Update FirstBy Downing for #1285

Author: marcharper

axelrod/strategies/axelrod_first.py

@@ -73,6 +73,7 @@ def strategy(self, opponent: Player) -> Action:
             return D
         return C
 
+
 class FirstByDowning(Player):
     """
     Submitted to Axelrod's first tournament by Downing
@@ -257,19 +258,20 @@ def strategy(self, opponent: Player) -> Action:
                 self.number_opponent_cooperations_in_response_to_C += 1
             return D
 
-
         if self.history[-2] == C and opponent.history[-1] == C:
             self.number_opponent_cooperations_in_response_to_C += 1
         if self.history[-2] == D and opponent.history[-1] == C:
             self.number_opponent_cooperations_in_response_to_D += 1
 
+        # Adding 1 to cooperations for assumption that first opponent move
+        # being a response to a cooperation. See docstring for more
+        # information.
         alpha = (self.number_opponent_cooperations_in_response_to_C /
-                 (self.cooperations + 1))  # Adding 1 to count for assumption
-                                           # that first opponent move being a
-                                           # response to a cooperation. See
-                                           # docstring for more information.
+                 (self.cooperations + 1))
+        # Adding 2 to defections on the assumption that the first two
+        # moves are defections, which may not be true in a noisy match
         beta = (self.number_opponent_cooperations_in_response_to_D /
-                 (self.defections))
+                 max(self.defections, 2))
 
         R, P, S, T = self.match_attributes["game"].RPST()
         expected_value_of_cooperating = alpha * R + (1 - alpha) * S