#!/usr/bin/env python3 """Independent standard-library verifier for the poker-stat sample-size bundle.""" import csv import hashlib import json import math from pathlib import Path ROOT = Path(__file__).resolve().parent JSON_PATH = ROOT / "reference.json" Z95 = 1.959963984540054 def close(actual, expected, tolerance=6e-12): return math.isclose(actual, expected, rel_tol=tolerance, abs_tol=tolerance) def wilson(successes, opportunities, z=Z95): assert isinstance(successes, int) assert isinstance(opportunities, int) assert 0 <= successes <= opportunities assert opportunities > 0 observed = successes / opportunities z_squared = z * z denominator = 1 + z_squared / opportunities center = (observed + z_squared / (2 * opportunities)) / denominator margin = z * math.sqrt( observed * (1 - observed) / opportunities + z_squared / (4 * opportunities * opportunities) ) / denominator return max(0.0, center - margin), min(1.0, center + margin) def wald(successes, opportunities, z=Z95): observed = successes / opportunities margin = z * math.sqrt(observed * (1 - observed) / opportunities) return observed - margin, observed + margin def exact_zero_event_upper(opportunities, alpha=0.05): assert isinstance(opportunities, int) and opportunities > 0 assert 0 < alpha < 1 return 1 - alpha ** (1 / opportunities) def read_csv(name): with (ROOT / name).open(newline="", encoding="utf-8") as handle: return list(csv.DictReader(handle)) def parse_bool(value): if value == "true": return True if value == "false": return False raise ValueError(f"Expected lowercase CSV boolean, got {value!r}") def verify_manifest(): expected_names = { "reference.json", "same-rate-wilson.csv", "zero-event-wilson.csv", "context-split.csv", "decision-threshold.csv", "opportunity-planning.csv", "wald-comparison.csv", "calculator.html", "generate.mjs", "verify.py", "verification-report.json", "README.md", "../../images/blog_images/poker-stat-sample-size-wilson.svg", } entries = {} for line in (ROOT / "MANIFEST.sha256").read_text(encoding="utf-8").splitlines(): digest, name = line.split(" ", 1) assert len(digest) == 64 and all(character in "0123456789abcdef" for character in digest) assert name not in entries entries[name] = digest assert set(entries) == expected_names for name, expected_digest in entries.items(): actual_digest = hashlib.sha256((ROOT / name).resolve().read_bytes()).hexdigest() assert actual_digest == expected_digest, name def main(): if not __debug__: raise SystemExit("Run verify.py without Python optimization; verification assertions must stay enabled.") model = json.loads(JSON_PATH.read_text(encoding="utf-8")) assert model["schemaVersion"] == 1 assert model["generatedOn"] == "2026-09-04" assert model["method"]["confidenceLevel"] == 0.95 assert close(model["method"]["zTwoSided"], Z95) benchmark = model["nistBenchmark"] assert (benchmark["successes"], benchmark["opportunities"]) == (8, 30) benchmark_lower, benchmark_upper = wilson(8, 30) assert close(benchmark["computedWilsonLower"], benchmark_lower) assert close(benchmark["computedWilsonUpper"], benchmark_upper) assert round(benchmark_lower, 6) == benchmark["publishedWilsonLowerSixDecimals"] == 0.141827 assert round(benchmark_upper, 6) == benchmark["publishedWilsonUpperSixDecimals"] == 0.444480 same_rows = model["sameObservedRate"]["rows"] assert [row["opportunities"] for row in same_rows] == [20, 40, 100, 200, 500, 1000] previous_width = math.inf for row in same_rows: assert close(row["successes"] / row["opportunities"], 0.25) lower, upper = wilson(row["successes"], row["opportunities"]) assert close(row["wilson95Lower"], lower) assert close(row["wilson95Upper"], upper) width = (upper - lower) * 100 assert close(row["widthPercentagePoints"], width, 6e-7) assert width < previous_width previous_width = width same_csv = read_csv("same-rate-wilson.csv") assert len(same_csv) == len(same_rows) for generated, published in zip(same_rows, same_csv): assert