UK Lotto Odds Calculator

This is the UK National Lottery Lotto, the Saturday-and-Wednesday 6-from-59 game, not EuroMillions, not Thunderball, not Set For Life. A line is £2. The operator was Camelot for decades; Allwyn has run the National Lottery since February 2024. The matrix changed from 6/49 to 6/59 in October 2015. This calculator models the jackpot as a pure 6/59 combination. The real drawing also produces a bonus ball used for some lower tiers, but this tool has no Bonus Matches field and no bonus pool—bonusPool is none—because the jackpot is six mains, not 5+bonus. Do not look for a Bonus Matches box; it is not on this form.

Tickets is how many distinct £2 Lotto boards you have for one draw. Five boards is Tickets = 5. A Lucky Dip and a picked slip are equivalent. Ticket Price defaults to 2. Leave it at £2. Lotto Extra / Lotto Plus style add-ons, if offered in a given era, are separate games; do not fold them into price unless you want them charged against jackpot EV. Jackpot is the advertised UK Lotto jackpot in pounds. It rolls when nobody hits six. Must Be Won draws are scheduled after a long roll or on special dates; on those nights the top prize may be shared down the tiers if there is no 6-match. Type the advertised jackpot for the night you are pricing. Defaults sit at £5,000,000 as a working mid-roll figure, not a promise of the Saturday start amount.

Main Matches is 0–6, because six balls are drawn from 59. Leave it at 6 for jackpot odds. Set it to 5 to see the odds of matching five mains (in the real game that tier also cares about the bonus ball, which this model does not separate). Set it to 3 for the famous £30-class hit. There is no Bonus Matches input. If you need a bonus-ball-aware lower tier, this is the wrong calculator; the odds you will get for Main Matches = 5 are “exactly five of the six mains,” which lumps together what the official table splits into 5+bonus versus 5-no-bonus.

Calculate. Jackpot Odds is 1 in C(59,6) = 1 in 45,057,474. This Prize Odds is the single-pool hypergeometric for your Main Matches. Jackpot Chance = 1−(1−p)^tickets. This Prize Chance uses the prize hypergeometric. Jackpot EV = tickets×(jackpot×jackpotP − price). At £5 million and £2, one ticket’s jackpot-only EV is 5e6/45,057,474 − 2 ≈ £0.111 − £2 = −£1.89. A fat rollover of £20 million still only yields about −£1.56 jackpot-only. Expected Jackpot Return is tickets×jackpot×jackpotP. Must Be Won rolldowns are not modelled as extra EV; they change who gets paid, not C(59,6).

UK Lotto is the original National Lottery flagship, launched in 1994 as 6/49 and redrawn as 6/59 from 10 October 2015. Camelot operated the licence until Allwyn took over in February 2024. Draws are Wednesday and Saturday. A line is £2. The jackpot is matching all six main numbers. A seventh bonus ball is drawn for lower-tier settlement (notably the 5+bonus prize), but it is not a second drum you pick on the playslip the way a Powerball or Lucky Star is. You choose six numbers from 59; the machine draws six plus a bonus. This calculator therefore omits bonus pool fields and prices C(59,6) as the jackpot denominator.

Rollovers are the drama. If nobody hits six, the jackpot rolls. After a designated number of rolls, or on marketed Must Be Won Saturdays, the top prize is guaranteed to be paid out somehow—shared among the highest winning tier if there is no six-match. Those events produce the famous “somebody has to win” headlines without changing the 1 in 45,057,474 chance of actually matching six. Historical 6/49 jackpots (the 1990s £20 million-plus rollovers, the 1996-era records) are not comparable to 6/59 combinatorics. C(49,6) = 13,983,816; C(59,6) = 45,057,474. The 2015 change more than tripled the jackpot difficulty and is why Saturday rollovers can now sit in ranges that 6/49 hit faster.

Allwyn’s National Lottery also sells EuroMillions, Thunderball, Set For Life and others. UK Lotto is the one that is six-from-fifty-nine, twice weekly, £2, no chosen bonus ball. Thunderball is 5/39 + Thunderball 1/14 at £1 with a fixed £500,000 top prize. EuroMillions is 5/50 + 2 stars from 12 at £2.50. Do not paste a EuroMillions £215 million sterling equivalent into this Jackpot field and expect UK Lotto odds. Operators are the same licence holder; games are not.

Famous UK Lotto moments are rollover Saturdays, Must Be Won nights, and the cultural memory of the 6/49 years (the first millionaires, the rollover craze). Under 6/59 the jackpot is simply harder. Prize tiers below six are a mix of fixed and pari-mutuel amounts that have been redesigned more than once; this page does not reproduce the current official table. It exists to answer “what are my 6/59 jackpot odds and jackpot-only EV at this advertised figure,” plus hypergeometric odds for matching exactly m of the six mains.

Use this calculator when the playslip is yellow Lotto, the pool is 59, and you picked six numbers. If you picked five plus a Thunderball, leave. If you picked five plus two stars, that is EuroMillions. If you are still quoting 1 in 14 million, you are remembering 6/49; the machine has not drawn that game since 2015.

United Kingdom Lotto jackpot arithmetic is a single binomial coefficient, not a two-drum product. Allwyn has run the National Lottery since February 2024 after Camelot’s long licence; the matrix since 10 October 2015 is six from fifty-nine. Matching all six mains wins the jackpot. A studio bonus ball is drawn for lower-tier settlement, notably five-plus-bonus, but you do not pick it, and it does not multiply the jackpot formula. Probability of the top prize is 1/C(59,6) = 1/45,057,474. A line costs two pounds. The working advertised figure here is five million pounds, a mid-roll, not a Must Be Won special.

Expand the combination. C(59,6) = 59×58×57×56×55×54 / 720 = 45,057,474. There is no extra C(bonus, r) in the jackpot identity. Pre-2015 Lotto was 6/49: C(49,6) = 13,983,816, more than three times easier. Mixing a 1990s rollover memory with 6/59 odds is the standard British category error. The 2015 enlargement is why Saturday banners can sit longer than they did under forty-nine.

Partial prizes on this model are single-pool hypergeometric. Exactly k mains among six drawn from fifty-nine: C(6,k)×C(53,6−k)/C(59,6). Matching five: C(6,5)×C(53,1)/45,057,474 = 318/45,057,474, about one in 141,690. The official table then splits those five-match tickets using the leftover bonus ball; this lecture does not. Matching three: C(6,3)×C(53,3)/45,057,474 with C(53,3) = 23,426, so 20×23,426 = 468,520 favourable, about one in 96, the mass-market consolation. Matching six remains one in 45,057,474.

Ten Lucky Dips: 1−(1−1/45,057,474)^10 ≈ 10/45,057,474, about one in 4,505,747. A year of one Saturday board is fifty-two independent drawings, not fifty-two lines on one night. Must Be Won nights make someone get paid, possibly below six mains; they do not raise your probability of matching six. Expected jackpot pounds at five million are 5,000,000/45,057,474 ≈ 0.11 against two pounds, so jackpot-only expectation is about minus 1.89 a line. A twenty million rollover still yields about minus 1.56. Break-even on the top prize alone would need about 90.1 million advertised, which this game does not reach.

Thunderball, EuroMillions, and Set For Life share a retailer and not a polynomial. Keep six from fifty-nine, two pounds, no chosen bonus in the jackpot product. Allwyn versus Camelot does not change C(59,6).