diff --git a/e2e/queue.spec.ts b/e2e/queue.spec.ts
index 73f3f0a..7d09d2b 100644
--- a/e2e/queue.spec.ts
+++ b/e2e/queue.spec.ts
@@ -569,8 +569,11 @@ test('a drained tank is topped up before a chained leg at exactly the rep-discou
   }, { timeout: 120_000, message: `waiting for the auto-chained leg ${DEST} → ${QUEUE}` }).toBe(true);
 
   const s = await getState(page);
-  expect(s.planes.find((x) => x.id === 'plane-starter')!.fuel).toBeCloseTo(target, 6); // departed with exactly the post-top-up level…
-  expect(s.account.cash).toBeCloseTo(cashBeforeChain - expectedCost, 6); // …at exactly the rep-discounted cost
+  // Exact fuel equality is impossible — this snapshot lands after leg 2's departure burn; the exact top-up level × rep-discounted price is pinned by the cash assertion below.
+  const fuel = s.planes.find((x) => x.id === 'plane-starter')!.fuel;
+  expect(fuel).toBeLessThanOrEqual(target); // can only have burned since departure…
+  expect(fuel).toBeGreaterThan(1.4 * required2); // …and a wrong top-up level (≤ required2, or none at all) lands below this bound
+  expect(s.account.cash).toBeCloseTo(cashBeforeChain - expectedCost, 6); // at exactly the rep-discounted cost
 
   // Let leg 2 finish so the next test starts from a known airport.
   await expect.poll(async () => {