diff --git a/tests/fixtures/efg/4cards_large_game.efg b/tests/fixtures/efg/4cards_large_game.efg
index 09deeac..023552a 100644
--- a/tests/fixtures/efg/4cards_large_game.efg
+++ b/tests/fixtures/efg/4cards_large_game.efg
@@ -4,20 +4,20 @@ From Gambit's sample games
 "
 
 c "" 1 "" { "A-K" 1/12 "A-Q" 1/12 "A-J" 1/12 "K-A" 1/12 "K-Q" 1/12 "K-J" 1/12 "Q-A" 1/12 "Q-K" 1/12 "Q-J" 1/12 "J-A" 1/12 "J-K" 1/12 "J-Q" 1/12 } 0
-p "player 1" 1 1 "A" { "raise" "check" } 0
-p "player 2" 2 1 "1rK" { "call" "fold" } 0
+p "" 1 1 "A" { "raise" "check" } 0
+p "" 2 1 "1rK" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 2 "Outcome 2" { 2, 0 }
-p "player 2" 2 2 "1pK" { "raise" "check" } 0
-p "player 1" 1 2 "1p2rA" { "call" "fold" } 0
+p "" 2 2 "1pK" { "raise" "check" } 0
+p "" 1 2 "1p2rA" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 3 "Outcome 3" { 0, 2 }
 t "" 2 "Outcome 2" { 2, 0 }
 p "" 1 1 "A" { "raise" "check" } 0
-p "player 2" 2 3 "1rQ" { "call" "fold" } 0
+p "" 2 3 "1rQ" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 2 "Outcome 2" { 2, 0 }
-p "player 2" 2 4 "1pQ" { "raise" "check" } 0
+p "" 2 4 "1pQ" { "raise" "check" } 0
 p "" 1 2 "1p2rA" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 3 "Outcome 3" { 0, 2 }
@@ -26,17 +26,17 @@ p "" 1 1 "A" { "raise" "check" } 0
 p "player 2" 2 5 "1rJ" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 2 "Outcome 2" { 2, 0 }
-p "player 2" 2 6 "1pJ" { "raise" "check" } 0
+p "" 2 6 "1pJ" { "raise" "check" } 0
 p "" 1 2 "1p2rA" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 3 "Outcome 3" { 0, 2 }
 t "" 2 "Outcome 2" { 2, 0 }
-p "player 1" 1 3 "K" { "raise" "check" } 0
+p "" 1 3 "K" { "raise" "check" } 0
 p "" 2 7 "1rA" { "call" "fold" } 0
 t "" 4 "Outcome 4" { -1, 3 }
 t "" 2 "Outcome 2" { 2, 0 }
-p "player 2" 2 8 "1pA" { "raise" "check" } 0
-p "player 1" 1 4 "1p2rK" { "call" "fold" } 0
+p "" 2 8 "1pA" { "raise" "check" } 0
+p "" 1 4 "1p2rK" { "call" "fold" } 0
 t "" 4 "Outcome 4" { -1, 3 }
 t "" 3 "Outcome 3" { 0, 2 }
 t "" 3 "Outcome 3" { 0, 2 }
@@ -58,12 +58,12 @@ p "" 1 4 "1p2rK" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 3 "Outcome 3" { 0, 2 }
 t "" 2 "Outcome 2" { 2, 0 }
-p "player 1" 1 5 "Q" { "raise" "check" } 0
-p "player 2" 2 7 "1rA" { "call" "fold" } 0
+p "" 1 5 "Q" { "raise" "check" } 0
+p "" 2 7 "1rA" { "call" "fold" } 0
 t "" 4 "Outcome 4" { -1, 3 }
 t "" 2 "Outcome 2" { 2, 0 }
 p "" 2 8 "1pA" { "raise" "check" } 0
-p "player 1" 1 6 "1p2rQ" { "call" "fold" } 0
+p "" 1 6 "1p2rQ" { "call" "fold" } 0
 t "" 4 "Outcome 4" { -1, 3 }
 t "" 3 "Outcome 3" { 0, 2 }
 t "" 3 "Outcome 3" { 0, 2 }
@@ -85,12 +85,12 @@ p "" 1 6 "1p2rQ" { "call" "fold" } 0
 t "" 1 "Outcome 1" { 3, -1 }
 t "" 3 "Outcome 3" { 0, 2 }
 t "" 2 "Outcome 2" { 2, 0 }
-p "player 1" 1 7 "J" { "raise" "check" } 0
+p "" 1 7 "J" { "raise" "check" } 0
 p "" 2 7 "1rA" { "call" "fold" } 0
 t "" 4 "Outcome 4" { -1, 3 }
 t "" 2 "Outcome 2" { 2, 0 }
 p "" 2 8 "1pA" { "raise" "check" } 0
-p "player 1" 1 8 "1p2rJ" { "call" "fold" } 0
+p "" 1 8 "1p2rJ" { "call" "fold" } 0
 t "" 4 "Outcome 4" { -1, 3 }
 t "" 3 "Outcome 3" { 0, 2 }
 t "" 3 "Outcome 3" { 0, 2 }
diff --git a/tests/fixtures/efg/zero_sum_chance_imperfect_info.efg b/tests/fixtures/efg/zero_sum_chance_imperfect_info.efg
index 1d5b844..45a930d 100644
--- a/tests/fixtures/efg/zero_sum_chance_imperfect_info.efg
+++ b/tests/fixtures/efg/zero_sum_chance_imperfect_info.efg
@@ -1,4 +1,4 @@
-EFG 2 R "Zero-sum with chance & imperfect info" { "1" "2" }
+EFG 2 R "Zero-sum with chance & imperfect info" { "Player 1" "Player 2" }
 "
 Example from
 
