diff --git a/experiments/analyze_estimated.py b/experiments/analyze_estimated.py
index 88f3933..f2c5159 100644
--- a/experiments/analyze_estimated.py
+++ b/experiments/analyze_estimated.py
@@ -69,6 +69,7 @@ def summarize(release: pd.DataFrame, results: pd.DataFrame) -> pd.DataFrame:
         realized_gain_pp=("realized_gain_pp", "mean"),
         robust_lower_bound_pp=("robust_lower_bound_pp", "mean"),
     )
+    # Gains are percentage points; tied repetitions can retain ~1e-14 roundoff.
     summary = repetition.groupby(["scenario", "alpha"], as_index=False).agg(
         repetitions=("realized_gain_pp", "size"),
         move_share=("move_share", "mean"),
@@ -82,7 +83,7 @@ def summarize(release: pd.DataFrame, results: pd.DataFrame) -> pd.DataFrame:
         conditional_gain_se=("conditional_gain_pp", "sem"),
         realized_gain_pp=("realized_gain_pp", "mean"),
         realized_gain_se=("realized_gain_pp", "sem"),
-        positive_realized_share=("realized_gain_pp", lambda x: (x > 0).mean()),
+        positive_realized_share=("realized_gain_pp", lambda x: (x > 1e-9).mean()),
         robust_lower_bound_pp=("robust_lower_bound_pp", "mean"),
     )
     summary["scenario"] = pd.Categorical(
diff --git a/experiments/analyze_oracle.py b/experiments/analyze_oracle.py
index ffa4c7b..f694731 100644
--- a/experiments/analyze_oracle.py
+++ b/experiments/analyze_oracle.py
@@ -33,6 +33,7 @@ def summarize(release: pd.DataFrame, results: pd.DataFrame) -> pd.DataFrame:
         realized_gain_pp=("realized_gain_pp", "mean"),
         joint_realized_gain_pp=("joint_realized_gain_pp", "mean"),
     )
+    # Gains are percentage points; tied repetitions can retain ~1e-14 roundoff.
     summary = (
         repetition_means.groupby("alpha", as_index=False)
         .agg(
@@ -52,7 +53,7 @@ def summarize(release: pd.DataFrame, results: pd.DataFrame) -> pd.DataFrame:
             expected_gain_pp=("expected_gain_pp", "mean"),
             realized_gain_pp=("realized_gain_pp", "mean"),
             realized_gain_se=("realized_gain_pp", "sem"),
-            positive_repetition_share=("realized_gain_pp", lambda x: (x > 0).mean()),
+            positive_repetition_share=("realized_gain_pp", lambda x: (x > 1e-9).mean()),
         )
         .sort_values("alpha")
     )
diff --git a/experiments/tests/test_positive_gain.py b/experiments/tests/test_positive_gain.py
new file mode 100644
index 0000000..d73e088
--- /dev/null
+++ b/experiments/tests/test_positive_gain.py
@@ -0,0 +1,33 @@
+"""Roundoff in tied repetitions must not count as a realized improvement."""
