Lottery odds explained: how jackpot chances are calculated

Lottery odds are calculated by counting every line a game allows. Only one of those lines matches the draw, so the jackpot odds are 1 in that count. The count comes from one formula, the number of combinations C(n, k), multiplied across each pool you must match. That is why a US Powerball line has a 1 in 292,201,338 chance of the jackpot while an Irish Lotto line has 1 in 8,145,060: the pools are different sizes, and Powerball adds a second pool.

Nothing you do with your numbers changes those odds. Buying more lines, playing a smaller game or playing for longer changes your chances; picking "hot", "overdue" or "lucky" numbers does not. Below is the arithmetic, worked for games played in the USA, UK, Ireland, Australia, South Africa and Canada, plus what the odds mean if you play every week for decades.

The one formula behind every lottery

Choosing lottery numbers is a combination: the order doesn't matter, so 7-12-30 is the same pick as 30-7-12. The number of ways to choose k numbers from a pool of n is:

C(n, k) = n! ÷ (k! × (n − k)!)

In practice you never need huge factorials. Multiply k numbers counting down from n, then divide by 1 × 2 × … × k.

Worked example: a 6-from-45 game (Irish Lotto)

Since 3 September 2026, the Irish Lotto draws 6 numbers from 45. Australia's Saturday Lotto uses the same 6-from-45 matrix.

• Top: 45 × 44 × 43 × 42 × 41 × 40 = 5,864,443,200
• Bottom: 6 × 5 × 4 × 3 × 2 × 1 = 720
• Result: 5,864,443,200 ÷ 720 = 8,145,060

One Irish Lotto line therefore has a 1 in 8,145,060 chance of the jackpot, the same figure the Irish National Lottery prints in its 2026 rules book. The 47-ball game it replaced had C(47, 6) = 10,737,573 combinations, so removing two balls cut the number of possible lines by about 24%.

Worked example: adding a bonus pool (Powerball)

When you must also match a number from a second pool, multiply the two counts. US Powerball draws 5 white balls from 69 and 1 red Powerball from 26:

• White balls: C(69, 5) = (69 × 68 × 67 × 66 × 65) ÷ 120 = 11,238,513
• Red Powerball: C(26, 1) = 26
• Jackpot: 11,238,513 × 26 = 292,201,338

That matches Powerball's official prize chart. EuroMillions works the same way with two pools: C(50, 5) × C(12, 2) = 2,118,760 × 66 = 139,838,160.

Jackpot odds in popular lotteries

Every figure below was recomputed from the game's matrix and, where the operator publishes jackpot odds, checked against its page in October 2026.

For Thunderball, Saturday Lotto and Powerball Australia we did not find official jackpot odds on the pages we checked, so those rows are our own calculation from each game's matrix. South Africa's matrices come from secondary sources, because the official rule pages could not be loaded. The live table below, built from LottaGo's data, adds draw days and line prices; the same comparison is always on our page of jackpot odds of every lottery side by side.

Why bonus balls make such a big difference

A second pool multiplies the odds rather than adding to them, because every set of main numbers can be paired with every bonus choice.

South Africa's PowerBall and EuroMillions share the same main game, 5 from 50. PowerBall then asks for one ball from 16, multiplying 2,118,760 by 16. EuroMillions asks for two Lucky Stars from 12, multiplying it by 66. That single design choice makes the EuroMillions jackpot about 4.1 times harder to win.

Australia's Powerball shows the same effect. Seven numbers from 35 alone would be 1 in 6,724,520. The Powerball barrel of 20 turns that into 1 in 134,490,400.

Small changes to the bonus pool matter too. When Mega Millions cut its Mega Ball pool from 25 to 24 on 8 April 2025, its jackpot odds went from 12,103,014 × 25 = 302,575,350 to 290,472,336. South Africa's PowerBall cut its PowerBall pool from 20 to 16 in June 2026, moving its odds from 2,118,760 × 20 = 42,375,200 to 33,900,160.

Jackpot odds vs the odds of winning any prize

Operators also publish the odds of winning anything. These are far better, because they include the small prizes:

• Powerball (US): 1 in 24.87 overall; matching the Powerball alone pays $4 at 1 in 38.32.
• Mega Millions: 1 in 23.08 overall, according to the California Lottery.
• EuroMillions: 1 in 13 overall; 2 main numbers win a prize at 1 in 22.
• Irish Lotto: 1 in 25.4, or 1 in 8.5 with Lotto Plus.
• Daily Million: 1 in 28, or 1 in 14 with Daily Million Plus.
• Lotto 6/49 (Canada): 1 in 6.6.

You can calculate a lower tier yourself. To match 5 white balls in Powerball but miss the red ball, take the 11,238,513 white-ball combinations and multiply by 26 ÷ 25, because 25 of the 26 red balls are "wrong": 1 in 11,688,053.52. For a 6-from-45 game like Irish Lotto, exactly 3 matches with no bonus can happen in C(6, 3) × C(38, 3) = 20 × 8,436 = 168,720 ways, so the odds are 8,145,060 ÷ 168,720 ≈ 1 in 48.

What does "1 in 2.6" mean?

"1 in X" odds are a probability: 1 ÷ X. Odds of 1 in 2.6 mean a 1 ÷ 2.6 ≈ 38% chance. Bookmaker-style odds such as "2.6 to 1" are different: they compare losing outcomes with winning ones, so "2.6 to 1" means a 1 in 3.6 chance. Lottery operators almost always use the "1 in X" form.

