diff --git a/tests/test_statops_compare.py b/tests/test_statops_compare.py
index e83be41..70bf8fe 100644
--- a/tests/test_statops_compare.py
+++ b/tests/test_statops_compare.py
@@ -4,6 +4,11 @@
 import pytest
 
 
+def montecarlo_is_lower_test(one, two, samples=1000):
+    rvs_one, rvs_two = [est._get_rv().rvs(samples) for est in (one, two)]
+    return sum(rvs_one < rvs_two) / samples
+
+
 def integ_approx(x):
     return pytest.approx(x, abs=tm.INTEGRATION_PRECISION)
 
@@ -23,6 +28,7 @@ def test_compare_equal():
     assert tm.estimate_is_lower(simple_estimate, simple_estimate) == 0.5
     concrete_estimate = data.Estimate.from_triple(2, 1, 3)
     assert tm.estimate_is_lower(concrete_estimate, concrete_estimate) == 0.5
+    assert montecarlo_is_lower_test(concrete_estimate, concrete_estimate) == pytest.approx(0.5, abs=0.05)
 
 
 def test_compare_clear():
@@ -47,7 +53,20 @@ def test_compare_overlapping():
     assert 0.5 < tm.estimate_is_lower(low_estimate, almost_low_estimate) < 0.6
     low_end_estimate = data.Estimate.from_triple(0.5, 0, 1)
     assert 0.1 < tm.estimate_is_lower(low_estimate, low_end_estimate) < 0.2
-    assert 0.8 < tm.estimate_is_lower(low_end_estimate, low_estimate) < 0.9
+    rate = tm.estimate_is_lower(low_end_estimate, low_estimate)
+    assert 0.8 < rate < 0.9
+    assert montecarlo_is_lower_test(low_end_estimate, low_estimate) == pytest.approx(rate, abs=0.05)
+
+
+def test_compare_general():
+    one = data.Estimate.from_triple(2, 1, 3)
+    two = data.Estimate.from_triple(1.5, -2, 4)
+    rate = tm.estimate_is_lower(one, two)
+    assert montecarlo_is_lower_test(one, two, 4000) == pytest.approx(rate, abs=0.01)
+    one = data.Estimate.from_triple(2.5, 1, 3)
+    two = data.Estimate.from_triple(1.5, 1, 4)
+    rate = tm.estimate_is_lower(one, two)
+    assert montecarlo_is_lower_test(one, two) == pytest.approx(rate, abs=0.05)
 
 
 def test_compare_weighted():