Feature: Penetration chance in the armor shot card

Shows the chance a shot penetrates in the dynamic armor shot card, right-aligned on the shot's result line.

- Penetration varies by ±5% (the same randomisation the armor highlighter shader uses), so the chance is the share of that range where the shot's final outcome is a penetration
- Re-runs the existing shot calculation at different penetration values, so spaced armor, HEAT gap losses and ricochets are taken into account
- For ricochets the chance is shown on the ricocheted shot's line; HE splashes don't count as penetrations
- Adds the `shot_card.stats.penetration_chance` string

Fixes #342

packages/website/src/components/Armor/components/ShotDisplayCard.tsx

@@ -128,20 +128,31 @@ export function ShotDisplayCard({ shot, ...props }: ShotDisplayCardProps) {
     ? shotStatusColors[shot.out.status]
     : undefined;
   const inTitleColor = shotStatusColors[shot.in.status];
+  const hasOutLayers = shot.out !== undefined && shot.out.layers.length > 0;
+  const penetrationChance = shot.penetrationChance !== undefined && (
+    <Text color="gray" weight="bold">
+      {literals(strings.common.units.percentage, {
+        value: (shot.penetrationChance * 100).toFixed(0),
+      })}
+    </Text>
+  );
 
   return (
     <Card variant="classic" {...props}>
       <Flex direction="column" gap="2">
         <Flex direction="column" gap="1">
+          <Flex justify="between" align="center" gap="4">
             <Text color={inTitleColor} weight="bold">
               {literals(
-              strings.website.tools.tankopedia.sandbox.dynamic.shot_card.status[
-                shot.in.status
-              ],
+                strings.website.tools.tankopedia.sandbox.dynamic.shot_card
+                  .status[shot.in.status],
                 { damage: Math.round(shot.damage).toLocaleString(locale) }
               )}
             </Text>
 
+            {!hasOutLayers && penetrationChance}
+          </Flex>
+
           <table
             style={{
               whiteSpace: "nowrap",
@@ -204,6 +215,7 @@ export function ShotDisplayCard({ shot, ...props }: ShotDisplayCardProps) {
               </Flex>
             </Inset>
 
+            <Flex justify="between" align="center" gap="4">
               <Text color={outTitleColor} weight="bold">
                 {literals(
                   strings.website.tools.tankopedia.sandbox.dynamic.shot_card
@@ -212,6 +224,9 @@ export function ShotDisplayCard({ shot, ...props }: ShotDisplayCardProps) {
                 )}
               </Text>
 
+              {penetrationChance}
+            </Flex>
+
             <Flex direction="column">
               {shot.out.layers.map((layer, index) => {
                 const layerName =

packages/website/src/components/Armor/components/SpacedArmorSceneComponent/index.tsx

@@ -63,6 +63,36 @@ export type ArmorUserData = {
     }
 );
 
+const PENETRATION_RANDOMIZATION = 0.05;
+
+function resolvePenetrationChance(shoot: (scale: number) => Shot | null) {
+  function penetrates(scale: number) {
+    const shot = shoot(scale);
+
+    return (shot?.out ?? shot?.in)?.status === "penetration";
+  }
+
+  let low = 1 - PENETRATION_RANDOMIZATION;
+  let high = 1 + PENETRATION_RANDOMIZATION;
+
+  if (penetrates(low)) return 1;
+  if (!penetrates(high)) return 0;
+
+  for (let iteration = 0; iteration < 16; iteration++) {
+    const middle = (low + high) / 2;
+
+    if (penetrates(middle)) {
+      high = middle;
+    } else {
+      low = middle;
+    }
+  }
+
+  return (
+    (1 + PENETRATION_RANDOMIZATION - high) / (2 * PENETRATION_RANDOMIZATION)
+  );
+}
+
 const omitMaterial = new MeshBasicMaterial({
   colorWrite: false,
   depthWrite: true,
@@ -89,6 +119,7 @@ export function SpacedArmorSceneComponent({
       intersections: Intersection[],
       allowRicochet: boolean,
       remainingPenetrationInput?: number,
+      penetrationScale = 1,
     ) => {
       const { customShell } = Tankopedia.state;
       const shell = customShell ?? Duel.state.antagonist.shell;
@@ -125,6 +156,7 @@ export function SpacedArmorSceneComponent({
         Duel.state.protagonist.equipmentMatrix,
       );
       const penetration =
+        penetrationScale *
         shell.penetration!.near *
         resolvePenetrationCoefficient(
           hasCalibratedShells,
@@ -367,6 +399,7 @@ export function SpacedArmorSceneComponent({
               ricochetIntersections,
               false,
               remainingPenetration,
+              penetrationScale,
             );
 
             shot.in.status = "ricochet";
@@ -422,6 +455,16 @@ export function SpacedArmorSceneComponent({
 
                   const shot = shoot(event.point, event.intersections, true)!;
 
+                  shot.penetrationChance = resolvePenetrationChance((scale) =>
+                    shoot(
+                      event.point,
+                      event.intersections,
+                      true,
+                      undefined,
+                      scale,
+                    ),
+                  );
+
                   Tankopedia.mutate((draft) => {
                     draft.shot = shot;
                   });

packages/website/src/stores/tankopedia.ts

@@ -43,6 +43,7 @@ export type Shot = {
   containsGaps: boolean;
   damage: number;
   splashRadius?: number;
+  penetrationChance?: number;
 
   in: {
     surfaceNormal: Vector3;