New York Chi-Square Randomness Test

A real statistical test — not a gut feeling — for whether a game's actual number frequencies are consistent with true randomness. Most of the time, the honest answer this tool gives is "yes, consistent with random" — which is a genuinely useful result, not a disappointing one: it's evidence the game is fair, not a strategy for beating it.

Game

Sample size

Chi-square statistic

—

Approximate p-value

—

This tests whether each number's observed frequency is consistent with every number being equally likely (a chi-square goodness-of-fit test against a uniform distribution). The p-value is an approximation (Wilson–Hilferty), verified against standard chi-square critical value tables before publishing — accurate to within a fraction of a percent for the sample sizes here. A low p-value (conventionally under 0.05) would suggest the numbers aren't behaving like a fair, uniform random process; a high p-value means there's no statistical evidence of that. This tests past data only and says nothing about future drawings — see how lottery odds actually work.

Why This Usually Comes Back "No Significant Deviation"

If a lottery is run properly, that's exactly the expected outcome — a high p-value here is evidence the game is behaving as a fair, random process should, not a disappointing result. A statistically significant deviation (a low p-value) wouldn't prove the game is rigged either, since with enough different samples and games tested, some will show apparent patterns purely by chance — that's what a 5% significance threshold means by definition. Pair this with the number heatmap to see the same frequency data visually, or the Monte Carlo simulator to see how much random variation looks like at different sample sizes.

This tests frequency only. For whether the order drawings happen in shows any pattern, see the sequential randomness tests (runs test and autocorrelation). For how often two drawings "coincidentally" share numbers, see the number collision analysis. To see this same test run on all three games side by side, see the cross-game randomness comparison. And for a look at where each sorted position (1st smallest through largest) tends to land, see position distribution. For a completely different angle — how each number relates to the previous drawing specifically — see repeat, adjacent & isolated numbers.