How many combinations are possible in a standard lottery?
A standard 6-from-49 draw has 13,983,816 possible combinations — just under 14 million. The number itself is easy to write down and impossible to feel. What’s worth understanding is how fast it grows when a game adds even one ball — which is exactly the lever the big jackpots pull.
How long are the odds — for any lottery?
Defaults to a standard 6-from-49 draw. Pick a real game, or drag the sliders to build your own.
That’s about as likely as flipping a coin 24 times and getting heads every single time. Buy one line every draw and you’d expect to hit the jackpot roughly once every 134,460 years.
Covering every possible line at $2 each would cost $27,967,632. Order never matters in a standard draw, so each set of numbers counts once.
Where 13,983,816 comes from
“Standard” here means the classic format used in maths classes and in dozens of real games: pick six numbers from a pool of 49. To count the possibilities you use the combination formula — 49 choices for the first number, 48 for the second, down to 44 for the sixth, then divide by the number of ways six numbers can be ordered.
That division is the whole trick. There are 10,068,347,520 ordered ways to draw six balls, but a lottery ticket wins no matter what order they come out. Dividing by 720 (that’s 6 × 5 × 4 × 3 × 2 × 1) collapses all those orderings into one, leaving 13,983,816 distinct combinations.
Combinations, not permutations
This is the single idea people most often get wrong. If order mattered — if 1-2-3-4-5-6 were different from 6-5-4-3-2-1 — the odds would be hundreds of times longer. Because it doesn’t, every set of six numbers is one ticket and one chance. Picking “lucky” patterns, birthdays or last week’s numbers changes nothing about your odds; it only changes how many other people you’d have to share a jackpot with.
One ball changes everything
Lotteries tune their odds by adjusting the pool. Move from 6/49 to 6/59 — as the UK National Lottery did in 2015 — and combinations jump from 13,983,816 to 45,057,474, more than tripling. The point isn’t to make winning harder for its own sake: longer odds mean the jackpot rolls over more often, climbs higher, and sells more tickets. The eye-watering headline jackpots are a direct product of the longer odds.
The American games push this furthest by bolting on a second pool. Powerball asks for 5 from 69 and1 Powerball from 26: that’s 11,238,513 × 26 = 292,201,338 combinations. Mega Millions, after its April 2025 redesign to 5 from 70 plus 1 Mega Ball from 24, sits at 290,472,336. Try them in the calculator above — the bonus pool is what tips a game from millions into hundreds of millions.
The man who bought every combination
Here’s the catch buried in the maths: if a game is small enough and its jackpot grows large enough, the combinations can cost less than the prize. Stefan Mandel, a Romanian-born economist, won lotteries fourteen times by exploiting exactly that.
His most famous hit was the 1992 Virginia Lottery, a 6-from-44 game with just 7,059,052 combinations. When the jackpot rolled past $27 million — comfortably more than the cost of every line — his syndicate raised the funds and set out to buy them all, printing and lodging millions of tickets in days. They won, and lawmakers across the world rewrote the rules to stop bulk-buying afterwards. The lesson is in the calculator: shrink the pool and the impossible becomes merely expensive.
The number isn’t found — it’s designed
It’s tempting to treat a lottery’s odds as a fact of nature, like the speed of light. They’re not. Every combination count is a decision made in a meeting: how big a pool, how many balls, whether to add a second wheel. Operators steer that number to a sweet spot where the odds feel impossible enough to produce giant rollovers, but the dream still feels purchasable for the price of a coffee.
Which is why the most useful thing the calculator does isn’t telling you that you’ll lose — you knew that. It’s showing you, ball by ball, that the “impossible” figure was tuned by someone, and could have landed almost anywhere.
Odds quiz — 5 questions
How many combinations are in a standard 6-from-49 lottery?
Sources
- Combination figures computed directly from the binomial coefficient C(n,k); verified against published jackpot odds.
- Powerball.com — game matrix (5/69 + 1/26) and 1 in 292,201,338 jackpot odds.
- Mega Millions / Maryland Lottery — post-April-2025 matrix (5/70 + 1/24), 1 in 290,472,336.
- UK National Lottery — 6-from-59 format adopted in 2015 (45,057,474 combinations).
- Reporting on Stefan Mandel and the 1992 Virginia Lottery (6/44, 7,059,052 combinations).
Related
So the standard answer is 13,983,816 — but the real answer is that the number is a dial, and the only people who ever beat it found a game where someone had set the dial too low.