Does a small p-value predict the next draw?

No. It describes a selected historical sample under a model, not the next independent outcome.

Can I test one chosen number?

Yes, but that is a different hypothesis test. If you test many numbers separately, adjust for multiple comparisons or report the resulting false-positive risk.

How does a chi-square test work for lottery draws?

A chi-square test asks whether the combined differences among all number frequencies are larger than reasonably expected under a random model. It does not identify numbers that will appear next.

What does the test examine?

Under the null hypothesis, every number has the same appearance probability, and the observed differences are treated as random variation. In Lotto, 6 of 49 numbers are drawn, so the expected count for one number over N draws is

E = N \cdot \frac{6}{49}

Formula

For each number, observed O is compared with expected E. The service first calculates standardized deviations and then uses

T = \frac{m - 1}{m} \sum_{i = 1}^{m} z_{i}^{2}

, where

z_{i} = \frac{O_{i} - E}{\sqrt{N p (1 - p)}}

. The factor (m−1)/m accounts for the dependence among number counts when several distinct numbers are drawn without replacement.

Worked example

Across 100 draws, the expected count is 100 × 6/49 = 12.245 for each number. Counts such as 8 or 17 alone do not prove a problem. The test combines deviations across all 49 numbers before comparing the pattern with its reference distribution.

Reading the result

A large χ² statistic and a small p-value mean that this much combined dispersion would be unusual under the stated model. The result does not establish a cause, select a better number or forecast another draw.

Limitations

Draws must come from a comparable mechanism, data must be complete and expected counts sufficiently large. Selecting a range after viewing results increases false-alarm risk.

Sources and further reading

See the Pewniaki methodology for game data and model assumptions. The NIST/SEMATECH e-Handbook of Statistical Methods provides the general test definition.

Frequently asked questions

Does a small p-value predict the next draw?: No. It describes a selected historical sample under a model, not the next independent outcome.
Can I test one chosen number?: Yes, but that is a different hypothesis test. If you test many numbers separately, adjust for multiple comparisons or report the resulting false-positive risk.

Check it on real draw data

Choose a draw range in Lotto Lab PRO and compare the observed result with the random model.

Open Lotto Lab PRO

Related Lotto Lab PRO guides

Last updated: 20.10.2026