Lottery Odds Explained: Maths of the Draw

The odds are just counting.

UK Lotto asks you to match 6 numbers from 59. There are 45,057,474 ways to choose six, and only one of them wins the jackpot. Every draw starts afresh, whatever came up last week.

Updated 14 October 2026 · 5 sources

Every draw is independent
No number is due
Spend only what you can lose
Clear maths, clear head

Compare the odds

THE SHORT ANSWER

Long odds,
no shortcuts.

Three things the maths makes clear.
None of them is a tip for playing.

THE ODDS

Choose 6 from 59

Counting every possible set of six from 59 gives 45,057,474 combinations. That is where the published jackpot odds come from.

Compare the prizes

HOT NUMBERS

The balls have no memory

Draws are independent, yet research finds players still chase past winners or wait for numbers they think are due. Neither changes the odds.

Why it happens

SUPPORT

Help is free, day or night

If gambling is causing harm, the National Gambling Helpline is free on 0808 8020 133, 24 hours a day, and NHS clinics take self-referrals.

Where to get help

Two mugs of tea on a kitchen table with a notebook open between them, as two people talk, seen only from the hands — AI-generated image, not a photograph of a real person or place.

IF IT STOPS BEING FUN

Support is free,
and it works.

The NHS lists signs worth noticing, such as betting more than you can afford, chasing losses or borrowing to gamble, and several places to turn.

Take the NHS self-check
Nine short questions on the NHS gambling addiction page. A score of 8 or more suggests gambling-related harm.
Call the helpline
The National Gambling Helpline, run by GamCare, is free on 0808 8020 133, 24 hours a day, 7 days a week.
Refer yourself to a clinic
In England you can self-refer to an NHS gambling clinic near you, or ask your GP what is available locally.
Support for those close to you
The NHS lists GamAnon and GamFam for family and friends, and GambleAware among the charities offering help.

TWO NUMBERS WORTH KNOWING

What you face,
and where it goes.

One figure on the jackpot odds,
one on where the money has gone since 1994.

1 in 45million

Chance of matching all six on one line

The published odds for the Lotto jackpot are 1 in 45,057,474 per line. The odds of winning any prize are 1 in 9.3.

JACKPOT ODDS · THE NATIONAL LOTTERY

£102bn+

Paid out in prizes since 1994

More than £102 billion has gone to players in prizes. Alongside it, £52 billion went to good causes, £22 billion in Lottery Duty and more than £8 billion to retailers.

PRIZES SINCE 1994 · THE NATIONAL LOTTERY

That split is the expected-value story in one line: part of every ticket goes to good causes, tax and retailers, so on average players get back less in prizes than they spend.

A QUICK ODDS CHECK

How likely is
each Lotto prize?

Pick a prize tier to see its published odds for one £2 Lotto line. The bar shows how likely that result is.

Odds from The National Lottery's Lotto game procedures. This is information about probability, not a reason to play.

Odds check

Choose a resultAny prize at allMatch 3Match 4Match 5 + bonusJackpot (match 6)

Any prize at all1 in 9.3

The most common outcome that pays anything. It still means around eight lines in nine win nothing.

Match 31 in 96.2

Roughly one line in a hundred matches three numbers. A Gresham College lecture shows there are 468,520 ways to match exactly three.

Match 41 in 2,180

Already a long shot: more than twenty times less likely than matching three.

Match 5 + bonus1 in 7,509,579

One in seven and a half million. Each line is far more likely to win nothing than to get this close.

Jackpot (match 6)1 in 45,057,474

One combination out of every possible set of six from 59. Covering every line would cost more than £90 million at £2 each.

Source: The National Lottery, Lotto game procedures (odds per line). Combination count from Professor Sarah Hart's Gresham College lecture, Lottery-winning mathematics.

A hand writing a probability fraction in pencil on squared paper beside a calculator on a wooden desk — AI-generated image, not a photograph of a real person or place.

HOT AND COLD NUMBERS

No number is
ever due.

Lottery draws are independent: the machine does not know what came up last week. Yet a 2020 study in Management Science found players both chase recent winners (the hot-hand fallacy) and avoid them (the gambler's fallacy).

The odds of any particular set of six stay exactly the same. Popular picks only change how many people might share a prize: a Gresham College lecture notes that 10,000 people pick 1, 2, 3, 4, 5, 6 every week.

In conversation

Questions people ask

What are the odds of winning the Lotto jackpot?

The National Lottery publishes the jackpot odds as 1 in 45,057,474 per line. That is the number of ways to choose 6 numbers from 59.

Are some numbers luckier than others?

No. Each draw is independent, so every set of six has the same chance. Research shows people still treat past results as a guide, in both directions.

What does expected value mean for a lottery?

It is the average you would get back per ticket over a huge number of plays. Because part of the money goes to good causes, Lottery Duty and retailers, prizes add up to less than what players spend.

Does buying more lines help?

Each extra line adds one more combination out of 45,057,474. Covering every combination would cost more than £90 million at £2 a line.

Where can I get help with gambling?

The National Gambling Helpline is free on 0808 8020 133, any time. In England you can self-refer to an NHS gambling clinic, and the NHS website lists charities including GambleAware and Gamblers Anonymous.

Sources

Each figure on this page comes from the sources below.

Six balls,
45 million ways.