refactor(api): move RandomSource to shared and add rollInclusive

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

apps/api/src/shared/roll-range.ts

@@ -0,0 +1,19 @@
+import type { RandomSource } from './random-source';
+
+/**
+ * Rolls an inclusive integer in [min, max] from one value of `random`.
+ *
+ * `RandomSource.next()` is documented as [0, 1), but the clamp keeps a
+ * misbehaving or hand-stubbed source from ever exceeding `max`.
+ */
+export function rollInclusive(
+  random: RandomSource,
+  min: number,
+  max: number,
+): number {
+  if (max <= min) {
+    return min;
+  }
+
+  return Math.min(max, min + Math.floor(random.next() * (max - min + 1)));
+}