+
+from pathlib import Path
+
+import pandas as pd
+import pytest
+
+from experiments import analyze_estimated, analyze_oracle
+
+
+@pytest.mark.parametrize(
+    ("analyzer", "experiment", "share"),
+    [
+        (analyze_oracle, "oracle", "positive_repetition_share"),
+        (analyze_estimated, "estimated", "positive_realized_share"),
+    ],
+)
+def test_positive_share_excludes_roundoff(analyzer, experiment, share) -> None:
+    directory = Path(__file__).parents[2] / "results" / experiment
+    template = pd.read_csv(directory / "matched_budget.csv", nrows=1).iloc[0]
+    rows = []
+    for repetition, gain in enumerate([1e-14, 0.1, -0.1]):
+        for alpha in [0.0, 1.0]:
+            row = template.copy()
+            row["repetition"] = repetition
+            row["alpha"] = alpha
+            row["realized_gain_pp"] = gain if alpha == 0 else 0.0
+            row["predicted_gain_pp"] = 0.0
+            rows.append(row)
+    release = pd.read_csv(directory / "release.csv", nrows=1)
+    summary = analyzer.summarize(release, pd.DataFrame(rows))
+    assert summary.loc[summary["alpha"] == 0, share].iloc[0] == pytest.approx(1 / 3)
+    assert summary.loc[summary["alpha"] == 1, share].iloc[0] == 0
diff --git a/paper/generated/estimated_summary.tex b/paper/generated/estimated_summary.tex
index a59770e..d57b5b7 100644
--- a/paper/generated/estimated_summary.tex
+++ b/paper/generated/estimated_summary.tex
@@ -20,9 +20,9 @@
 Weak innovation & 1.0 & 3.02 & 8.3 & 8.3 & 8.3 & 0.00 [0.00, 0.00] & 0.00 [0.00, 0.00] \\
 Overconfident & 0.0 & 0.00 & 0.0 & 12.4 & 0.0 & 7.21 [7.07, 7.35] & 0.00 [0.00, 0.00] \\
 Overconfident & 0.5 & 5.42 & 9.4 & 12.9 & 9.5 & 0.35 [0.31, 0.38] & 0.15 [0.13, 0.17] \\
-Overconfident & 1.0 & 7.57 & 13.3 & 13.3 & 13.3 & 0.00 [0.00, 0.00] & 0.00 [0.00, 0.00] \\
+Overconfident & 1.0 & 7.58 & 13.3 & 13.3 & 13.3 & 0.00 [0.00, 0.00] & 0.00 [0.00, 0.00] \\
 Underconfident & 0.0 & 0.00 & 0.0 & 12.3 & 0.0 & 7.41 [7.26, 7.56] & 0.00 [0.00, 0.00] \\
-Underconfident & 0.5 & 2.76 & 3.8 & 12.5 & 3.5 & 3.03 [2.93, 3.13] & 0.84 [0.80, 0.88] \\
+Underconfident & 0.5 & 2.77 & 3.8 & 12.5 & 3.5 & 3.03 [2.93, 3.13] & 0.84 [0.80, 0.88] \\
 Underconfident & 1.0 & 7.45 & 13.4 & 13.4 & 13.4 & 0.00 [0.00, 0.00] & 0.00 [0.00, 0.00] \\
 \bottomrule
 \end{tabular}
diff --git a/paper/main.pdf b/paper/main.pdf
index 79f7c40..40d2929 100644
Binary files a/paper/main.pdf and b/paper/main.pdf differ
diff --git a/results/estimated_summary.csv b/results/estimated_summary.csv
index 55ea139..e2423e8 100644
--- a/results/estimated_summary.csv
+++ b/results/estimated_summary.csv
@@ -1,18 +1,18 @@
 scenario,alpha,repetitions,move_share,nfr,operational_nfr,joint_nfr,joint_conditional_gain_pp,joint_conditional_gain_se,predicted_gain_pp,conditional_gain_pp,conditional_gain_se,realized_gain_pp,realized_gain_se,positive_realized_share,robust_lower_bound_pp,acceptance_rate,stress_pass
 well_estimated,0,50,0,0,0.123477571421,0,0,0,7.75135887102,7.56409770084,0.0676617912284,7.535,0.173973992635,1,6.41365629137,1,True
 well_estimated,0.25,50,0.0219333333333,0.0317658811534,0.12609410242,0.0313582841209,1.44743109627,0.0267787808885,4.08223593139,3.95369070105,0.0459930542857,3.97166666667,0.175086794155,1,3.06944844625,1,True
