fix: apply cbrt and cap to runestone formula to prevent AFK windfalls

apps/api/src/services/prestige.ts

@@ -20,6 +20,13 @@ const runestonesPerPrestigeLevel = 10;
 const milestoneInterval = 5;
 const milestoneRunestonesPerInterval = 25;
 
+/*
+ * Hard cap on the base runestone yield (before multipliers) to prevent
+ * extreme AFK accumulation from producing game-breaking runestone counts.
+ * With all upgrades (5.625× max) this caps out at ~281 per prestige.
+ */
+const maxBaseRunestones = 50;
+
 /**
  * Calculates the gold threshold required for the next prestige.
  * Formula: BASE * SCALE_FACTOR^prestigeCount — each prestige makes the next threshold harder.
@@ -107,7 +114,9 @@ interface RunestoneParameters {
 
 /**
  * Calculates how many runestones the player earns from a prestige.
- * Formula: floor(sqrt(totalGoldEarned / threshold)) * RUNESTONES_PER_PRESTIGE_LEVEL * runestoneMultiplier.
+ * Formula: min(floor(cbrt(totalGoldEarned / threshold)) * RUNESTONES_PER_PRESTIGE_LEVEL, MAX_BASE) * multipliers.
+ * Uses cube root for stronger diminishing returns than sqrt, and caps the base before multipliers
+ * to prevent extended AFK sessions from producing runestone windfalls.
  * @param parameters - The parameters for the runestone calculation.
  * @param parameters.totalGoldEarned - The total gold earned in the current run.
  * @param parameters.prestigeCount - The current prestige count.
@@ -123,9 +132,11 @@ const calculateRunestones = (parameters: RunestoneParameters): number => {
     echoRunestoneMultiplier = 1,
   } = parameters;
   const threshold = calculatePrestigeThreshold(prestigeCount);
-  const base
+  const base = Math.min(
-    = Math.floor(Math.sqrt(totalGoldEarned / threshold))
+    Math.floor(Math.cbrt(totalGoldEarned / threshold))
-    * runestonesPerPrestigeLevel;
+    * runestonesPerPrestigeLevel,
+    maxBaseRunestones,
+  );
   const runestoneMult = getCategoryMultiplier(
     purchasedUpgradeIds,
     "runestones",

apps/api/test/services/prestige.spec.ts

@@ -99,21 +99,27 @@ describe("isEligibleForPrestige", () => {
 
 describe("calculateRunestones", () => {
   it("calculates basic runestones formula", () => {
-    // floor(sqrt(4_000_000 / 1_000_000)) × 10 = floor(2) × 10 = 20
+    // floor(cbrt(4_000_000 / 1_000_000)) × 10 = floor(cbrt(4)) × 10 = 1 × 10 = 10
     const result = calculateRunestones({ totalGoldEarned: 4_000_000, prestigeCount: 0, purchasedUpgradeIds: [] });
-    expect(result).toBe(20);
+    expect(result).toBe(10);
   });
 
   it("applies echo runestone multiplier", () => {
-    // floor(sqrt(4) × 10) = 20; × 2 = 40
+    // floor(cbrt(4)) × 10 = 10; × 2 = 20
     const result = calculateRunestones({ totalGoldEarned: 4_000_000, prestigeCount: 0, purchasedUpgradeIds: [], echoRunestoneMultiplier: 2 });
-    expect(result).toBe(40);
+    expect(result).toBe(20);
   });
 
   it("applies purchased runestone upgrade multiplier", () => {
-    // With "runestones_1" purchased (multiplier 1.25): floor(20 × 1.25) = 25
+    // With "runestone_gain_1" purchased (multiplier 1.25): floor(10 × 1.25) = 12
     const result = calculateRunestones({ totalGoldEarned: 4_000_000, prestigeCount: 0, purchasedUpgradeIds: ["runestone_gain_1"] });
-    expect(result).toBeGreaterThan(20);
+    expect(result).toBe(12);
+  });
+
+  it("caps base runestones before multipliers", () => {
+    // cbrt(300_000_000 / 1_000_000) = cbrt(300) ≈ 6.67 → floor = 6 → 6 × 10 = 60, capped at 50
+    const result = calculateRunestones({ totalGoldEarned: 300_000_000, prestigeCount: 0, purchasedUpgradeIds: [] });
+    expect(result).toBe(50);
   });
 });