Irish Lotto Odds Calculator

Use this Irish Lotto odds calculator when you want 6-from-47 jackpot math for the Irish National Lottery, not the Plus game and not a UK Lotto 6/59 comparison. Set Tickets to the number of standard Lotto lines you will play on a given Wednesday or Saturday draw. Each ticket is one unordered 6-number combination from 1 to 47. If you play a system bet that expands into multiple combinations, enter the expanded line count, not “one system slip.” The chance output assumes independent distinct combinations; duplicate lines do not help.

Price defaults to 2 because a standard Irish Lotto line is €2. If you also bought Lotto Plus 1 / Plus 2, do not fold those add-on euros into this Price field unless you are doing a rough all-in cost check—those are separate prize tables with the same numbers but different funds. For a clean jackpot EV on the main Lotto, keep Price at €2 per main line. Jackpot is the advertised Lotto jackpot in euros. Irish jackpots start lower than EuroMillions and can roll; paste the figure from the National Lottery before the draw. The EV result uses only that top prize.

Main Matches is the lever for lower tiers on the six main balls. Leave it at 6 for jackpot-style matching. Set it to 5 to see the hypergeometric odds of exactly five of your six numbers landing in the draw, which in the real Irish game is the Match 5 band (the live prize table further splits Match 5 with and without the bonus ball). This calculator does not expose a Bonus Matches field because the engine instance is a pure 6/47 jackpot model: there is no bonusPool in the tool definition. The bonus ball that appears on Irish TV for Match 5 + bonus and similar tiers is real, but it is not an input here.

Read Jackpot Odds as 1 in C(47,6) for a single line. This Prize Odds follows whatever Main Matches you picked. Jackpot Chance is 1 − (1 − p)^tickets, the probability that at least one of your lines is the jackpot combination. Jackpot EV is tickets × (jackpot × p − price). If you are comparing a €2 Saturday line against a pile of extra lines because the jackpot “looks overdue,” raise Tickets and watch Chance crawl while EV goes more negative. That is the intended use: quantify the Irish 6/47, keep Plus and bonus-ball folklore out of the jackpot equation unless you are looking at Main Matches for a lower tier.

Irish National Lottery Lotto is a 6-from-47 game drawn on Wednesday and Saturday. The operator is the Irish National Lottery (Premier Lotteries Ireland as licensee in the current era). A standard line costs €2. The format is close to classic European 6/49 lotteries but one ball friendlier: 47 numbers instead of 49, which cuts the combination count from 13,983,816 to 10,737,573. That is still a wall. It is not “easy,” and it is not the UK National Lottery Lotto, which moved to 6/59 in 2015.

The live Irish prize table uses a bonus ball drawn from the remaining numbers to differentiate some Match 5 prizes and to fill lower tiers. This calculator deliberately models the jackpot as 6/47 without a bonus-pool field. Matching six of six on the main balls is the jackpot event; the bonus ball is irrelevant to that top tier. If you came here because a TV graphic showed “bonus ball,” use Main Matches to explore exact-k hits on the six, and remember that official Match 5 + bonus odds are a refinement this page does not claim to reprint.

Lotto Plus is a parallel game that reuses your main numbers against a separate draw for a smaller extra stake. Plus is not EuroMillions and not this calculator. EuroMillions is the Tuesday/Friday 5/50 plus two stars product sold in Ireland alongside Lotto; people confuse the two because both are on Irish retail terminals. If your question is Irish Lotto jackpot odds, you want 6/47. If your question is Euromillions, leave this page.

Irish Lotto jackpots can roll and are sometimes described in the press as life-changing without being American-scale. The tool’s default jackpot is a few million euros, which is the right order of magnitude for a typical advertised pot, not a record-chasing headline. History, rollovers, and Must-Be-Won style marketing do not change C(47,6). Use this page when you want the National Lottery’s main 6/47 math in one place: tickets, euro price, advertised jackpot, and a match-count slider that stays honest about what is and is not in the model.

Irish Lotto under Premier Lotteries Ireland is six from forty-seven, a wall just shy of classic 6/49 and unrelated to the UK National Lottery's 6/59. Jackpot probability in this model is 1/C(47,6) with no second pool in the denominator. C(47,6) = 47×46×45×44×43×42 / 720 = 10,737,573, so p = 1/10,737,573. Matching six of six mains is the top event; the television bonus ball drawn from the remaining forty-one splits some Match-5 classes in the live table and does not multiply this jackpot. Lotto Plus 1 and Plus 2 reuse the same numbers against other draws for extra stakes; they are other prize funds, not extra factors on C(47,6). Standard line is two euros, Wednesday and Saturday.

Computing C(47,6) by the falling product 47×46×45×44×43×42 / 720 yields 10,737,573. Two fewer balls than 6/49 cuts the combination count from 13,983,816 to this 10.74 million, about a 23 percent friendlier jackpot, still a lottery. Pascal's recurrence would rebuild the same coefficient from C(46,5) and C(46,6); either route is combination counting, not a permutation of six ordered balls.

Hypergeometric exact m is C(6,m)×C(41,6−m)/C(47,6). Five mains: 6×41 = 246, about 1 in 43,649. Four mains: 15×820 = 12,300, about 1 in 873. Three mains: 20×C(41,3) = 20×10,660 = 213,200, about 1 in 50.4. Those are exact-m figures, not at-least-m, and they do not attach the official bonus-ball split for Match 5 plus bonus.

Independent lines give 1−(1−p)^n. Five lines ≈ 4.66×10^−7; fifty lines ≈ 4.66×10^−6. Covering the matrix at two euros costs about 21.48 million euros and still risks a split. EuroMillions sold at the same Irish terminals is 5/50 plus two stars; that is a different polynomial.

Expected jackpot value is n×(J/10,737,573 − 2). Jackpot-only breakeven sits at 2×10,737,573 = 21,475,146 euros advertised, ignoring splits and lower ranks. Two and a half million over 10.74 million is about 23.3 cents against two euros, so about −1.767 per line. Ten lines ≈ −17.67. Plus stakes and bonus-ball tiers sit outside this identity. Keep forty-seven, keep six, keep PLC's domestic Lotto off both UK 6/59 and EuroMillions stars.