int(published["successes"]) == generated["successes"] assert int(published["eligible_opportunities"]) == generated["opportunities"] assert close(float(published["observed_rate"]), generated["observedRate"]) assert close(float(published["wilson_95_lower"]), generated["wilson95Lower"]) assert close(float(published["wilson_95_upper"]), generated["wilson95Upper"]) assert close(float(published["interval_width_percentage_points"]), generated["widthPercentagePoints"], 6e-7) zero_rows = model["zeroEvents"]["rows"] assert [row["opportunities"] for row in zero_rows] == [10, 25, 50, 100, 250] for row in zero_rows: _, two_sided_upper = wilson(0, row["opportunities"]) exact_upper = exact_zero_event_upper(row["opportunities"]) assert close(row["wilson95TwoSidedUpperEndpoint"], two_sided_upper) assert close(row["exactBinomial95OneSidedUpper"], exact_upper) assert row["wilson95TwoSidedUpperEndpoint"] > 0 assert row["exactBinomial95OneSidedUpper"] > 0 assert row["ruleOfThreeApplicable"] == (row["opportunities"] > 30) if row["opportunities"] > 30: assert close(row["ruleOfThreeUpperApproximation"], 3 / row["opportunities"]) else: assert row["ruleOfThreeUpperApproximation"] is None zero_csv = read_csv("zero-event-wilson.csv") assert len(zero_csv) == len(zero_rows) for generated, published in zip(zero_rows, zero_csv): assert int(published["successes"]) == generated["successes"] assert int(published["eligible_opportunities"]) == generated["opportunities"] assert close(float(published["observed_rate"]), generated["observedRate"]) assert close(float(published["wilson_95_two_sided_upper_endpoint"]), generated["wilson95TwoSidedUpperEndpoint"]) assert close(float(published["exact_binomial_95_one_sided_upper"]), generated["exactBinomial95OneSidedUpper"]) assert parse_bool(published["rule_of_three_applicable_n_gt_30"]) == generated["ruleOfThreeApplicable"] if generated["ruleOfThreeApplicable"]: assert close(float(published["rule_of_three_upper_approximation"]), generated["ruleOfThreeUpperApproximation"]) else: assert published["rule_of_three_upper_approximation"] == "" context_rows = model["contextSplit"]["rows"] assert len(context_rows) == 3 assert all(row["simulated"] is True for row in context_rows) assert close(context_rows[0]["observedRate"], 0.40) assert close(context_rows[1]["observedRate"], 0.10) assert context_rows[2]["successes"] == context_rows[0]["successes"] + context_rows[1]["successes"] assert context_rows[2]["opportunities"] == context_rows[0]["opportunities"] + context_rows[1]["opportunities"] assert close(context_rows[2]["observedRate"], 0.25) context_csv = read_csv("context-split.csv") assert len(context_csv) == len(context_rows) for generated, published in zip(context_rows, context_csv): assert published["context_key"] == generated["key"] assert published["context_label"] == generated["label"] assert int(published["successes"]) == generated["successes"] assert int(published["eligible_opportunities"]) == generated["opportunities"] assert close(float(published["observed_rate"]), generated["observedRate"]) assert close(float(published["wilson_95_lower"]), generated["wilson95Lower"]) assert close(float(published["wilson_95_upper"]), generated["wilson95Upper"]) assert parse_bool(published["simulated"]) == generated["simulated"] threshold_rows = model["decisionThresholdIllustration"]["rows"] assert len(threshold_rows) == 2 assert all(row["simulated"] is True for row in threshold_rows) assert all(close(row["predeclaredThreshold"], 0.30) for row in threshold_rows) assert threshold_rows[0]["relationToThreshold"] == "crosses" assert threshold_rows[0]["wilson95Lower"] < 0.30 < threshold_rows[0]["wilson95Upper"] assert threshold_rows[1]["relationToThreshold"] == "below" assert threshold_rows[1]["wilson95Upper"] < 0.30 threshold_csv = read_csv("decision-threshold.csv") assert len(threshold_csv) == len(threshold_rows) for generated, published in zip(threshold_rows, threshold_csv): assert int(published["successes"]) == generated["successes"] assert