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Lottery Odds Calculator

Calculates the odds of winning any lottery from the pool size and how many numbers are drawn, including every partial-match tier.

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Optional — the separate ball pool, as in Powerball. Leave at 0 if there is none.
Enter your figures and press Calculate.
In short Choosing 6 numbers from 49 gives 13,983,816 possible combinations, so the jackpot odds are 1 in 13,983,816. The count is C(49,6) — the number of ways to choose 6 things from 49 when the order does not matter — and every one of those combinations is exactly as likely as any other. That includes 1-2-3-4-5-6. Picking numbers that "look random" does not improve your chance of winning at all; it only changes how many people you would share a prize with, since consecutive runs and date-shaped picks are chosen by a great many players. Buying more tickets helps exactly in proportion and no more: ten tickets make it 1 in 1,398,382, which is still a number nobody can act on. At two draws a week with one ticket each, you would expect a jackpot roughly once every 134,460 years. Partial matches are a different calculation, and they use the same hypergeometric distribution the card page runs on — matching 3 of 6 from 49 is about 1 in 57, which is why smaller prizes feel achievable while the top one never arrives. One thing this page does not answer: whether a ticket is worth buying. That depends on the prize and how many others play, and it is the expected-value calculator's question, not this one's.

How to use the Lottery Odds Calculator

  1. Enter your figures in the input fields.
  2. The result updates as you type, together with the full working.
  3. Check the breakdown table to see exactly how the number was reached.

About the Lottery Odds Calculator

Jackpot and partial-match odds for any pick-N-from-M lottery.

What people use it for

  • Comparing the odds of different lotteries.
  • Seeing what buying more tickets actually changes.
  • Working out the odds of a smaller prize tier.

Details

6 from 491 in 13,983,816
Matching 3 of 6about 1 in 57
Every combinationequally likely, including 1-2-3-4-5-6
Ten ticketsexactly ten times the chance, and no more
One ticket, two draws a weeka jackpot about every 134,460 years

The maths behind it

This tool uses Combinations = C(pool, picks), multiplied by C(bonus pool, bonus picks) when there is a separate ball; the jackpot chance is one divided by that. Every intermediate value is shown on screen, so the result can be checked by hand.

For random numbers rather than odds, the lottery number generator produces a quick pick. This page only counts.

Where this tool stops

The tiers assume prizes depend only on how many main numbers you match. Real lotteries add bonus-ball rules, rollovers and shared jackpots, so use the jackpot figure to compare games and the operator's table for the rest.

Frequently asked questions

Do some numbers come up more often?
Over enough draws every number appears about equally. Apparent hot and cold streaks are what randomness looks like, and a physical draw has no memory of previous results.
Should I avoid 1-2-3-4-5-6?
Not for your chance of winning — it is exactly as likely as any other combination. Avoid it because a lot of people pick patterns, so you would be more likely to share the prize.
Does a syndicate improve the odds?
It multiplies your chance of a win by the number of tickets and divides the prize by the number of members. The expected value is unchanged; what changes is the shape of the outcome.
Why are the smaller prizes so much easier?
Because matching a few numbers has many more ways to happen. That is the hypergeometric distribution, and the table shows every tier from the same calculation.
Do I need an account to use the Lottery Odds Calculator?
There is no cost and no cap. The Lottery Odds Calculator is not a demo of a paid product, so nothing is held back or watermarked.
Is what I paste into the Lottery Odds Calculator stored?
No. The Lottery Odds Calculator runs entirely in your browser using JavaScript. Because the work happens locally, the tool also keeps working if your connection drops, and closing the tab is all it takes to discard everything.
What formula does the Lottery Odds Calculator use?
It uses Combinations = C(pool, picks), multiplied by C(bonus pool, bonus picks) when there is a separate ball; the jackpot chance is one divided by that. The full working is printed under the result, so you can follow every step rather than trusting a black box.
Give me a worked example.
Enter 6 from 49 and the Lottery Odds Calculator returns 1 in 13,983,816.
What do people use the Lottery Odds Calculator for most?
Typical uses: comparing the odds of different lotteries. Seeing what buying more tickets actually changes. Working out the odds of a smaller prize tier. It is built for exactly those cases rather than being a general-purpose tool with this bolted on.
When is the Lottery Odds Calculator not the right tool?
The tiers assume prizes depend only on how many main numbers you match. Real lotteries add bonus-ball rules, rollovers and shared jackpots, so use the jackpot figure to compare games and the operator's table for the rest. Knowing where a tool stops being trustworthy matters more than the cases where it works.
Which values should I know?
6 from 49 is 1 in 13,983,816. Matching 3 of 6 is about 1 in 57. Every combination is equally likely, including 1-2-3-4-5-6. These are printed on the page itself, so you do not have to take them on trust.
How precise is the result?
The calculation runs in double precision and the result is shown to ten significant figures, so converting a value and converting it back returns the original. What is displayed is rounded for readability; what is copied is not.

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