diff --git a/src/trio/_tests/test_socket.py b/src/trio/_tests/test_socket.py
index b75b37421a..74c39b1a62 100644
--- a/src/trio/_tests/test_socket.py
+++ b/src/trio/_tests/test_socket.py
@@ -1124,20 +1124,23 @@ async def receiver() -> None:
 async def test_many_sockets() -> None:
     total = 5000  # Must be more than MAX_AFD_GROUP_SIZE
     sockets = []
-    for _x in range(total // 2):
+    # Open at most <total> socket pairs
+    for opened in range(0, total, 2):
         try:
             a, b = stdlib_socket.socketpair()
-        except OSError as e:  # pragma: no cover
-            # the noqa is "Found assertion on exception `e` in `except` block"
-            assert e.errno in (errno.EMFILE, errno.ENFILE)  # noqa: PT017
+        except OSError as exc:  # pragma: no cover
+            # Semi-expecting following errors (sockets are files):
+            # EMFILE: "Too many open files" (reached kernel cap)
+            # ENFILE: "File table overflow" (beyond kernel cap)
+            assert exc.errno in (errno.EMFILE, errno.ENFILE)  # noqa: PT017
+            print(f"Unable to open more than {opened} sockets.")
+            # Stop opening any more sockets if too many are open
             break
         sockets += [a, b]
     async with _core.open_nursery() as nursery:
-        for s in sockets:
-            nursery.start_soon(_core.wait_readable, s)
+        for socket in sockets:
+            nursery.start_soon(_core.wait_readable, socket)
         await _core.wait_all_tasks_blocked()
         nursery.cancel_scope.cancel()
-    for sock in sockets:
-        sock.close()
-    if _x != total // 2 - 1:  # pragma: no cover
-        print(f"Unable to open more than {(_x-1)*2} sockets.")
+    for socket in sockets:
+        socket.close()