feat: change the initialguess based on average metrics derived from the testing branch

Proj2.hs

@@ -36,7 +36,10 @@
 -- As the performer, we must guess the target in as few steps as possible given
 -- the feedback from the composer at each turn.
 --
--- TODO: finish explanation of initialGuess
+-- To pick the best first guess, we play musician with a range of first-guess
+-- candidates and calculate the average number of guesses needed over all
+-- targets. The guess with the lowest average was [A1, D2, G3]. some
+-- justifying metrics are provided in a comment above `initialGuess`.
 --
 -- To pick the best next guess, we filter the game state to contain only
 -- targets that are consistent with the received feedback from the previous
@@ -161,17 +164,26 @@ feedback target guess = (pitches, notes, octaves)
 -- which is all possible starting guesses. characteristics of these guesses
 -- are described in the documentation for `allChords`
 --
--- currently, the best first guess is "vibes based". there is a TODO to
--- actually evaluate the best guess properly.
+-- a pretty good first guess was found by playing musician over all possible
+-- targets and calculating the average number of guesses (given a first guess)
+--
+-- here are some convincing metrics:
+--
+-- [A1, D2, G3]: 4.25
+-- [C1, D2, E3]: 4.27
+-- [A2, D2, G2]: 4.32
+-- [C2, D2, E2]: 4.34
+-- [D1, D2, D3]: 4.80
+--
+-- we choose [A1, D2, G3] as it has the lowest average number of guesses
 --
 initialGuess :: ([Pitch], GameState)
 initialGuess = (bestFirstGuess, allChords)
   where
-    -- TODO: is this really the best first guess?
     bestFirstGuess =
-      [ Pitch C One,
+      [ Pitch A One,
         Pitch D Two,
-        Pitch E Three
+        Pitch G Three
       ]
 
 -- takes in the previous guess, the game state, and the feedback for the