diff --git a/crates/border-wars/src/hex.rs b/crates/border-wars/src/hex.rs
index c775ded..0f9aa3a 100644
--- a/crates/border-wars/src/hex.rs
+++ b/crates/border-wars/src/hex.rs
@@ -47,12 +47,12 @@ impl<T: HexNumber> HexPosition<T> {
     /// ```
     pub fn distance_to(&self, other: &Self) -> T {
         // Calculate the difference between the q and r coordinates.
-        let dq = self.q - other.q;
-        let dr = self.r - other.r;
-        let dz = self.q + self.r - other.q - other.r;
+        let dq = (self.q - other.q).abs();
+        let dr = (self.r - other.r).abs();
+        let ds = dq + dr;
 
         // Manhattan distance = (abs(dq) + abs(dr) + abs(ds)) / 2
-        (dq.abs() + dr.abs() + dz.abs()) / (T::one() + T::one())
+        (dq + dr + ds) / (T::one() + T::one())
     }
 }