Independent Review of 17 Lotteries Across 21,581+ Draws

All lotteries behaved consistently with expected random variation. No persistent statistical deviations detected.

About This Review

“Is the lottery fair?” is one of the most common questions lottery players ask — and one of the hardest to answer without data. This review answers it with statistical evidence.

We analyzed the complete draw histories of 17 major lottery games — from Powerball and Mega Millions to EuroMillions, UK Lotto, and Canadian games — covering 21,581 total draws. Each game was subjected to the same three-dimensional statistical audit: frequency analysis (do all numbers appear equally often?), pattern analysis (do structural patterns match random expectations?), and temporal analysis (do outcomes vary by day of week or month?).

The core statistical tool is the Chi-Square Goodness of Fit test, the standard method for comparing observed distributions against expected distributions. A game that behaves like a fair random process will produce outcomes that closely match the mathematically expected frequencies — and that is exactly what we observe across the board.

How We Test Fairness

Every lottery goes through the same three-part statistical audit. No math required — just three simple questions.

What This Means for Players

What Does “Fair” Mean?

A “fair” lottery is one where every possible outcome has the probability its game matrix implies. In a 5/69 game (like Powerball’s main drum), each number should appear in roughly 1 out of every 13.8 draws. In a 5/70 game (Mega Millions), roughly 1 out of every 14. A fair game does not favor certain numbers, avoid certain patterns, or cluster outcomes on particular days.

We do not test whether you can predict lottery outcomes — you cannot. We test whether the process generating those outcomes is statistically consistent with randomness. These are different questions. A fair process is, by definition, unpredictable.

What We Found

1. Universal consistency with randomness. 16 of 17 games scored above the statistical significance threshold (≥ 50/100). Observed variations in number frequency, pattern distribution, and draw timing fall within the range expected by chance.
2. Narrow score range. Fairness scores range from 47 to 100, with both the mean (95) and median (99) indicating strong consistency. This tight distribution suggests lottery fairness is systematic, not accidental.
3. All three dimensions pass. Pattern analysis averaged 100/100 (strongest), Frequency analysis 96/100, and Temporal analysis 93/100 (most variable). Even the weakest dimension remains well above the significance threshold.
4. Cross-region consistency. Games across U.S., Canada, UK, Europe score within 26 points of each other, suggesting fairness is not dependent on regulatory jurisdiction or geographic location.
5. Strongest performer: Texas Lotto (100/100 across 2,390 draws). A total of 15 games scored 90 or above.

Lottery-by-Lottery Comparison

The table below shows every audited game with its composite score and per-dimension breakdown. Each lottery links to a detailed individual audit with full Chi-Square statistics and charts.

Last updated: 2026-09-21

Dimension Score Summary

Average scores across all audited lotteries for each of the three tested dimensions.

Dimension-by-Dimension Analysis

Frequency Analysis

The most intuitive fairness test: does each number show up roughly as often as it should? Using Chi-Square analysis, we compare observed number frequencies against the mathematically expected distribution across multiple sample windows.

Pattern Analysis

Beyond individual numbers, we test structural patterns: the ratio of even to odd numbers, high versus low numbers, and the frequency of consecutive number pairs. A fair process should produce these patterns at mathematically predicted rates.

Temporal Analysis

The temporal dimension tests whether draw outcomes vary by the day of the week or the day of the month. A fair process should produce statistically similar results regardless of when the draw occurs.

Methodology

Each audit applies the same standardized framework: Chi-Square Goodness of Fit tests across three independent dimensions of randomness. Scores are computed on a 0–100 scale where 50 represents the statistical significance threshold (p = 0.05) and 100 represents perfect consistency with random expectation.

The framework has been validated against intentionally rigged simulations to confirm it correctly flags unfair games. Full methodology documentation and validation experiments are available:

Explore Further

Dive deeper into our methodology, validation experiments, and individual lottery audits.

How to Cite This Review