Room for ChanceThe science of chance

Free interactive tool

Lottery Draw Overlap Calculator

Calculate the exact distribution of shared labels between two independent k-of-n draws.

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

How Often Do Lottery Numbers Repeat Between Draws? explains the derivation and common interpretation errors. Compare it with the published Two fresh draws, one million times: how many numbers repeat?.

Observed category counts from 1,000,000 independent draw pairs beside exact hypergeometric expectations. Every category from zero to six is retained, including very rare categories with little or no observed mass.
Figure 1. Observed category counts from 1,000,000 independent draw pairs beside exact hypergeometric expectations. Every category from zero to six is retained, including very rare categories with little or no observed mass.
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