PYTHON-5689 Fix Retry Backoff is Enforced prose test

pymongo/asynchronous/client_session.py

@@ -717,7 +717,7 @@ async def callback(session, custom_arg, custom_kwarg=None):
         while True:
             if retry:  # Implement exponential backoff on retry.
                 jitter = random.random()  # noqa: S311
-                backoff = jitter * min(_BACKOFF_INITIAL * (1.5**retry), _BACKOFF_MAX)
+                backoff = jitter * min(_BACKOFF_INITIAL * (1.5 ** (retry - 1)), _BACKOFF_MAX)
                 if _would_exceed_time_limit(start_time, backoff):
                     assert last_error is not None
                     raise last_error

pymongo/synchronous/client_session.py

@@ -715,7 +715,7 @@ def callback(session, custom_arg, custom_kwarg=None):
         while True:
             if retry:  # Implement exponential backoff on retry.
                 jitter = random.random()  # noqa: S311
-                backoff = jitter * min(_BACKOFF_INITIAL * (1.5**retry), _BACKOFF_MAX)
+                backoff = jitter * min(_BACKOFF_INITIAL * (1.5 ** (retry - 1)), _BACKOFF_MAX)
                 if _would_exceed_time_limit(start_time, backoff):
                     assert last_error is not None
                     raise last_error

test/asynchronous/test_transactions.py

@@ -677,7 +677,9 @@ async def callback(session):
         async with self.client.start_session() as s:
             await s.with_transaction(callback)
         end = time.monotonic()
-        self.assertLess(abs(end - start - (no_backoff_time + 2.2)), 1)  # sum of 13 backoffs is 2.2
+        self.assertLess(
+            abs(end - start - (no_backoff_time + 1.8)), 0.5
+        )  # sum of 13 backoffs is 1.8
 
         random.random = _original_random_random
 

test/test_transactions.py

@@ -661,7 +661,9 @@ def callback(session):
         with self.client.start_session() as s:
             s.with_transaction(callback)
         end = time.monotonic()
-        self.assertLess(abs(end - start - (no_backoff_time + 2.2)), 1)  # sum of 13 backoffs is 2.2
+        self.assertLess(
+            abs(end - start - (no_backoff_time + 1.8)), 0.5
+        )  # sum of 13 backoffs is 1.8
 
         random.random = _original_random_random