Three Tools in One Page
The Stats Toolkit brings together three statistical tools for exploring lottery data scientifically. All three reinforce the same message from different angles: lottery draws are random.
Tab 1: Randomness Score
The Randomness Score uses Shannon entropy to measure how evenly distributed each state's digit frequencies are. If all 10 digits appeared exactly 10% of the time, the score would be 100. In practice, scores range from 75–98 depending on sample size and window.
States near the bottom aren't "rigged" — they just have smaller sample sizes or shorter data windows, which produces more apparent variance.
Tab 2: Expected vs Actual
Select any digit (0–9) to see a bar chart of that digit's frequency in every US state over the last 90 days. A blue reference line marks the expected 10%. Most bars will cluster within 1–2% of that line — demonstrating the law of large numbers in action.
Tab 3: Independence Test
Select two states and click "Run Test" to perform a chi-squared contingency table test. The result shows whether the two states' digit distributions are statistically similar. In practice, nearly all state pairs will show p ≥ 0.10 — meaning the distributions are consistent with being independently drawn from the same uniform distribution.
For informational and educational purposes only. Past results do not predict future draws. Play responsibly.