Room for ChanceThe science of chance

Free interactive tool

Expected Lottery Frequency Calculator

Compare one specified label’s observed count with the mean and spread predicted by a binomial model.

Inputs and results stay in this page. These tools set no cookies, save no browser preferences and send no input data to our server. A CSV downloads only when you request it. Displayed probabilities are rounded; combination counts use exact integer arithmetic.

Understand the result

Expected vs Observed Lottery Frequencies: Reading a Table Properly explains the derivation and common interpretation errors. Compare it with the published Ten million 6/49 draws: how uneven does fair look?.

All 49 inclusion counts from 10,000,000 synthetic 6/49 draws, centered on N × 6/49 and scaled by the standard deviation for one prespecified label. The counts are dependent; this is not a simultaneous significance test.
Figure 1. All 49 inclusion counts from 10,000,000 synthetic 6/49 draws, centered on N × 6/49 and scaled by the standard deviation for one prespecified label. The counts are dependent; this is not a simultaneous significance test.
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