diff --git a/simulator/equal.toml b/simulator/equal.toml
new file mode 100644
index 0000000..3212071
--- /dev/null
+++ b/simulator/equal.toml
@@ -0,0 +1,23 @@
+food_amount = 100
+view_dist = 200
+red_count = 10
+blu_count = 10
+
+[weapon]
+kills_user = false
+type = "ball"
+radius = 200
+
+[red_policy]
+aggressive = false
+food = [1,0]
+kin = [-0.3,0.02]
+nonkin = [-0.3,-0.02]
+none= [0.3, 0.01]
+
+[blu_policy]
+aggressive = false
+food = [1,0]
+kin = [-0.3,0.02]
+nonkin = [-0.3,-0.02]
+none= [0.3, 0.01]
diff --git a/simulator/src/main.rs b/simulator/src/main.rs
index f6e7797..614e616 100644
--- a/simulator/src/main.rs
+++ b/simulator/src/main.rs
@@ -661,6 +661,85 @@ fn load_config(path: &std::path::Path) -> SimConfig {
     toml::from_str(&text).unwrap()
 }
 
+/// Online mean/variance accumulator (Welford's algorithm), used to report how
+/// much headless outcomes vary from seed to seed rather than only their mean.
+#[derive(Debug, Clone, Copy, Default)]
+struct Variance {
+    n: u64,
+    mean: f64,
+    m2: f64,
+}
+
+impl Variance {
+    fn push(&mut self, x: f64) {
+        self.n += 1;
+        let delta = x - self.mean;
+        self.mean += delta / self.n as f64;
+        self.m2 += delta * (x - self.mean);
+    }
+
+    /// Unbiased sample variance (`n - 1` denominator); `None` for `n < 2`.
+    fn sample_variance(&self) -> Option<f64> {
+        (self.n > 1).then(|| self.m2 / (self.n - 1) as f64)
+    }
+
+    fn std_dev(&self) -> Option<f64> {
+        self.sample_variance().map(f64::sqrt)
+    }
+
+    fn std_err(&self) -> Option<f64> {
+        self.std_dev().map(|s| s / (self.n as f64).sqrt())
+    }
+
+    /// Confidence interval for the mean, using `z` as the critical value of the
+    /// standard normal distribution (e.g. 1.96 for ~95%). Normal is a good
+    /// approximation here because the harness normally runs many samples.
+    fn confidence_interval(&self, z: f64) -> Option<(f64, f64)> {
+        self.std_err()
+            .map(|se| (self.mean - z * se, self.mean + z * se))
+    }
+
+    fn describe(&self) -> String {
+        match (self.sample_variance(), self.std_dev(), self.confidence_interval(1.96)) {
+            (Some(var), Some(sd), Some((lo, hi))) => format!(
+                "{:.4} (sd {sd:.4}, var {var:.4}, 95% CI [{lo:.4}, {hi:.4}])",
+                self.mean
+            ),
+            _ => format!("{:.4} (n={}, no variance estimate)", self.mean, self.n),
+        }
+    }
+}
+
+/// Summarise per-seed headless runs in terms of each team's proportion of the
+/// initial food, including the variance of those proportions and of the RED-BLU
+/// difference (which is what a fair match should centre on zero).
+fn print_run_stats(results: &[(i32, i32)], food_amount: usize) {
+    if food_amount == 0 {
+        println!("no food configured (food_amount = 0); nothing to measure");
+        return;
+    }
+
+    let mut red = Variance::default();
+    let mut blu = Variance::default();
+    let mut diff = Variance::default();
+    for &(r, b) in results {
+        let r_share = r as f64 / food_amount as f64;
+        let b_share = b as f64 / food_amount as f64;
+        red.push(r_share);
+        blu.push(b_share);
+        diff.push(r_share - b_share);
+    }
+
+    let winner = if red.mean > blu.mean { "red" } else { "blue" };
+    println!(
+        "{winner} wins on average over {} runs! (share of initial {food_amount} food)",
+        results.len().max(1)
+    );
+    println!("  RED share:     {}", red.describe());
+    println!("  BLU share:     {}", blu.describe());
+    println!("  RED-BLU share: {}", diff.describe());
+}
+
 fn print_average(red: i32, blu: i32, iters: u64) {
     let iters = iters.max(1) as f32;
     let red = red as f32 / iters;
@@ -677,11 +756,11 @@ fn main() {
     if cli.no_gui {
         let config = load_config(&cli.config);
         let iters = cli.run_count.unwrap_or(1);
-        let (red, blu) = (0..iters)
+        let results: Vec<(i32, i32)> = (0..iters)
             .into_par_iter()
             .map(|s| run_headless_simulation(s, &config))
-            .reduce(|| (0, 0), |a, b| (a.0 + b.0, a.1 + b.1));
-        print_average(red, blu, iters);
+            .collect();
+        print_run_stats(&results, config.food_amount);
     } else {
         macroquad::Window::new("Adversarial Foraging Simulator", gui_main(cli));
     }
@@ -712,6 +791,10 @@ mod tests {
         toml::from_str(include_str!("../conf.toml")).unwrap()
     }
 
+    fn equal_config() -> SimConfig {
+        toml::from_str(include_str!("../equal.toml")).unwrap()
+    }
+
     /// The analytic replacements must agree with parry bit-for-bit, both on
     /// whether a contact exists and on the reported `point1.distance(origin)`.
     /// This is the load-bearing test behind the whole speedup: the hot path no
@@ -789,6 +872,32 @@ mod tests {
         assert_eq!(blu, 9088, "blu total over 200 seeds");
     }
 
+    /// `equal.toml` gives both teams identical policies and mirrored starting
+    /// geometry, so both teams should collect the same proportion of the
+    /// initial food. Verify that zero lies inside the 95% confidence interval
+    /// of the RED-BLU proportion difference.
+    #[test]
+    fn equal_config_is_balanced() {
+        let config = equal_config();
+        let mut diff = Variance::default();
+        for seed in 0..200u64 {
+            let (red, blu) = run_headless_simulation(seed, &config);
+
+            let r_share = red as f64 / config.food_amount as f64;
+            let b_share = blu as f64 / config.food_amount as f64;
+            diff.push(r_share - b_share);
+        }
+
+        let (lo, hi) = diff
+            .confidence_interval(1.96)
+            .expect("need at least two samples for a confidence interval");
+        assert!(
+            lo <= 0.0 && 0.0 <= hi,
+            "RED-BLU food share mean {:.4} with 95% CI [{lo:.4}, {hi:.4}] excludes zero",
+            diff.mean,
+        );
+    }
+
     /// Same seed twice must produce the same result (no hidden global state).
     #[test]
     fn deterministic() {