diff --git a/axelrod/match.py b/axelrod/match.py
index 19c83abd9..a72af171d 100644
--- a/axelrod/match.py
+++ b/axelrod/match.py
@@ -130,7 +130,8 @@ def _cache_update_required(self):
         A boolean to show whether the deterministic cache should be updated.
         """
         return (
-            not self.noise
+            not self._stochastic
+            and not self.noise
             and self._cache.mutable
             and not (any(Classifiers["stochastic"](p) for p in self.players))
         )
@@ -182,28 +183,29 @@ def play(self):
             turns = self.turns
         cache_key = (self.players[0], self.players[1])
 
-        if self._stochastic or not self._cached_enough_turns(cache_key, turns):
-            for p in self.players:
-                if self.reset:
-                    p.reset()
-                p.set_match_attributes(**self.match_attributes)
-                # Generate a random seed for the player, if stochastic
-                if Classifiers["stochastic"](p):
-                    p.set_seed(self._random.random_seed_int())
-            result = []
-            for _ in range(turns):
-                plays = self.simultaneous_play(
-                    self.players[0], self.players[1], self.noise
-                )
-                result.append(plays)
-
-            if self._cache_update_required:
-                self._cache[cache_key] = result
-        else:
-            result = self._cache[cache_key][:turns]
+        if self._cached_enough_turns(cache_key, turns):
+            self.result = self._cache[cache_key][:turns]
+            return self.result
+
+        for p in self.players:
+            if self.reset:
+                p.reset()
+            p.set_match_attributes(**self.match_attributes)
+            # Generate a random seed for the player, if stochastic
+            if Classifiers["stochastic"](p):
+                p.set_seed(self._random.random_seed_int())
+        result = []
+        for _ in range(turns):
+            plays = self.simultaneous_play(
+                self.players[0], self.players[1], self.noise
+            )
+            result.append(plays)
+
+        if self._cache_update_required:
+            self._cache[cache_key] = result
 
         self.result = result
-        return result
+        return self.result
 
     def scores(self):
         """Returns the scores of the previous Match plays."""