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How lotteries work:
structure, probabilities, principles

This page provides structured information on how licensed lotteries operate in Australia. We look at the basics of how they work, how mathematical probabilities are calculated, and how results are generated in different formats.

How the mechanics work

Most Australian lotteries use a number combination system, in which several numbers are selected from a specific range. For example, in the Powerball format, participants select 7 numbers from 35, as well as one additional number from a separate range of 1–20.
The process is carried out according to a strictly regulated procedure:

• all numbers are selected at random from transparent lottery drums or through certified software;
• the equipment is tested before each draw;
• the process is verified by independent auditors;
• the results are recorded and published on official websites.

This ensures not only control but also traceability for anyone analyzing the systems or checking the archives.

How probabilities are calculated

The basics of combinatorial mathematics in lottery formats
The probability of any result is based on the formula for combinations without repetition. For example, for a 6 out of 45 format, the number of possible combinations is calculated as C(45,6) — that is 8,145,060 options. In two-field formats, such as Powerball, the total number of combinations is calculated as the product of the combinations from the first field and the number of options in the second field.

We do not evaluate probabilities in terms of profit, but provide only a mathematical basis for understanding the structure of each format.

the presence of bonus numbers;
the number of result levels;
the distribution of categories in the format (e.g., 7+1, 6+1, 6, etc.).

How results are generated

Verification, control, and transparency of distribution
The results of any licensed format in Australia are generated according to a clear algorithm:

the verification system includes the registration of each draw and the storage of an archive;
there are regulated categories into which results are classified depending on the match of the main and additional numbers;
each category is verified manually or through an automated system on a certified server.

Depending on the format, there can be between 3 and 9 result categories, which differ in terms of eligibility. These rules are published by the operators in advance and are binding. All results are publicly available via the websites of operators such as The Lott, NSW Lotteries, and Lotterywest.