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How long should the gap between number appearances be?
Under independent draws, waiting time to another appearance follows a geometric distribution. A long current gap does not increase the probability in the next draw.
Table of contents
Hit probability
For one Lotto number, the appearance probability in a draw is .
Geometric distribution
If G is the number of draws up to and including the next appearance, . Mean waiting time is 1/p, about 8.17 draws.
Example
The probability that a number is absent from 10 consecutive draws is . Such a gap is compatible with randomness.
Memorylessness
After ten draws without that number, its probability in the eleventh draw remains 6/49. The geometric distribution is memoryless.
Comparing with data
The analysis compares empirical gap lengths with expected frequencies. Assess the full distribution rather than a single record.
Limitations
The model assumes constant p and independent draws. An incomplete history or a pool-size change requires separating periods.
Frequently asked questions
Is an overdue number more likely next?
No, when draws are independent and rules have not changed.
Why can a record gap be long?
Many numbers over many draws create many opportunities for a rare event to occur.
Check it on real draw data
Choose a draw range in Lotto Lab PRO and compare the observed result with the random model.
Related Lotto Lab PRO guides
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