Lottery probability describes the chance of a defined outcome under a set of draw rules. It is different from the size of a prize, the chance of receiving any payment, or the expected financial return. A large headline prize does not make a matching result more likely.
The examples below are mathematical models. They are not current product offers or recommendations about buying entries.
Why combinations matter
In a number draw where order does not matter, the relevant count is a combination. The formula, explained in OpenStax’s combinations chapter, is C(n,k) = n! / [k!(n−k)!]. Here n is the pool size, k is the number selected, and the exclamation mark denotes a factorial.
For example, selecting the same six numbers in a different order does not create a different set. Counting every possible ordering as a separate winning result would overcount the outcomes.
The calculation assumes distinct numbers drawn without replacement, equally likely sets and a rule requiring an exact set match. If order matters, numbers can repeat, or an additional selection is required, the model changes.
Two hypothetical draw structures
For a six-from-49 model, C(49,6) equals 13,983,816. If exactly one equally likely set is drawn, a specified six-number set has probability 1 in 13,983,816 of matching it completely.
For six from 59, the count is C(59,6) = 45,057,474. This illustrates how increasing the pool changes the number of possible sets even though the count drawn remains six.
| Illustrative model | Possible sets | Probability of an exact match |
|---|---|---|
| 6 distinct numbers from 49 | 13,983,816 | 1 in 13,983,816 |
| 6 distinct numbers from 59 | 45,057,474 | 1 in 45,057,474 |
These results do not establish the rules or odds of every game with a similar name. Separate number pools, additional balls and secondary prize conditions need their own calculation.
Any prize, a top prize and a profit
The probability of any prize combines the qualifying outcomes for all relevant prize tiers. It cannot be substituted for the probability of matching every required number. Nor does receiving a payment necessarily mean making a profit.
In a hypothetical £5 entry returning £2, the net result is a £3 loss. A payment equal to the entry cost only breaks even on that entry. Earlier spending remains part of the overall financial result.
The maximum displayed prize also says nothing by itself about whether a payment is shared, fixed, conditional or subject to a cap. Those are questions about prize rules rather than combinations alone.
Independence and the idea that a result is due
Where successive draws are independent and use the same model, past results do not change the probability of a specified set in the next draw. A pattern appearing unusual does not make it impossible, and a number absent from recent draws is not thereby owed an appearance.
Independence between separate draws should not be confused with independence within a draw. Drawing balls without replacement changes the remaining pool during that draw. This is why the counting assumptions must be stated explicitly.
Raffles use a different denominator
In a simple raffle with one uniformly selected winning entry among N eligible entries, a specified entry has probability 1/N. The total eligible entry count is therefore essential to that model.
For a fixed number-selection model, additional entries held by other people do not change the probability that a specified set is drawn. Depending on the rules, they can affect how a shared prize is divided. Neither observation provides a guaranteed route to profit.
Expected return and information standards
Expected return depends on both probabilities and payments. In a hypothetical £1-entry model with a one-in-ten chance of £5 and otherwise no payment, expected return is 50p and expected net loss is 50p. An individual entry still returns either £5 or nothing under those assumptions.
The Gambling Commission’s RTS 3 standard addresses rules, prize information and relevant chances of winning for products within scope. A general article cannot replace the applicable draw rules.
Gambling protection and support
Probability does not remove the risk of financial harm. GAMSTOP provides online self-exclusion, and GamCare provides information and support. Self-exclusion protections should be maintained. Seeking a different game or software provider is not a substitute for them.
Reviewed 22 October 2026. Numerical examples are illustrative calculations under the assumptions stated above.