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Odds and tables

Lottery odds, honestly worked out

Every lottery ticket has the same tiny chance. Here is how tiny, how to work it out for any game, and a few comparisons that make the number feel real.

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By Stuck at Home, LLC · · 17 official formats checked

Where the big number comes from.

A lottery asks you to match a handful of numbers drawn from a drum. The odds against the jackpot are simply the number of different tickets that could be written. Choosing 6 numbers from 49, where order does not matter, can be done in 13,983,816 ways — so one ticket has a 1 in 13,983,816 chance. Add a separate bonus ball drawn from its own drum and you multiply: 5 from 69 gives 11,238,513 combinations; times 26 possible bonus balls makes 292,201,338.

The formula, for the curious

Ways to choose k from n = n! ÷ (k! × (n − k)!)

For 6 from 49: 49 × 48 × 47 × 46 × 45 × 44 ÷ (6 × 5 × 4 × 3 × 2 × 1) = 13,983,816. The calculator below does this with exact integer arithmetic for any format.

What a 1-in-292-million chance feels like.

Nobody can picture 292 million of anything, so here are three translations. It is roughly the chance of calling 28 coin flips in a row correctly. Buying one ticket every week, the average wait for a jackpot is about 5.6 million years. And a ticket every week for a 70-year adult life adds up to a lifetime chance of about 1 in 80,000. The calculator makes these for any game you enter.

None of this means you shouldn’t play; it means you should play for the fun of the ticket, not the plan.

Any game, any country

Work out the odds.

Enter how many numbers you pick and how many are in the drum. Add a bonus ball if the game has one.

Chance of the jackpot with one ticket

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    Enter a format to begin.

    Jackpot odds only; most games also pay smaller prizes at much shorter odds. The arithmetic is exact and runs in your browser.

    Official formats and jackpot oddsChecked on the operators’ own pages; the date is when we looked. Formats change — the source link is the final word.
    LotteryFormatJackpot oddsChecked
    PowerballUnited States · MUSL5 of 69 + 1 of 26Mon, Wed, Sat · since 7 Oct 20151 in 292,201,3382026-10-05
    Mega MillionsUnited States · Mega Millions consortium5 of 70 + 1 of 24Tue, Fri · since 8 Apr 20251 in 290,472,3362026-10-05
    EuroMillions9 European countries · National Lottery (UK) and partners5 of 50 + 2 of 12Tue, Fri · since 27 Sep 20161 in 139,838,1602026-10-05
    Eurojackpot19 European countries · German state lotteries (LOTTO.de)5 of 50 + 2 of 12Tue, Fri · since 25 Mar 20221 in 139,838,1602026-10-05
    Lotto (two-round format)United Kingdom · Allwyn / The National LotteryEach line now plays two draws of 6 from 59; the operator quotes 1 in 22,528,738 per line per draw. Six from 59 alone is 1 in 45,057,474.6 of 59Wed, Sat · since June 20261 in 22,528,7382026-10-05
    SuperEnalottoItaly · Sisal6 of 90Tue, Thu, Fri, Sat1 in 622,614,6302026-10-05
    LOTTO 6aus49Germany · Deutscher Lotto- und TotoblockThe Superzahl (0–9) is the last digit of the play slip, not chosen by the player.6 of 49 + 1 of 10Wed, Sat1 in 139,838,1602026-10-05
    LOTTO 6/49 (Classic Draw)Canada · OLG / Interprovincial Lottery Corp.The classic 6-of-49 match now pays a fixed $5 million; the rolling jackpot moved to a separate Gold Ball draw.6 of 49Wed, Sat · since 11 Sep 20221 in 13,983,8162026-10-05
    LOTOFrance · FDJ5 of 49 + 1 of 10Mon, Wed, Sat1 in 19,068,840computed from the format; the operator prints no exact figure2026-10-05
    Powerball (Australia)Australia · Lotterywest / The Lott7 of 35 + 1 of 20Thu1 in 134,490,4002026-10-05
    Oz LottoAustralia · Lotterywest / The Lott7 of 47Tue1 in 62,891,4992026-10-05
    Mega-SenaBrazil · CAIXA6 of 60Tue, Thu, Sun (per CAIXA, Oct 2026)1 in 50,063,8602026-10-05
    LOTO 6Japan · Takarakuji6 of 43Mon, Thu1 in 6,096,454computed from the format; the operator prints no exact figure2026-10-05
    LOTO 7Japan · Takarakuji7 of 37Fri1 in 10,295,472computed from the format; the operator prints no exact figure2026-10-05
    PowerBallSouth Africa · Sizekhaya (National Lottery)The PowerBall range shrank from 1–20 to 1–16 when the licence changed hands in June 2026.5 of 50 + 1 of 16Tue, Fri · since June 20261 in 33,900,160computed from the format; the operator prints no exact figure2026-10-05
    LottoDenmark · Danske Spil7 of 36Sat1 in 8,347,6802026-10-05
    LottoNorway · Norsk TippingNorsk Tipping prints the rounded figure “1 : 5.4 million per line”.7 of 34Sat1 in 5,379,616computed from the format; the operator prints no exact figure2026-10-05

    Things that don’t change the odds.

    • “Due” numbers. Balls have no memory. A number that hasn’t appeared for a year is exactly as likely next draw as one that came up last week.
    • “Hot” numbers. Same reason, other direction. Past frequency in a fair draw tells you nothing about the next one.
    • Quick pick versus your own numbers. Every combination is equally likely, full stop.
    • Patterns. 1-2-3-4-5-6 has exactly the same chance as any other line. It only looks less likely because we notice it.

    The one thing you can influence.

    You cannot change your chance of winning, but you can change how many people you would share with. Lines made of birthdays (1–31) and tidy patterns are popular, so when they win, the jackpot is split many ways. Picking less fashionable numbers — or letting the machine pick — doesn’t make winning more likely; it makes a win, if it comes, less crowded.

    Want a line anyway?

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