-well_estimated,0.5,50,0.0382,0.066738232659,0.127274628633,0.0678076770685,0.497233310081,0.0124399437654,1.34749711525,1.28189993484,0.0247851070307,1.17,0.122496702718,0.92,0.733285052,1,True
-well_estimated,0.75,50,0.05635,0.103253395862,0.129943799377,0.102753442398,0.0632836203793,0.00539940067628,0.229264979575,0.200351962465,0.0103543917344,0.258333333333,0.0574520405334,0.74,-0.0367964744625,1,True
+well_estimated,0.5,50,0.0382,0.066738232659,0.127274628633,0.0678076770685,0.497233310081,0.0124399437654,1.34749711525,1.28189993484,0.0247851070307,1.17,0.122496702718,0.88,0.733285052,1,True
+well_estimated,0.75,50,0.05635,0.103253395862,0.129943799377,0.102753442398,0.0632836203793,0.00539940067628,0.229264979575,0.200351962465,0.0103543917344,0.258333333333,0.0574520405334,0.68,-0.0367964744625,1,True
 well_estimated,1,50,0.0742333333333,0.134473867648,0.134473867648,0.134473867648,0,0,0,0,0,0,0,0,0,1,True
 small_history,0,50,0,0,0.133866055385,0,0,0,8.52793462902,6.83575611963,0.0881430170301,6.715,0.184644200357,1,3.9887414436,1,True
 small_history,0.25,50,0.0231333333333,0.033595957268,0.136363906521,0.0366157421643,1.32631643861,0.0384292566535,4.50157633221,3.33999413466,0.0680039833984,3.29333333333,0.154912747002,1,1.11523198515,1,True
 small_history,0.5,50,0.0411166666667,0.0750156106985,0.139556440045,0.0765086650212,0.363788923952,0.0232749956275,1.47775074038,0.899797545113,0.0607260111686,0.901666666667,0.135916515993,0.82,-0.519612571383,1,True
-small_history,0.75,50,0.0610833333333,0.113380060614,0.143996160872,0.113578521213,0.0104359462426,0.0149652624254,0.243998068892,0.032819411748,0.0325898562188,0.005,0.0889409215623,0.5,-0.62088004321,1,True
+small_history,0.75,50,0.0610833333333,0.113380060614,0.143996160872,0.113578521213,0.0104359462426,0.0149652624254,0.243998068892,0.032819411748,0.0325898562188,0.005,0.0889409215623,0.46,-0.62088004321,1,True
 small_history,1,50,0.0788,0.148559261205,0.148559261205,0.148559261205,0,0,0,0,0,0,0,0,0,1,True
 weak_innovation,0,44,0,0,0.0801359159636,0,0,0,1.39801975535,0.99787074852,0.0199574788768,1.14962121212,0.148488477667,0.840909090909,0.323438761433,0.88,True
-weak_innovation,0.25,44,0.0127272727273,0.0192990745185,0.0808567666527,0.0200150708955,0.11104741661,0.00818757170337,0.79659030554,0.495948663703,0.0181939017366,0.564393939394,0.108066145967,0.75,-0.0173584483399,0.88,True
-weak_innovation,0.5,44,0.0189393939394,0.0400410701441,0.0810988063993,0.0407113808756,0.0327787380114,0.00626469767122,0.334644119595,0.15387428644,0.0140084373206,0.183712121212,0.103652874727,0.613636363636,-0.198755857247,0.88,True
-weak_innovation,0.75,44,0.0250568181818,0.0612320434923,0.0814181656663,0.0614687578399,-0.0140977505256,0.00583804044168,0.0791901651637,-0.000188120011818,0.00895259059699,0.032196969697,0.0658231469253,0.590909090909,-0.176321578516,0.88,True
+weak_innovation,0.25,44,0.0127272727273,0.0192990745185,0.0808567666527,0.0200150708955,0.11104741661,0.00818757170337,0.79659030554,0.495948663703,0.0181939017366,0.564393939394,0.108066145967,0.727272727273,-0.0173584483399,0.88,True
