diff --git a/Lib/random.py b/Lib/random.py
index 91065b7..f32ff1c 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -94,6 +94,14 @@ class Random(_random.Random):
         self.seed(x)
         self.gauss_next = None
 
+    def __init_subclass__(cls):
+        # Only call self.getrandbits if the original random() builtin method
+        # has not been overridden or if a new getrandbits() was supplied.
+        if type(cls.random) is not _BuiltinMethodType and type(cls.getrandbits) is not _MethodType:
+            # There's an overridden random() method but no new getrandbits() method,
+            # so we can only use random() from here.
+            cls._randbelow = cls._randbelow_fallback
+
     def seed(self, a=None, version=2):
         """Initialize internal state from hashable object.
 
@@ -221,22 +229,18 @@ class Random(_random.Random):
 
         return self.randrange(a, b+1)
 
-    def _randbelow(self, n, int=int, maxsize=1<<BPF, type=type,
-                   Method=_MethodType, BuiltinMethod=_BuiltinMethodType):
+    def _randbelow(self, n):
         "Return a random int in the range [0,n).  Raises ValueError if n==0."
 
-        random = self.random
         getrandbits = self.getrandbits
-        # Only call self.getrandbits if the original random() builtin method
-        # has not been overridden or if a new getrandbits() was supplied.
-        if type(random) is BuiltinMethod or type(getrandbits) is Method:
-            k = n.bit_length()  # don't use (n-1) here because n can be 1
-            r = getrandbits(k)          # 0 <= r < 2**k
-            while r >= n:
-                r = getrandbits(k)
-            return r
-        # There's an overridden random() method but no new getrandbits() method,
-        # so we can only use random() from here.
+        k = n.bit_length()  # don't use (n-1) here because n can be 1
+        r = getrandbits(k)          # 0 <= r < 2**k
+        while r >= n:
+            r = getrandbits(k)
+        return r
+
+    def _randbelow_fallback(self, n, int=int, maxsize=1<<BPF):
+        random = self.random
         if n >= maxsize:
             _warn("Underlying random() generator does not supply \n"
                 "enough bits to choose from a population range this large.\n"