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Lottery Odds Calculator

Find your chance of winning the lottery.

How it is calculated

A lottery draw where the order of the numbers does not matter is counted with combinations: C(n, k) = n! / (k! × (n − k)!), where n is the total count of balls in the pool and k is how many numbers you pick. The tool computes it with the multiplicative form, so large factorials are never formed, and shows the number of possible combinations and the odds of one ticket winning as 1 in that number. Both inputs must be whole numbers, k cannot be greater than n, and n is limited to 90. The result is the chance of matching all the main numbers only. Bonus balls, lower prizes, games with a separate pool (such as a star or power number) and tickets with several lines are not included.

Worked example

In a game where you pick 6 numbers from 49, n = 49 and k = 6. C(49, 6) = (49 × 48 × 47 × 46 × 45 × 44) / (6 × 5 × 4 × 3 × 2 × 1) = 10,068,347,520 / 720 = 13,983,816 combinations. A single ticket therefore has odds of 1 : 13,983,816 of matching all six numbers. Buying 10 different tickets improves the chance to 10 in 13,983,816, which is still roughly 1 in 1.4 million.

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Common mistakes

  • Applying the result to a game that has a second pool (bonus or star number); the odds of the full game are the product of both pools.
  • Entering the number of tickets or the numbers already drawn instead of the pool size and picks.
  • Believing that numbers which have not come up recently are "due"; each draw is independent.
  • Confusing odds for the jackpot with odds of winning any prize, which are much better but not given here.
  • Using a game where order matters, such as a three-digit game in which 123 differs from 321, where the count is a different formula.

About this calculator

This calculator uses the combinations formula (n choose k, written C(n,k) = n!/(k!(n-k)!)) to work out how many possible number combinations exist in a lottery, and inverts that figure to give the odds of any single ticket matching the winning numbers. It covers only the main numbers: bonus balls, games with a separate pool (such as a star or power number) and tickets with several lines are not included, so jackpot odds in such games are even longer than shown.

It's used by lottery players comparing the odds of different games (the main-number odds of a 6/49 draw versus a 5/70 draw, for example), and by anyone wanting to understand, in concrete terms, just how unlikely a jackpot win actually is — often expressed as 1 in tens or hundreds of millions.

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Comments (1)

  • Editorial team

    Check the result against a known game: picking 6 numbers from 49 gives 13,983,816 combinations, so one ticket has a 1 in 13,983,816 chance of the jackpot. Which numbers you choose does not change that, and ten different tickets simply give ten times the chance of a still very small figure. Prize tiers, bonus balls and separate pools are not included. Tell us which lottery format you are checking and how it is drawn.

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