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Lottery Odds Calculator

Choose a game or enter your own lottery format. The calculator gives the exact probability of matching a chosen number of balls — as “1 in X”, as a percentage and in words.

Picking a game fills in its format. Changing any number below switches to “Custom lottery”.

How many numbers the balls are drawn from, e.g. 49.

How many numbers the machine draws, e.g. 6 in Lotto or 20 in Keno.

How many numbers you mark on one line of the ticket.

Exactly how many of your numbers should be among the drawn ones.

Some lotteries draw a second, separate set of numbers. The two pools are independent, so their probabilities multiply.

Odds: 1 in 13,983,816

Probability
In words
What these numbers mean
  • Result for the settings above: 1 in 13,983,816. It updates as soon as any field changes.
  • We compute it from the formula shown below — not from a prediction model and not from draw history.
  • The result describes a single draw. It does not accumulate over consecutive games: the chance is the same every time.
  • The calculator computes, it does not advise. It does not point to numbers and does not say how much to play.

The numbers come from the formula and the values you typed above. They are not a forecast — no calculator changes the probability of a single draw.

How to use this page
  1. Fill in the fields in the form above — the result recomputes at once, with no page reload.
  2. Under the result you will find the interpretation scale, if the calculator has one: it says which range your value fell into.
  3. The formula we use is shown lower on this page — you can check the arithmetic yourself.
  4. To compute the same for another game or variant, change it in the select field — prices and pools update automatically.

What this page does not do: It does not point to numbers to play and does not predict a draw — every draw is independent of the previous ones.

Further reading

Formula

P(m) = C(D, m) × C(N − D, P − m) ÷ C(N, P) · two pools: P = P₁ × P₂
N is the pool size, D the numbers drawn, P the numbers you pick and m the exact number of matches. C(n, k) is the binomial coefficient. This is the hypergeometric distribution: it counts the tickets with exactly m matches and divides them by all possible tickets. With two independent pools, as in Eurojackpot, the two probabilities are multiplied.

The calculator counts, it does not guess. For a given lottery format it works out how many of all possible tickets have exactly the number of matches you ask about, and divides that by the number of all possible tickets. In Lotto 6/49 there are 13,983,816 possible tickets and exactly one of them matches all six numbers — hence 1 in 13,983,816.

“Exactly m matches” is not the same as “at least m matches”. Three matches in Lotto (about 1 in 56.66) means exactly three: tickets with four, five or six matches are counted separately. The Keno odds calculator and the hypergeometric distribution calculator show the whole table at once — they work for any single pool, not only for Keno.

Eurojackpot has two separate pools: 5 numbers from 50 and 2 Euro numbers from 12. They are drawn independently, so the odds of the jackpot are C(50, 5) × C(12, 2) = 2,118,760 × 66 = 139,838,160 to one.

Odds describe one ticket in one draw. Past draws do not change them — every draw starts from scratch — and no system, statistic or “lucky” number makes a single ticket more likely to win. To see how the total chance grows with more tickets or more draws, use the multiple tickets calculator.

The presets use the Polish game formats shown on this site. “Custom lottery” lets you enter any other format; we do not add presets for foreign games whose current rules we have not verified.

Read more

Frequently asked questions

What are the odds of winning the Lotto jackpot?

In Lotto 6/49 the odds of matching all six numbers are exactly 1 in 13,983,816 — the number of ways to choose 6 numbers out of 49.

Why does the calculator say “exactly” and not “at least”?

Because the hypergeometric formula gives the probability of one exact number of matches. For “at least three” add up the rows for three, four, five and six matches — the hypergeometric distribution calculator does this for you as P(X ≥ k).

Can I calculate the odds for a lottery from my country?

Yes. Choose “Custom lottery” and enter the pool size and how many numbers are drawn and picked. If the lottery draws an extra number from a separate pool, switch on the second pool.

See also

← All calculators

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