diff --git a/Lib/multiprocessing/managers.py b/Lib/multiprocessing/managers.py
index 0f5f9f64c2de9e..2c9594e0a74ec8 100644
--- a/Lib/multiprocessing/managers.py
+++ b/Lib/multiprocessing/managers.py
@@ -856,20 +856,21 @@ def _incref(self):
         dispatch(conn, None, 'incref', (self._id,))
         util.debug('INCREF %r', self._token.id)
 
-        self._idset.add(self._id)
+        refid = f'{self._id}.{id(self)}'
+        self._idset.add(refid)
 
         state = self._manager and self._manager._state
 
         self._close = util.Finalize(
             self, BaseProxy._decref,
-            args=(self._token, self._authkey, state,
+            args=(self._token, refid, self._authkey, state,
                   self._tls, self._idset, self._Client),
             exitpriority=10
             )
 
     @staticmethod
-    def _decref(token, authkey, state, tls, idset, _Client):
-        idset.discard(token.id)
+    def _decref(token, refid, authkey, state, tls, idset, _Client):
+        idset.discard(refid)
 
         # check whether manager is still alive
         if state is None or state.value == State.STARTED:
diff --git a/Misc/ACKS b/Misc/ACKS
index b031eb7c11f73f..a3cca790c3db0d 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -732,6 +732,7 @@ Larry Hastings
 Tim Hatch
 Zac Hatfield-Dodds
 Shane Hathaway
+Akinori Hattori
 Michael Haubenwallner
 Janko Hauser
 Flavian Hautbois
diff --git a/Misc/NEWS.d/next/Library/2022-10-15-10-18-20.gh-issue-71936.MzJjc_.rst b/Misc/NEWS.d/next/Library/2022-10-15-10-18-20.gh-issue-71936.MzJjc_.rst
new file mode 100644
index 00000000000000..ac1081e060ba2d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2022-10-15-10-18-20.gh-issue-71936.MzJjc_.rst
@@ -0,0 +1 @@
+Fix a race condition in :class:`multiprocessing.Pool`.