diff --git a/tests/fixtures/efg/zero_sum_imperfect_info.efg b/tests/fixtures/efg/zero_sum_imperfect_info.efg
index 161567e..def1021 100644
--- a/tests/fixtures/efg/zero_sum_imperfect_info.efg
+++ b/tests/fixtures/efg/zero_sum_imperfect_info.efg
@@ -1,4 +1,4 @@
-EFG 2 R "Matching pennies (zero-sum with imperfect info)" { "1" "2" }
+EFG 2 R "Matching pennies (zero-sum with imperfect info)" { "Player 1" "Player 2" }
 
 p "" 1 1 "P1 choice" { "Heads" "Tails" } 0
 p "" 2 1 "P2 Response" { "Heads" "Tails" } 0
diff --git a/tests/fixtures/efg/zero_sum_perfect_info.efg b/tests/fixtures/efg/zero_sum_perfect_info.efg
index 9836234..bfba90e 100644
--- a/tests/fixtures/efg/zero_sum_perfect_info.efg
+++ b/tests/fixtures/efg/zero_sum_perfect_info.efg
@@ -1,4 +1,4 @@
-EFG 2 R "Zero-sum with perfect info" { "1" "2" }
+EFG 2 R "Zero-sum with perfect info" { "Player 1" "Player 2" }
 ""
 
 p "" 1 1 "" { "L" "R" } 0
diff --git a/tests/fixtures/efg/zero_sum_perfect_info_missing_outcome.efg b/tests/fixtures/efg/zero_sum_perfect_info_missing_outcome.efg
index 4bbd84e..ff10b0c 100644
--- a/tests/fixtures/efg/zero_sum_perfect_info_missing_outcome.efg
+++ b/tests/fixtures/efg/zero_sum_perfect_info_missing_outcome.efg
@@ -1,4 +1,4 @@
-EFG 2 R "Zero-sum with perfect info" { "1" "2" }
+EFG 2 R "Zero-sum with perfect info" { "Player 1" "Player 2" }
 ""
 
 p "" 1 1 "" { "L" "R" } 0
diff --git a/tests/sequence_form_helper.py b/tests/sequence_form_helper.py
index a9a0cd5..5bc6678 100644
--- a/tests/sequence_form_helper.py
+++ b/tests/sequence_form_helper.py
@@ -6,6 +6,9 @@
 
 EMPTY: tuple[()] = ()  # empty sequence
 
+PLAYER_1 = "Player 1"
+PLAYER_2 = "Player 2"
+
 
 def lcp_from_data(M: list[list[Fr]], q: list[Fr], d: list[Fr]) -> lcp:
     """Creates an LCP instance with given M, q, d."""
@@ -44,7 +47,8 @@ def build_sequence_form_lcp(game):
     #         .  -F  .   .   .  .            f
     #         .   F  .   .   .  .           -f
 
-    p1, p2 = game.players[0], game.players[1]
+    p1 = game.players[PLAYER_1]
+    p2 = game.players[PLAYER_2]
 
     # sequences for each player (infoset, action)
     seqs1, seqs2 = [EMPTY], [EMPTY]
@@ -58,7 +62,7 @@ def build_sequence_form_lcp(game):
 
     def dfs(node, s1, s2, prob, u1=Fr(0), u2=Fr(0)):
         # accumulate payoffs from outcome nodes along the path
-        if node.outcome is not None:
+        if node.outcome:
             u1 += Fr(node.outcome[p1])
             u2 += Fr(node.outcome[p2])
 
@@ -228,7 +232,7 @@ def solve_via_sequence_form(game):
     x = x_y[:ns1]
     y = x_y[ns1:]
 
-    x_probs = get_action_probabilities(game.players[0], infoset_to_parent1, idx1, x)
-    y_probs = get_action_probabilities(game.players[1], infoset_to_parent2, idx2, y)
+    x_probs = get_action_probabilities(game.players[PLAYER_1], infoset_to_parent1, idx1, x)
+    y_probs = get_action_probabilities(game.players[PLAYER_2], infoset_to_parent2, idx2, y)
 
     return x_probs, y_probs