diff --git a/src/ale/python/env.py b/src/ale/python/env.py
index 1adaf4a00..9133f65d4 100644
--- a/src/ale/python/env.py
+++ b/src/ale/python/env.py
@@ -102,13 +102,13 @@ def __init__(
             raise error.Error(
                 f"Invalid stochastic frameskip length of {len(frameskip)}, expected length 2."
             )
-        elif isinstance(frameskip, tuple) and frameskip[0] > frameskip[1]:
+        elif isinstance(frameskip, tuple) and frameskip[0] >= frameskip[1]:
             raise error.Error(
-                "Invalid stochastic frameskip, lower bound is greater than upper bound."
+                "Invalid stochastic frameskip, lower bound must be strictly less than upper bound."
             )
         elif isinstance(frameskip, tuple) and frameskip[0] <= 0:
             raise error.Error(
-                "Invalid stochastic frameskip lower bound is greater than upper bound."
+                "Invalid stochastic frameskip, lower bound must be positive."
             )
 
         if render_mode is not None and render_mode not in {"rgb_array", "human"}:
diff --git a/tests/python/test_atari_env.py b/tests/python/test_atari_env.py
index cdc028508..2aa37faf2 100644
--- a/tests/python/test_atari_env.py
+++ b/tests/python/test_atari_env.py
@@ -239,7 +239,9 @@ def test_gym_reset_with_infos(tetris_env):
     assert "frame_number" in info
 
 
-@pytest.mark.parametrize("frameskip", [0, -1, 4.0, (-1, 5), (0, 5), (5, 2), (1, 2, 3)])
+@pytest.mark.parametrize(
+    "frameskip", [0, -1, 4.0, (-1, 5), (0, 5), (5, 2), (4, 4), (1, 2, 3)]
+)
 def test_frameskip_warnings(tetris_rom_path, frameskip):
     with patch("ale_py.roms.Tetris", create=True, new_callable=lambda: tetris_rom_path):
         with pytest.raises(gymnasium.error.Error):