diff --git a/src/rtichoke/performance_data/performance_data.py b/src/rtichoke/performance_data/performance_data.py
index a07e57a6..d734ac99 100644
--- a/src/rtichoke/performance_data/performance_data.py
+++ b/src/rtichoke/performance_data/performance_data.py
@@ -19,6 +19,34 @@
 import numpy as np
 
 
+def _probs_with_r_binary_cutoff_semantics(
+    probs: Dict[str, np.ndarray], by: float
+) -> Dict[str, np.ndarray]:
+    """Place exact binary cutoffs on R's predicted-negative side.
+
+    R's binary implementation uses ``prob > cutoff``. The shared Python binning
+    machinery is left-closed because the time-dependent path intentionally
+    follows a ``prob >= cutoff`` convention. Move only binary probabilities
+    exactly equal to a public cutoff one representable float downward before
+    bin assignment; all other probabilities and the public cutoff grid remain
+    unchanged.
+    """
+    cutoffs = create_breaks_values(None, "probability_threshold", by)
+    nonzero_cutoffs = cutoffs[cutoffs > 0]
+    adjusted = {}
+
+    for reference_group, values in probs.items():
+        values_array = np.asarray(values, dtype=float).copy()
+        for cutoff in nonzero_cutoffs:
+            equal_to_cutoff = values_array == cutoff
+            values_array[equal_to_cutoff] = np.nextafter(
+                values_array[equal_to_cutoff], -np.inf
+            )
+        adjusted[reference_group] = values_array
+
+    return adjusted
+
+
 def prepare_binned_classification_data(
     probs: Dict[str, np.ndarray],
     reals: Union[np.ndarray, Dict[str, np.ndarray]],
@@ -69,9 +97,15 @@ def prepare_binned_classification_data(
         breaks=breaks,
     )
 
+    probs_for_binning = (
+        _probs_with_r_binary_cutoff_semantics(probs, by)
+        if "probability_threshold" in stratified_by
+        else probs
+    )
+
     list_data_to_adjust = _create_list_data_to_adjust_binary(
         aj_data_combinations,
-        probs,
+        probs_for_binning,
         reals,
         stratified_by=stratified_by,
         by=by,
diff --git a/tests/test_cutoff_boundary_semantics.py b/tests/test_cutoff_boundary_semantics.py
new file mode 100644
index 00000000..9fddf44e
--- /dev/null
+++ b/tests/test_cutoff_boundary_semantics.py
@@ -0,0 +1,97 @@
+import numpy as np
+import polars as pl
+from polars.testing import assert_frame_equal
+
+from rtichoke import prepare_performance_data, prepare_performance_data_times
+
+
+EXPECTED_BINARY_COUNTS_AT_HALF = {
+    "true_positives": 1.0,
+    "false_positives": 0.0,
+    "true_negatives": 1.0,
+    "false_negatives": 1.0,
+}
+
+
+def test_binary_probability_equal_to_cutoff_is_predicted_negative_like_r():
+    result = prepare_performance_data(
+        probs={"model": np.array([0.4, 0.5, 0.6])},
+        reals=np.array([0, 1, 1]),
+        by=0.5,
+    )
+
+    row = result.filter(pl.col("chosen_cutoff") == 0.5).row(0, named=True)
+
+    for column, expected in EXPECTED_BINARY_COUNTS_AT_HALF.items():
+        assert row[column] == expected
+
+
+def test_time_probability_equal_to_cutoff_remains_positive_for_dcurves_parity():
+    result = prepare_performance_data_times(
+        probs={"model": np.array([0.4, 0.5, 0.6])},
+        reals=np.array([1, 1, 1]),
+        times=np.array([3.0, 1.0, 1.0]),
+        fixed_time_horizons=[2.0],
+        by=0.5,
+    )
+
+    row = result.filter(pl.col("chosen_cutoff") == 0.5).row(0, named=True)
+
+    assert row["true_positives"] == 2.0
+    assert row["false_positives"] == 0.0
+    assert row["true_negatives"] == 1.0
+    assert row["false_negatives"] == 0.0
+
+
+def test_binary_cutoff_zero_still_predicts_everyone_positive():
+    result = prepare_performance_data(
+        probs={"model": np.array([0.0, 0.5, 1.0])},
+        reals=np.array([0, 1, 1]),
+        by=0.5,
+    )
+
+    row = result.filter(pl.col("chosen_cutoff") == 0.0).row(0, named=True)
+
+    assert row["predicted_positives"] == 3
+    assert row["true_negatives"] == 0
+    assert row["false_negatives"] == 0
+
+
+def test_binary_cutoff_one_predicts_everyone_negative():
+    result = prepare_performance_data(
+        probs={"model": np.array([0.0, 0.5, 1.0])},
+        reals=np.array([0, 1, 1]),
+        by=0.5,
+    )
+
+    row = result.filter(pl.col("chosen_cutoff") == 1.0).row(0, named=True)
+
+    assert row["predicted_positives"] == 0
+    assert row["true_positives"] == 0
+    assert row["false_positives"] == 0
+
+
+def test_binary_cutoff_adjustment_does_not_change_ppcr_stratification():
+    probs = {"model": np.array([0.1, 0.2, 0.5, 0.5, 0.8, 0.9])}
+    reals = np.array([0, 0, 1, 0, 1, 1])
+
+    ppcr_only = prepare_performance_data(
+        probs=probs,
+        reals=reals,
+        stratified_by=("ppcr",),
+        by=0.5,
+    ).sort(["reference_group", "chosen_cutoff"])
+
+    combined_ppcr = (
+        prepare_performance_data(
+            probs=probs,
+            reals=reals,
+            stratified_by=("probability_threshold", "ppcr"),
+            by=0.5,
+        )
+        .filter(pl.col("stratified_by") == "ppcr")
+        .sort(["reference_group", "chosen_cutoff"])
+        .select(ppcr_only.columns)
+    )
+
+    assert_frame_equal(combined_ppcr, ppcr_only)