diff --git a/GameCli.Tests/RewardTests.cs b/GameCli.Tests/RewardTests.cs
index 8c7f639..cdbdf81 100644
--- a/GameCli.Tests/RewardTests.cs
+++ b/GameCli.Tests/RewardTests.cs
@@ -53,4 +53,19 @@ public class RewardTests
         Assert.True(rMain < rNoop, "firing main should be worse than noop");
         Assert.True(rLeft < rNoop, "firing left should be worse than noop");
     }
+
+    [Fact]
+    public void AngleWrap_FullRevolutionsProduceSameReward()
+    {
+        // Physically identical poses (angle differs by 2π) must produce the same reward.
+        // Otherwise a spinning ship accumulates unbounded angle penalty.
+        var upright   = new ShipState(0.5f, 0.5f, 0f, 0f, 0f, 0f);
+        var oneSpin   = new ShipState(0.5f, 0.5f, 0f, 0f,  2f * MathF.PI, 0f);
+        var fiveSpins = new ShipState(0.5f, 0.5f, 0f, 0f, 10f * MathF.PI, 0f);
+        float r0 = Reward.Compute(upright,   target: (0.5f, 0.5f), action: 0);
+        float r1 = Reward.Compute(oneSpin,   target: (0.5f, 0.5f), action: 0);
+        float r5 = Reward.Compute(fiveSpins, target: (0.5f, 0.5f), action: 0);
+        Assert.Equal(r0, r1, precision: 4);
+        Assert.Equal(r0, r5, precision: 4);
+    }
 }
diff --git a/GameCli/Reward.cs b/GameCli/Reward.cs
index 5c36bdf..3d79ebe 100644
--- a/GameCli/Reward.cs
+++ b/GameCli/Reward.cs
@@ -3,8 +3,10 @@ namespace GameCli;
 /// <summary>
 /// Reward = -distance_to_target
 ///        - λ_v · speed
-///        - λ_θ · |angle|
+///        - λ_θ · |wrap(angle)|
 ///        - λ_fuel · engine_on
+/// The angle is wrapped to [-π, π] so a ship that has completed N revolutions
+/// gets the same upright-penalty as a physically identical pose that hasn't.
 /// Coefficients are public so training scripts can log/inspect them.
 /// </summary>
 public static class Reward
@@ -19,11 +21,12 @@ public static class Reward
         float dy = target.Y - s.Y;
         float distance = MathF.Sqrt(dx * dx + dy * dy);
         float speed    = MathF.Sqrt(s.VX * s.VX + s.VY * s.VY);
+        float wrapped  = MathF.Atan2(MathF.Sin(s.Angle), MathF.Cos(s.Angle));
         float engineOn = action == Physics.ActionNoop ? 0f : 1f;
 
         return -distance
              - LambdaVelocity * speed
-             - LambdaAngle    * MathF.Abs(s.Angle)
+             - LambdaAngle    * MathF.Abs(wrapped)
              - LambdaFuel     * engineOn;
     }
 }