+weak_innovation,0.5,44,0.0189393939394,0.0400410701441,0.0810988063993,0.0407113808756,0.0327787380114,0.00626469767122,0.334644119595,0.15387428644,0.0140084373206,0.183712121212,0.103652874727,0.590909090909,-0.198755857247,0.88,True
+weak_innovation,0.75,44,0.0250568181818,0.0612320434923,0.0814181656663,0.0614687578399,-0.0140977505256,0.00583804044168,0.0791901651637,-0.000188120011818,0.00895259059699,0.032196969697,0.0658231469253,0.568181818182,-0.176321578516,0.88,True
 weak_innovation,1,44,0.0301515151515,0.0832420901079,0.0832420901079,0.0832420901079,0,0,0,0,0,0,0,0,0,0.88,True
 overconfident,0,50,0,0,0.124001249212,0,0,0,13.297468534,7.20955487781,0.0730558320349,7.26833333333,0.18194106469,1,6.19198146459,1,True
 overconfident,0.25,50,0.0308333333333,0.0521561640822,0.125286575002,0.0582480659418,1.31352085727,0.0276209830263,4.86667765447,2.31867942026,0.0434447409033,2.44833333333,0.125985682878,1,1.59034093976,1,True
@@ -22,5 +22,5 @@ overconfident,1,50,0.07575,0.133489740744,0.133489740744,0.133489740744,0,0,0,0,
 underconfident,0,50,0,0,0.122689982655,0,0,0,3.59685262596,7.41181167603,0.0760351134181,7.41166666667,0.172572407492,1,-1.59916957243,1,True
 underconfident,0.25,50,0.0161666666667,0.0153343060963,0.124162724625,0.0120737878598,1.04960405099,0.0227025274188,2.59462263478,5.43567667773,0.0652556463509,5.41166666667,0.167994877635,1,-1.55422963494,1,True
 underconfident,0.5,50,0.02765,0.0379797971411,0.125361888717,0.0350972105935,0.835869256963,0.0207528356764,1.41654747007,3.03007772993,0.048789975116,2.95333333333,0.137852002536,1,-1.40953147912,1,True
-underconfident,0.75,50,0.04395,0.0760228321802,0.127275766639,0.0732942189106,0.279794401894,0.0132801067999,0.400906442563,0.866100585498,0.0337971182139,0.86,0.12248466978,0.84,-0.974361441367,1,True
+underconfident,0.75,50,0.04395,0.0760228321802,0.127275766639,0.0732942189106,0.279794401894,0.0132801067999,0.400906442563,0.866100585498,0.0337971182139,0.86,0.12248466978,0.82,-0.974361441367,1,True
 underconfident,1,50,0.0745166666667,0.133708863823,0.133708863823,0.133708863823,0,0,0,0,0,0,0,0,0,1,True
diff --git a/results/oracle_summary.csv b/results/oracle_summary.csv
index 1557355..9866c15 100644
--- a/results/oracle_summary.csv
+++ b/results/oracle_summary.csv
@@ -5,8 +5,8 @@ alpha,repetitions,mean_move_share,mean_nfr,operational_nfr,joint_nfr,baseline_ac
 0.3,200,0.019972,0.0360178433364,0.124051722306,0.0361565196259,0.575304,0.000666035989792,0.6088,0.000708937913236,0.587916,0.000669403634686,1.2612,0.0331779547805,3.35029971973,3.3496,0.049794141045,1,1000,0
 0.4,200,0.026076,0.050314254323,0.12462105275,0.0501018973576,0.587376,0.000698959111248,0.60961,0.000698117713361,0.596224,0.000679217048516,0.8848,0.0288619100069,2.22567854196,2.2234,0.0413357645041,1,1000,0
 0.5,200,0.032846,0.0649130556089,0.125604955768,0.0646613122956,0.596482,0.00070647997123,0.610188,0.00068222462002,0.60207,0.000675988388589,0.5588,0.0293225486494,1.35884915958,1.3706,0.038227541441,0.98,1000,0
-0.6,200,0.04073,0.0797496655137,0.126626200997,0.0794229383907,0.603142,0.000693761997044,0.610892,0.000686242174169,0.606136,0.000687838008275,0.2994,0.0275045578681,0.751339848438,0.775,0.0373670507588,0.93,1000,0
