diff --git a/specs/phase1/custody-game.md b/specs/phase1/custody-game.md
index af3aadc96..822970a19 100644
--- a/specs/phase1/custody-game.md
+++ b/specs/phase1/custody-game.md
@@ -192,10 +192,10 @@ def get_custody_atoms(bytez: bytes) -> Sequence[bytes]:
 def compute_custody_bit(key: BLSSignature, data: bytes) -> bit:
     full_G2_element = bls.signature_to_G2(key)
     s = full_G2_element[0].coeffs
-    bits = [legendre_bit(sum(s[i % 2]**i * int.from_bytes(atom, "little")), BLS12_381_Q)
-            for i, atom in enumerate(get_custody_atoms(data))]
-    # XOR all atom bits
-    return bit(sum(bits) % 2)
+    custody_atoms = get_custody_atoms(data)
+    n = len(custody_atoms)
+    return legendre_bit(sum(s[i % 2]**i * int.from_bytes(atom, "little"))
+            for i, atom in enumerate(custody_atoms) + s[n % 2]**n, BLS12_381_Q)
 ```
 
 ### `get_randao_epoch_for_custody_period`