Lottery Odds Calculator

What this generator does

Works out, for a lottery of any shape you describe, the exact probability of every possible match count — not just the jackpot. It gives each as a fraction in lowest terms, as a '1 in N' figure, and as the count of distinct tickets that would produce that result. Because the arithmetic is done in exact integers rather than floating point, the jackpot line is the true value and not a rounded one, which matters when the denominators run to eight digits and beyond.

How to use this tool

1. Set how many numbers are in the pool and how many are drawn.
2. Add a bonus-ball pool if the game you are checking has one.
3. Press Calculate.
4. Read the table: every possible match count, with exact odds and the number of tickets that would produce it.

Understanding the controls

Numbers in the pool

How many balls the game has to choose from. This is the number that dominates everything: going from 49 to 59 balls makes the jackpot roughly four times harder while the ticket price stays the same.

Numbers drawn

How many are picked. Drawing more numbers from the same pool makes the jackpot harder but the lower tiers easier, which is how games are tuned to feel winnable while paying out less.

Bonus pool

Some games draw extra balls from a second, separate pool. Where that applies, the two draws are independent and their probabilities multiply, which is why adding a small bonus pool has such a large effect on the top prize.

Worked examples

6 from 49

Jackpot 1 in 13,983,816. Match 3: 1 in 57. Match 4: 1 in 1,033.

5 from 59

Jackpot 1 in 5,006,386 — before any bonus ball is taken into account.

Why a syndicate helps less than expected

Ten tickets in a 6-from-49 game is 1 in 1,398,382 — still far beyond picturing.

The tier gap

In 6-from-49, matching three is about 245,000 times more likely than matching six.

Common use cases

• Checking what a lottery's smaller prize tiers are actually worth against their odds
• Comparing two lottery formats before deciding either is worth playing
• Teaching the hypergeometric distribution with a case everybody has heard of
• Settling an argument about whether a syndicate meaningfully changes the odds
• Understanding why 'one in fourteen million' is a number nobody can picture

How this generator works

A lottery is a hypergeometric distribution, and the sum is the same one every time: to match exactly k numbers you must choose k of the drawn balls and the remaining picks from the balls that were not drawn. That gives C(drawn, k) x C(pool − drawn, drawn − k) favourable tickets out of C(pool, drawn) total. The calculation is carried out entirely in arbitrary-precision integers, which matters more than it sounds — C(49,6) is 13,983,816 and the intermediate values in a naive factorial approach are far larger than any double can hold exactly. The tiers are also checked against each other: every match count from zero upward must sum to exactly one, and the tool computes that sum as an exact fraction rather than trusting it.

Randomness and fairness

Nothing here is random. It is pure arithmetic over the format you describe, so the same inputs always give the same table, and every figure is derived rather than sampled. No simulation is used anywhere — a simulation would only ever approximate numbers that can be computed exactly.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

• Every ball is equally likely and draws are independent of one another, which is what a properly run lottery guarantees.
• A ticket is a set of distinct numbers, so ordering does not matter and no number appears twice.

Limitations and good to know

• It calculates odds, not value. Whether a ticket is worth buying depends on the prize pool, how many people share it and the tax treatment, none of which this knows.
• Rollovers change prize sizes but never change odds. A bigger jackpot is exactly as hard to win as a small one.
• Games with unusual mechanics — multipliers, guaranteed raffle codes, second-chance draws — are outside what a hypergeometric model describes.
• The odds shown are per ticket for a single draw. Playing the same numbers every week does not accumulate any advantage, and the tool has nothing to say about strategies because there are none.

Common mistakes

Believing some numbers are 'due'

Balls have no memory. A number that has not appeared for a year is exactly as likely as any other on the next draw, and the odds table here does not change no matter what happened previously.

Thinking buying more tickets improves the odds proportionally in any meaningful sense

It does improve them proportionally, and that is the problem: ten tickets in a 14-million game leaves you at one in 1.4 million. The multiplication is real and the result is still negligible.

Comparing jackpot odds between games and stopping there

Look at the full tier table. Two games with similar jackpot odds can differ enormously in how often they pay anything at all, which is what actually determines the experience of playing.

Practical tips

• Compare the '1 in N' figures rather than the percentages. Nobody has intuition for 0.0000000715, and everybody has some for 'one in fourteen million'.
• Check the lowest winning tier first. That number tells you how often a game pays anything, which is a better description of what playing feels like than the jackpot.
• If you are teaching this, work the match-3 case by hand first. It is small enough to check and it makes the general formula obvious.

Troubleshooting

My country's lottery odds do not match

Check whether the game includes a bonus ball drawn from a separate pool, or a supplementary draw. Those change the published odds substantially and need the bonus pool set here.

The numbers are too large to compare

Use the ratio column, which expresses each tier against the jackpot. It answers 'how much easier is this' directly, which raw odds do not.

Privacy and your data

The only things entered are numbers describing a lottery format, and they never leave your browser. Nothing is stored, nothing is placed in the page address, and analytics records only that the calculator was used — never the format you checked.

Frequently asked questions

Do the odds change if the jackpot rolls over?

No. A rollover changes only the prize. The chance of any given ticket matching is fixed by the format — pool size and how many balls are drawn — and nothing about the prize pool enters that calculation.

Are the figures exact or rounded?

Exact. Everything is computed in arbitrary-precision integers and shown as a fraction in lowest terms alongside the '1 in N' form. The only rounding is in that final phrase, which is rounded to a whole number for readability.

Does picking unusual numbers improve anything?

Not your chance of winning, which is identical for every combination. It can improve your chance of not sharing a jackpot, because many people pick birthdays and consecutive runs — but that affects the size of a win, not the likelihood of one.