int(published["eligible_opportunities"]) == generated["opportunities"] assert close(float(published["observed_rate"]), generated["observedRate"]) assert close(float(published["wilson_95_lower"]), generated["wilson95Lower"]) assert close(float(published["wilson_95_upper"]), generated["wilson95Upper"]) assert close(float(published["predeclared_threshold"]), generated["predeclaredThreshold"]) assert published["relation_to_threshold"] == generated["relationToThreshold"] assert parse_bool(published["simulated"]) == generated["simulated"] plan_rows = model["opportunityPlanning"]["rows"] assert len(plan_rows) == 12 assert {(row["targetOpportunities"], row["assumedEligibilityRate"]) for row in plan_rows} == { (target, rate) for target in [20, 100, 500] for rate in [0.05, 0.10, 0.25, 0.50] } for row in plan_rows: assert close(row["expectedTotalHands"], row["targetOpportunities"] / row["assumedEligibilityRate"]) plan_csv = read_csv("opportunity-planning.csv") assert len(plan_csv) == len(plan_rows) for generated, published in zip(plan_rows, plan_csv): assert int(published["target_eligible_opportunities"]) == generated["targetOpportunities"] assert close(float(published["assumed_eligibility_rate"]), generated["assumedEligibilityRate"]) assert close(float(published["expected_total_hands"]), generated["expectedTotalHands"]) comparison_rows = model["waldComparison"]["rows"] assert len(comparison_rows) == 6 for row in comparison_rows: wilson_lower, wilson_upper = wilson(row["successes"], row["opportunities"]) wald_lower, wald_upper = wald(row["successes"], row["opportunities"]) assert close(row["wilson95Lower"], wilson_lower) assert close(row["wilson95Upper"], wilson_upper) assert close(row["wald95LowerRaw"], wald_lower) assert close(row["wald95UpperRaw"], wald_upper) assert row["waldProducesImpossibleBound"] == (wald_lower < 0 or wald_upper > 1) assert row["waldCollapsesAtBoundary"] == (row["successes"] in [0, row["opportunities"]]) assert comparison_rows[0]["waldCollapsesAtBoundary"] is True assert comparison_rows[1]["waldProducesImpossibleBound"] is True comparison_csv = read_csv("wald-comparison.csv") assert len(comparison_csv) == len(comparison_rows) for generated, published in zip(comparison_rows, comparison_csv): assert int(published["successes"]) == generated["successes"] assert int(published["eligible_opportunities"]) == generated["opportunities"] assert close(float(published["observed_rate"]), generated["observedRate"]) assert close(float(published["wilson_95_lower"]), generated["wilson95Lower"]) assert close(float(published["wilson_95_upper"]), generated["wilson95Upper"]) assert close(float(published["wald_95_lower_raw"]), generated["wald95LowerRaw"]) assert close(float(published["wald_95_upper_raw"]), generated["wald95UpperRaw"]) assert parse_bool(published["wald_impossible_bound"]) == generated["waldProducesImpossibleBound"] assert parse_bool(published["wald_boundary_collapse"]) == generated["waldCollapsesAtBoundary"] assert len(model["sources"]) == 6 assert all(source["accessed"] == "2026-09-04" for source in model["sources"]) assert any("stable underlying rate" in item for item in model["limitations"]) assert any("selection issues" in item for item in model["limitations"]) report = json.loads((ROOT / "verification-report.json").read_text(encoding="utf-8")) assert report["status"] == "pass" assert report["verifiedAt"] == "2026-09-04T17:35:06Z" assert len(report["implementations"]) == 2 assert report["checks"] == { "nistPublishedRoundedLimits": 2, "sameRateRows": 6, "zeroEventRows": 5, "contextRows": 3, "decisionThresholdRows": 2, "opportunityPlanningRows": 12, "waldComparisonRows": 6, "sha256Artifacts": 13, } verify_manifest() print( "Verified 6 same-rate rows, 5 zero-event rows, 3 context rows, " "2 threshold rows, 12 opportunity-plan rows, 6 Wald comparisons, " "the NIST 8/30 benchmark, and 13 SHA-256 artifacts." ) if __name__ == "__main__": main()