2026 Statistical Audit of U.S. & World Lotteries

Independent Chi-Square fairness analysis across 35 major lottery games and 91,349 total draws. Updated automatically as new results are published.

Key Finding (2026)

Across 117 statistical tests spanning 35 lotteries, we observed many short-term “flares” — including several p < 0.05 results — which is expected in high-volume monitoring. The strongest non-structural deviation we observed was UK Thunderball’s bonus numbers pattern (p = 0.000; effect size 0.070), a small fluctuation consistent with normal variance, not manipulation. Outside of expected structural artifacts, we find no evidence of persistent bias.

Executive Summary

  • Scope: 35 lotteries, 117 statistical tests across frequency, patterns, and temporal stability over 91,349 total draws
  • Raw signals: 8 frequency/pattern tests hit p < 0.05 (expected ~6 under simple chance assumptions). Temporal sub-tests inflate this count further.
  • After correction: 1 result survives Bonferroni correction; those that do carry negligible effect sizes
  • Closest non-structural flare: UK Thunderball bonus numbers (p = 0.000, effect size 0.070) — negligible in practice

What This Means

  • We built a smoke detector for randomness — and we’re showing you what smoke looks like in a fair system.
  • Short-term “flares” (p < 0.05 in individual tests) are expected and occur at rates consistent with chance.
  • Temporal testing spans ~70 sub-tests per lottery and includes rule/pool changes, both of which inflate raw signal counts beyond the naive 5% expectation.
  • No non-structural deviation persists across time windows or survives correction for multiple comparisons with a meaningful effect size.
  • Even the most detectable anomaly (UK Thunderball bonus numbers) is far too small in magnitude to create a predictable advantage.

Closest Call

We monitor 35 lotteries continuously. Statistical “flares” happen — but outside of rule-change artifacts, none persist or imply a practical edge. Here is the single closest result to a genuine anomaly.

Closest Call

In 2,809 UK Thunderball draws, number 3 appeared 24 times vs ~201 expected (p = 0.00e+0). The effect size is small and does not survive multiple-testing correction — consistent with normal fluctuation.

Technical Detail

UK Thunderball — Frequency (bonus numbers)

Raw p-value 0.00e+0 — nominally significant at α = 0.05
Effect size (Cramér’s V) 0.070 — negligible magnitude
χ² statistic 179.60 (df = 13)
Draws analyzed 2,809
After correction Survives correction — but effect size is negligible. (Bonferroni α = 0.0004)

Multiple testing context: With 117 independent frequency and pattern tests at α = 0.05, we’d expect ~6 false positives by chance alone. We observed 8. After Bonferroni correction (α = 0.0004), 1 result survive, with negligible effect sizes.

Note: Our temporal dimension runs ~70 additional sub-tests per lottery and spans rule/pool changes. Both factors inflate raw p < 0.05 counts well beyond the naive 5% expectation. The figures above reflect frequency and pattern tests only.

Score Distribution

How the 35 audited games distribute across scoring tiers. Higher scores indicate stronger statistical consistency with random processes.

Score Verdict Distribution
90–100 Highly Trustworthy
34 (97%)
75–89 Generally Fair
1 (3%)
50–74 Average
0 (0%)
Below 50 Anomalies Detected
0 (0%)

Cross-Lottery Dimensional Analysis

Each audit tests three independent dimensions of randomness. Average scores across all games reveal which aspects of lottery draws are most and least consistent with fair random processes.

Dimension What It Tests Average
🔢 Pattern Analysis Even/odd, high/low, and consecutive number distributions 100/100
🎲 Frequency Analysis Individual number occurrence rates vs. expected values 98/100
📅 Temporal Analysis Day-of-week and day-of-month outcome distributions 98/100

Insight: Pattern Analysis (avg 100/100) is the strongest dimension, while Temporal Analysis (avg 98/100) shows the most variation. Even the weakest dimension remains well above the significance threshold, suggesting no systematic bias in any measurement area.

Regional Comparison

Fairness scores grouped by geographic region. Consistent scores across independent regulatory environments strengthen the finding that lottery draws behave like fair random processes.

Region Games Avg Score Total Draws
U.S. 29 99/100 83,873
UK 2 97/100 4,007
Canada 2 100/100 1,836
Europe 2 100/100 1,633

Cross-region consistency: Average scores range from 97 to 100 — a spread of just 3 points. Lottery fairness does not appear to be region-dependent.

What These Audits Test

Each audit applies the same multi-dimensional statistical framework to a lottery’s official draw history. Three independent dimensions of randomness are tested:

🎲 Frequency Analysis

Does each number appear approximately as often as expected? Tested across multiple windows (100, 200, 500, and full history).

🔢 Pattern Analysis

Do combination structures (even/odd, high/low, consecutive numbers) occur at rates consistent with randomness?

📅 Temporal Analysis

Do outcomes vary meaningfully by day of week or day of month? Tests for temporal clustering beyond chance.

Audit Results — All Games

All 35 audited lotteries with per-dimension scores. Click any lottery name to read the full audit with charts, Chi-Square statistics, and detailed analysis.

