The Odds of Winning the Lottery

Where a jackpot odds figure comes from

Every draw game on this site is the same question in different clothing: how many different tickets could you buy? Answer that and you have the jackpot odds, because exactly one of those tickets matches the draw.

The count is a binomial coefficient, written C(n, k) and read as "n choose k": the number of ways to pick k things from n when order does not matter. The formula is C(n, k) = n! / (k! × (n − k)!), though nobody computes it that way. In practice you multiply k descending terms and divide by k factorial. For a 6-of-49 game: (49 × 48 × 47 × 46 × 45 × 44) ÷ (6 × 5 × 4 × 3 × 2 × 1) = 13,983,816.

That is the whole calculation. No history of past draws enters it, no ball weight, no jackpot size. The matrix is the odds.

Powerball, worked out line by line

Powerball asks for five numbers from 1 to 69 plus one Powerball from a separate pool of 1 to 26. Two independent choices, so the counts multiply.

C(69, 5) = (69 × 68 × 67 × 66 × 65) ÷ 120 = 11,238,513. Multiply by the 26 possible Powerballs and you get 292,201,338 distinct tickets. That figure matches the one Powerball publishes on its own prize chart, which is a useful sanity check: if your arithmetic disagrees with the operator, one of you has the matrix wrong.

Mega Millions works the same way with different sizes. C(70, 5) = 12,103,014, times 24 Mega Balls, gives 290,472,336. EuroMillions asks for five from 50 and two Lucky Stars from 12: C(50, 5) = 2,118,760, times C(12, 2) = 66, gives 139,838,160.

Why the figures vary so wildly between games

Adding a second pool is the cheapest way to make a jackpot harder to win, which is why almost every big game has one. Powerball's second pool multiplies the difficulty by 26 without asking players to pick a single extra main number.

Growing the main pool is the other lever, and it bites harder than people expect. The UK Lotto moved from 6-of-49 to 6-of-59 in 2015. Ten extra balls took the jackpot odds from 1 in 13,983,816 to 1 in 45,057,474, more than tripling the difficulty for a change that looks small on the ticket. Allwyn ran the same lever backwards in June 2026, leaving the 59 balls alone and putting every line into two rounds a night, which brought the published per-line figure to 1 in 22,528,738.

Smaller national games sit at the friendly end. A 5-of-36 daily draw has C(36, 5) = 376,992 combinations, which is roughly 775 times easier than Powerball. The prize is smaller in about the same proportion, and that is not a coincidence: the payout is engineered against the matrix.

Overall odds are a different, much kinder number

Operators advertise two figures and they get confused constantly. Jackpot odds are your chance of the top prize. Overall odds are your chance of winning anything, including the small fixed prizes that pay less than the ticket cost.

Powerball's overall odds are about 1 in 24.87 on a $2 play. That sounds encouraging until you notice what most of those wins are: matching the Powerball alone returns $4 on a $2 ticket, and matching one number plus the Powerball also returns $4. A large share of "winning" tickets hand you back roughly what you spent.

EuroMillions quotes overall odds near 1 in 13, and the same caveat applies. Neither number tells you anything about expected return. For that you need the prize at each tier and the odds of each tier, which is what a full division table gives you.

Comparisons that actually help

Numbers past a few million stop meaning anything, so it helps to convert them into something a body can feel. Every comparison below is a division or a logarithm of the odds themselves, so you can check each one on a calculator.

A 1 in 292,201,338 chance is about the same as calling 28 consecutive coin flips correctly, because 2 to the power of 28.1 is roughly 292 million. It is also one specific second chosen out of 9.3 years, since a year holds 31,557,600 seconds.

Buying one line for every Powerball draw, three draws a week, you would expect one jackpot after roughly 1.9 million years of continuous play. The comparison is not there to be depressing. It is there because a ticket is a small purchase of anticipation, and the anticipation is easier to enjoy honestly when the price of it is clear.

What the odds do not depend on

Nothing about how you choose your numbers moves any of these figures. A quick pick, your children's birthdays, last week's winning line and 1-2-3-4-5-6 all sit on the same probability. This follows from the arithmetic above rather than from anyone's opinion: the count of possible tickets never mentions which ticket you hold.

Frequency tables, overdue-number lists and hot-and-cold analysis do not enter the calculation either. They describe what already happened, and a ball has no memory of it.

One thing genuinely does vary with your choices, and it is not the odds. If you pick numbers that thousands of other players also pick, you are more likely to share a jackpot rather than take it whole. That changes what you would win, never whether you win.

What the odds leave out

Odds tell you how often a ticket wins. They say nothing about what it wins, and both halves are needed before a ticket can be valued.

Take Powerball's eight fixed prize tiers and multiply each prize by its published probability. The $1,000,000 tier contributes about 8.6 cents, the $50,000 tier about 5.5 cents, and the two $4 tiers together about 14.8 cents. Add all eight and a $2 ticket carries roughly 32 cents of expected value from its fixed prizes. Everything else a ticket is worth has to come from the jackpot, which is why the same $2 buys a very different proposition in a minimum draw and a record rollover.

Two further deductions apply before an advertised jackpot becomes money. The headline figure is usually the annuity total paid over decades; the cash option is materially smaller. Both are taxable, and the rate depends on where you live.

Then there is the deduction nobody advertises. A jackpot is shared between everyone holding the winning line, and ticket sales rise steeply as jackpots grow, so the probability of splitting is highest in exactly the draws that look most worth entering. We follow that calculation to its conclusion in does buying more tickets help.

None of this changes the odds. It changes what a given set of odds is worth, which is the number people actually care about and the one least often published next to the prize.

Looking up a specific game

We keep the full arithmetic for every game we cover on the lottery odds hub, including each prize division, the exact number of tickets that land in it, and the overall chance of any prize. Those tables are computed from each game's own matrix with exact integer arithmetic, not copied from a marketing page.

If a figure there ever disagrees with the operator's published rules, the operator is right and we want to know. Write to hello@vibenumbers.com and we will correct it.