What "1 in 292 million" means if you play for years

Odds per line are hard to feel. A better question is: what is my chance over a lifetime of play? The probability of winning at least once in n independent draws with one line each is:

P = 1 − (1 − p)ⁿ, where p = 1 ÷ (jackpot odds)

When p is tiny, this is very close to n × p. Here is what it gives for one line in every draw for 50 years:

Put another way: playing one Powerball line in every draw, you would expect to wait 292,201,338 ÷ 156 draws a year ≈ 1.87 million years for a jackpot. Playing every day is no shortcut either. One Daily Million panel in both daily draws for a full year is 730 draws, which gives a chance of about 1 in 4,470 of winning the €1 million at least once.

Can you improve your lottery odds?

Only in three ways, and each one costs money or prize size:

1. Buy more lines. Ten different Irish Lotto lines give 10 in 8,145,060, or 1 in 814,506. Your chance grows in a straight line with your spending.
2. Play a game with a smaller matrix. Daily Million (1 in 3,262,623) or Daily Lotto (1 in 376,992) are far easier than Powerball, with much smaller top prizes.
3. Play more draws. The table above shows how slowly that adds up.

What does not work: choosing hot, overdue or "lucky" numbers, avoiding numbers that came up last week, or using a "system" sold online. Every line in a game has the same odds. Quick picks and chosen numbers are equally likely to win; how you choose only affects how many other players might share a prize with you, which is the subject of our quick pick vs your own numbers guide.

Expected value: what a line is worth on average

Expected value multiplies each prize by its probability and adds them up. For the top prize alone it is simple. A Daily Million panel costs €1, the top prize is a fixed €1,000,000, and the odds are 1 in 3,262,623:

€1,000,000 ÷ 3,262,623 ≈ €0.31

So the top prize returns about 31 cents per €1 panel on average, and less when it is shared. The lower prizes add a little more, but lotteries are designed so that the total stays below the ticket price. That is not a reason to feel cheated; it is the price of entertainment, and a good reason to set a budget.

Why no number is ever "due"

The jackpot odds stay the same in every draw because a draw has no memory. The balls don't know which of them came up last week, so each draw starts from the full set again.

In US Powerball, each white ball has a 5 in 69 chance (about 7.2%) of being drawn, so on average it turns up every 69 ÷ 5 = 13.8 draws. Long gaps are still normal. The chance that a given ball misses 30 draws in a row is (64 ÷ 69)³⁰ ≈ 10%, so at any moment about seven of the 69 balls are typically on a gap of 30 draws or more. Believing that a long absence makes a number more likely is the gambler's fallacy.

LottaGo's statistics show this in real data. In Powerball, the six white balls drawn most often since Oct 7, 2015 are 21, 61, 64, 28, 23, and 27, over 1,418 draws. Each lottery page also runs a χ² uniformity test, where a p-value above 0.05 means the differences between numbers look like ordinary random variation, and a walk-forward backtest of the AI Agent's strategies. The strategies perform like random picks. Our guide on why no number is ever due walks through that backtest. For the two biggest US games side by side, see the Powerball vs Mega Millions comparison.

FAQ

How do you calculate lottery odds?

Count the possible lines with the combinations formula C(n, k) = n! ÷ (k! × (n − k)!) for each pool, then multiply the pools together. For a 6-from-45 game that is 8,145,060 lines, so the jackpot odds are 1 in 8,145,060. For Powerball, 11,238,513 white-ball combinations × 26 red balls = 1 in 292,201,338.

What lottery has the best odds of winning the jackpot?

Among the games in this guide, South Africa's Daily Lotto has the best jackpot odds at 1 in 376,992, followed by Ireland's Daily Million at 1 in 3,262,623. Better odds come with smaller top prizes: Daily Million pays a fixed €1 million. The odds comparison page ranks every lottery on LottaGo.

What are the odds of winning the lottery if you play every day?

It depends on the game, but they stay small. One Daily Million panel in both daily draws for a year (730 draws) gives about a 1 in 4,470 chance of winning the €1 million at least once. For US Powerball, even one line in every draw for 50 years gives only about a 1 in 37,462 chance.

Does buying more tickets improve my odds?

Yes, in proportion to the number of different lines you buy. Ten different lines give ten times the chance of one line, and cost ten times as much. In a 6-from-45 game that turns 1 in 8,145,060 into about 1 in 814,506. Buying the same line twice doesn't add any chance; it only doubles your share if it wins.

Do quick picks have better odds than chosen numbers?

No. A quick pick is one more line out of the same set of combinations, so its odds are identical to numbers you pick yourself. The only difference is how often other players choose the same numbers, which affects prize sharing, not your chance of winning.

How can you beat lotto odds?

You can't beat them, only change which odds you face. Every line in a draw has the same chance, so no pattern, number history or software can raise it. Playing a game with a smaller matrix, or buying more lines, are the only levers, and both cost money or prize size.

Can statistics improve my odds?

No. Statistics describe past draws, and every combination keeps the same chance in the next one. They are useful for curiosity and for checking that the results look random, not for predicting a draw.

Lotteries are for adults (18+); play for fun, with a budget you can afford to lose.