Lottery Score Verdict Frequency Patterns Temporal Draws
Pick 4 (NC) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Daily 4 (TX) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Pick 3 (NC) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Fantasy 5 (GA) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 4,046
Daily 4 (CA) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 3,226
Pick 3 (TX) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
UK Lotto Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 1,198
New York Lotto Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 2,622
Cash 3 (GA) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Lotto Max Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 58
Texas Lotto Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 2,408
Powerball Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 1,423
Take 5 (NY) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 3,837
Pick-6 (NJ) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 487
Numbers (NY) Fairness Audit 100 Highly Trustworthy 67/100 100/100 100/100 5,000
Lotto America Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 1,160
Win 4 (NY) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Cash 4 (GA) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Pick 3 (FL) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Millionaire for Life Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 252
Pick 4 (FL) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
California SuperLotto Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 446
Pick 4 (NJ) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 1,459
Daily 3 (CA) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 5,000
Loto (FDJ) Fairness Audit 100 Highly Trustworthy 100/100 100/100 100/100 579
Mega Millions Fairness Audit 99 Highly Trustworthy 100/100 100/100 98/100 940
Lotto 6/49 Fairness Audit 99 Highly Trustworthy 100/100 100/100 99/100 1,778
Fantasy 5 (CA) Fairness Audit 99 Highly Trustworthy 100/100 100/100 99/100 1,368
Jersey Cash 5 Fairness Audit 99 Highly Trustworthy 100/100 100/100 99/100 1,093
Fantasy 5 (FL) Fairness Audit 99 Highly Trustworthy 100/100 100/100 97/100 1,256
EuroMillions Fairness Audit 99 Highly Trustworthy 100/100 100/100 99/100 1,054
Illinois Lotto Fairness Audit 99 Highly Trustworthy 100/100 100/100 99/100 825
UK Thunderball Fairness Audit 94 Highly Trustworthy 89/100 100/100 100/100 2,809
Florida Lotto Fairness Audit 91 Highly Trustworthy 100/100 100/100 64/100 564
Pick 3 (NJ) Fairness Audit 75 Generally Fair 67/100 100/100 75/100 1,461

Audit Data & Citation Terms

© Lucky Picks. All rights reserved. Journalists, researchers, and educators may cite summary findings with clear attribution and a direct link back to Lucky Picks. Automated scraping, bulk redistribution, or commercial reuse in competing lottery tools or publications is prohibited under our Terms of Service.

📊 View / Copy Dataset (CSV, 35 rows) 
Lottery,Region,Fairness Score,Frequency Score,Patterns Score,Temporal Score,Total Draws,Verdict
"Pick 4 (NC)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Daily 4 (TX)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Pick 3 (NC)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Fantasy 5 (GA)","U.S.",100,100,100,100,4046,"Highly Trustworthy"
"Daily 4 (CA)","U.S.",100,100,100,100,3226,"Highly Trustworthy"
"Pick 3 (TX)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"UK Lotto","UK",100,100,100,100,1198,"Highly Trustworthy"
"New York Lotto","U.S.",100,100,100,100,2622,"Highly Trustworthy"
"Cash 3 (GA)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Lotto Max","Canada",100,100,100,100,58,"Highly Trustworthy"
"Texas Lotto","U.S.",100,100,100,100,2408,"Highly Trustworthy"
"Powerball","U.S.",100,100,100,100,1423,"Highly Trustworthy"
"Take 5 (NY)","U.S.",100,100,100,100,3837,"Highly Trustworthy"
"Pick-6 (NJ)","U.S.",100,100,100,100,487,"Highly Trustworthy"
"Numbers (NY)","U.S.",100,67,100,100,5000,"Highly Trustworthy"
"Lotto America","U.S.",100,100,100,100,1160,"Highly Trustworthy"
"Win 4 (NY)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Cash 4 (GA)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Pick 3 (FL)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Millionaire for Life","U.S.",100,100,100,100,252,"Highly Trustworthy"
"Pick 4 (FL)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"California SuperLotto","U.S.",100,100,100,100,446,"Highly Trustworthy"
"Pick 4 (NJ)","U.S.",100,100,100,100,1459,"Highly Trustworthy"
"Daily 3 (CA)","U.S.",100,100,100,100,5000,"Highly Trustworthy"
"Loto (FDJ)","Europe",100,100,100,100,579,"Highly Trustworthy"
"Mega Millions","U.S.",99,100,100,98,940,"Highly Trustworthy"
"Lotto 6/49","Canada",99,100,100,99,1778,"Highly Trustworthy"
"Fantasy 5 (CA)","U.S.",99,100,100,99,1368,"Highly Trustworthy"
"Jersey Cash 5","U.S.",99,100,100,99,1093,"Highly Trustworthy"
"Fantasy 5 (FL)","U.S.",99,100,100,97,1256,"Highly Trustworthy"
"EuroMillions","Europe",99,100,100,99,1054,"Highly Trustworthy"
"Illinois Lotto","U.S.",99,100,100,99,825,"Highly Trustworthy"
"UK Thunderball","UK",94,89,100,100,2809,"Highly Trustworthy"
"Florida Lotto","U.S.",91,100,100,64,564,"Highly Trustworthy"
"Pick 3 (NJ)","U.S.",75,67,100,75,1461,"Generally Fair"

Methodology & Validation

Every audit uses the same standardized statistical framework. The methodology and its validation against rigged simulations are documented separately:

View Full Methodology
Validation Experiments
What Is a Fairness Score?

Limitations

  • Statistical audits test distributional properties of published outcomes. They cannot detect insider manipulation that does not produce distribution anomalies.
  • Short-term deviations may occur within expected variance and do not constitute evidence of unfairness.
  • All audits rely on publicly available historical draw data as published by official lottery operators.
  • The Chi-Square framework tests aggregate distribution. It does not test the security of random number generation hardware or operational procedures.

How to Cite This Audit

APA Format

Lucky Picks Research. (2026). 2026 Statistical Audit of U.S. & World Lotteries: Chi-Square Fairness Analysis of 35 Games. Lucky Picks. https://luckypicks.io/research/statistical-fairness/

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Lucky Picks 2026 Statistical Audit — updated automatically as new draws are published.