diff --git a/tests/test_wave_01.py b/tests/test_wave_01.py
index ef48e03b..09e360cb 100644
--- a/tests/test_wave_01.py
+++ b/tests/test_wave_01.py
@@ -73,4 +73,19 @@ def test_draw_letters_returns_different_hands():
     hand3 = draw_letters()
 
     # Assert
-    assert hand1 != hand2 or hand2 != hand3
\ No newline at end of file
+    assert hand1 != hand2 or hand2 != hand3
+
+def test_ever_draws_duplicate_letters():
+    # Arrange
+    def has_dupes(letter_bank):
+        unique_letters = set(letter_bank)
+        return len(unique_letters) != len(letter_bank)
+
+    # Act
+    saw_a_duplicate = False
+    for i in range(1000):
+        letters = draw_letters()
+        saw_a_duplicate = saw_a_duplicate or has_dupes(letters)
+
+    # Assert
+    assert saw_a_duplicate
diff --git a/tests/test_wave_04.py b/tests/test_wave_04.py
index e586621c..6e311adf 100644
--- a/tests/test_wave_04.py
+++ b/tests/test_wave_04.py
@@ -110,7 +110,7 @@ def test_get_highest_word_many_ties_pick_shortest():
 
 def test_get_highest_word_does_not_return_early_after_first_tiebreaker():
     # Arrange
-    words = ["WWW", "MMMM", "BBBBBB", "AAAAAAAAD", "JQ", "KFHK"]
+    words = ["WWW", "MMMM", "BBBBBB", "AAAAAAAAD", "JQ", "KFHK", "A"]
 
     # Act
     best_word = get_highest_word_score(words)