+0.6,200,0.04073,0.0797496655137,0.126626200997,0.0794229383907,0.603142,0.000693761997044,0.610892,0.000686242174169,0.606136,0.000687838008275,0.2994,0.0275045578681,0.751339848438,0.775,0.0373670507588,0.925,1000,0
 0.7,200,0.048592,0.0940754535204,0.128051552541,0.0937360231974,0.607252,0.000691858236271,0.611212,0.000683349186399,0.608786,0.000682392347981,0.1534,0.0236112186945,0.36529035871,0.396,0.0283055830209,0.815,1000,0
-0.8,200,0.056732,0.107869842161,0.129754471169,0.10762128478,0.609926,0.000698858092295,0.6114,0.000686507437914,0.610374,0.000679338001736,0.0448,0.0191530414027,0.139798207193,0.1474,0.0231100969906,0.665,1000,0
-0.9,200,0.064258,0.120917478786,0.131005951916,0.120609930734,0.611294,0.00070010467272,0.611608,0.000688845571304,0.611392,0.000687981301604,0.0098,0.0113757124687,0.0292674529149,0.0314,0.0158482185166,0.555,1000,0
+0.8,200,0.056732,0.107869842161,0.129754471169,0.10762128478,0.609926,0.000698858092295,0.6114,0.000686507437914,0.610374,0.000679338001736,0.0448,0.0191530414027,0.139798207193,0.1474,0.0231100969906,0.66,1000,0
+0.9,200,0.064258,0.120917478786,0.131005951916,0.120609930734,0.611294,0.00070010467272,0.611608,0.000688845571304,0.611392,0.000687981301604,0.0098,0.0113757124687,0.0292674529149,0.0314,0.0158482185166,0.525,1000,0
 1,200,0.070698,0.132757004413,0.132757004413,0.132757004413,0.611602,0.000699596423504,0.611602,0.000699596423504,0.611602,0.000699596423504,0,0,0,0,0,0,1000,0
diff --git a/uv.lock b/uv.lock
index c0c18a9..70969d6 100644
--- a/uv.lock
+++ b/uv.lock
@@ -708,7 +708,7 @@ wheels = [
 
 [[package]]
 name = "pandas"
-version = "3.0.6"
+version = "3.1.0"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
     { name = "numpy", version = "2.4.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.12'" },
@@ -716,65 +716,65 @@ dependencies = [
     { name = "python-dateutil" },
     { name = "tzdata", marker = "sys_platform == 'emscripten' or sys_platform == 'win32'" },
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/e2/17/d7b106e05bfa642e8694451e7d3d759c6a241c5386a5d962e4f66c047e06/pandas-3.0.6.tar.gz", hash = "sha256:66b07ef7315a31bfe1089cd3d71a7de781c9dca986762d0b4fe7c0ef17465d10", size = 4667686, upload-time = "2026-09-17T23:23:18.345Z" }
+sdist = { url = "https://files.pythonhosted.org/packages/55/b1/a10c0d1a7e3ce44eb42635771004aa503e3b9ddde0bd39c524dda65f7eff/pandas-3.1.0.tar.gz", hash = "sha256:ecb9b2d8a817b1e1ba1fdb90c0abe9eab31b4fdf2562b7a56b86ac66ace17e49", size = 5933421, upload-time = "2026-10-22T11:57:03.087Z" }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/7d/48/88e8d250d28efa8163294f6809a71683c7ee67f63ac7c33021c0503b3547/pandas-3.0.6-cp311-cp311-macosx_10_9_x86_64.whl", hash = "sha256:085e3786ae6b2e82b406266bce36690f72b9dc1421903ba9296b2981a9fcf586", size = 10391798, upload-time = "2026-09-17T23:20:20.96Z" },
-    { url = "https://files.pythonhosted.org/packages/55/a6/39db5d41f3eb5d7846626312cb30e0cea48e988fc47a3725698bc931ad3c/pandas-3.0.6-cp311-cp311-macosx_11_0_arm64.whl", hash = "sha256:d7564d86a94c2eb8ab290b07f63ddaae5c032fa53897c29a2ff2197d43aee8af", size = 10023718, upload-time = "2026-09-17T23:20:25.094Z" },
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