingArrowStats(20, { coldArrow: 20, iceArrow: 20 })
+    expect(s20Syn.coldSynergyMultiplier).toBe(3.4) // 1 + 20 * 0.12
+    expect(s20Syn.lenSynergyMultiplier).toBe(2.0) // 1 + 20 * 0.05
+    expect(s20Syn.minColdDamage).toBe(Math.floor(310 * 3.4))
+    expect(s20Syn.maxColdDamage).toBe(Math.floor(320 * 3.4))
+    expect(s20Syn.freezeFrames).toBe(Math.floor(50 * 2.0))
+
+    // Monotonicity checks
+    for (let lvl = 1; lvl < 30; lvl++) {
+      const cur = calculateFreezingArrowStats(lvl)
+      const nxt = calculateFreezingArrowStats(lvl + 1)
+      expect(nxt.minColdDamage).toBeGreaterThanOrEqual(cur.minColdDamage)
+      expect(nxt.maxColdDamage).toBeGreaterThanOrEqual(cur.maxColdDamage)
+      expect(nxt.toHitBonusPct).toBeGreaterThan(cur.toHitBonusPct)
+      expect(nxt.manaCost).toBeGreaterThan(cur.manaCost)
+      expect(nxt.radiusPx).toBe(80)
+    }
+
+    // Boundary resilience
+    const sZero = calculateFreezingArrowStats(0)
+    expect(sZero.minColdDamage).toBe(40)
+    expect(sZero.manaCost).toBe(9.0)
+
+    const sNeg = calculateFreezingArrowStats(-7)
+    expect(sNeg.minColdDamage).toBe(40)
+
+    const sNan = calculateFreezingArrowStats(NaN)
+    expect(sNan.minColdDamage).toBe(40)
+
+    const sFrac = calculateFreezingArrowStats(15.8)
+    expect(sFrac.minColdDamage).toBe(calculateFreezingArrowStats(15).minColdDamage)
+  })
 })