El Gordo Odds Calculator

El Gordo in this calculator is El Gordo de la Primitiva, SELAE's Sunday 5/54 plus clave, not the Sorteo Extraordinario de Navidad. Default Ticket Price is 1.50 euros, default Jackpot 10,000,000. You pick five mains from 54 and the game attaches a clave digit 0–9 (bonus pool 10, one drawn). Tickets is the number of independent Sunday apuestas. If you arrived here looking for the Christmas décimo raffle, stop: that product has no 5/54 matrix, no clave in this sense, and odds this engine cannot describe.

Tickets: one line is one 5-subset of 54 plus one clave. Ten lines are ten independent pairs. Jackpot probability is 1/C(54,5) × 1/10 = 1/31,625,100. That is easier than Primitiva's 6+Reintegro (1 in 139.8 million) and harder than Bonoloto's plain 6/49 (1 in 14.0 million). Sunday-only frequency means Tickets should stay a single-draw count unless you are aggregating many weeks on purpose; if you do aggregate, you are mixing independent Sundays and the 1−(1−p)^n formula still applies across weeks.

Ticket Price is 1.50, higher than Primitiva's euro and triple Bonoloto. It is the Sunday premium for a different matrix. Do not enter 20 euros because you are thinking of a Navidad décimo. That is a different stake for a different game. Price only affects EV.

Jackpot defaults to 10 million euros, a plausible Gordo de la Primitiva bote order of magnitude. Navidad's "Gordo" prize is a different number on a raffle table. Paste SELAE's Sunday advertisement when you have it. The engine assumes an unshared lump sum.

Main Matches is 0–5 on the 54-ball grid. Bonus Matches is the clave: 1 hit, 0 miss. Top prize is 5 and 1. Five mains without clave is a lower top-adjacent class. Real El Gordo de la Primitiva also uses a complementary number for some rungs; this bonus field is the clave 0–9, matching bonusPool 10. Setting Bonus Matches as if it were a complementary from the remaining 49 will give you the wrong 1/10 versus 1/49 story.

Read Jackpot Odds (1 in 31,625,100), This Prize Odds for your (k, clave) pair, multi-ticket chances, Jackpot EV, Expected Jackpot Return. At 10 million euros and 1.50 euros a line, jackpot × p ≈ 0.316, EV ≈ −1.184 euros per ticket. The Christmas raffle has no such p. If your question is "what are my odds of the Navidad Gordo," this page is the wrong tool and the right answer is the décimo's 1/100,000-class raffle arithmetic, not C(54,5).

El Gordo de la Primitiva launched on 23 October 1993 as SELAE's Sunday companion to La Primitiva. The nickname "El Gordo" is a branding collision with the Sorteo Extraordinario de Navidad, the December raffle whose first prize is also called El Gordo and whose décimos are a Spanish cultural season of their own. This calculator is the 1993 numbered game: five from 54, clave 0–9, 1.50 euros, Sundays. It is not a tombola of printed tickets. It is not 22 December. SEO confusion between the two is the main reason the about text has to open with a negation.

The matrix is unusual in the SELAE family. Primitiva and Bonoloto are 6/49. El Gordo de la Primitiva is 5/54 plus a ten-way clave. C(54,5) = 3,162,510 main combinations; times ten claves, 31,625,100 jackpot combinations. Five-from-54 is closer in spirit to a mid-pool transnational game than to 6/49, but the Sunday monopoly inside Spain keeps it from competing head-to-head with Thursday Primitiva. Players who "always do El Gordo" often mean Navidad in December and this game the other 51 Sundays; those are not the same habit.

Operator is SELAE throughout. Prize fund, category table, complementary ball, and clave refund-style rules are Spanish state-lottery policy. This model uses clave as the bonus ball (pool 10, drawn 1) because that is the jackpot digit. Complementary-number classes exist in the real table and are not Bonus Matches. Joker-style add-ons that appear in the broader SELAE ticket culture are out of scope.

Compared with Bonoloto, you pay triple per line, you play once a week instead of six times, and your jackpot odds are about 2.26 times harder than Bonoloto's 6/49 (31.6 million versus 14.0 million) while the default jackpot here is ten times Bonoloto's default million. Compared with Primitiva, you play a different polynomial: 5/54×1/10 versus 6/49×1/10, 31.6 million versus 139.8 million, Sunday versus Thursday/Saturday, 1.50 versus 1.00 euro. None of those comparisons involve Navidad.

1993 sits in the same SELAE expansion era as Bonoloto (1988) and the modern Primitiva (1985). The brand borrowed the word Gordo because it already meant a fat prize in Spanish lottery speech. Decades later the homonym still sends English-language searchers to the wrong calculator. Use this page for the Sunday 5/54. Use a raffle model for Navidad. Use Primitiva for 6/49 plus Reintegro. The clave is a 1-from-10 object like Reintegro and like German Superzahl; the mains are not 6/49. That is the whole product.

El Gordo de la Primitiva is SELAE's Sunday 5/54 with a clave digit, not the Christmas raffle that borrows the same nickname. The Sorteo Extraordinario de Navidad is a printed-décimo lottery whose first prize is also called El Gordo; it has no 5/54 drum. The weekly game, launched in 1993, asks for five mains from fifty-four and a clave from 0 to 9. Jackpot probability is therefore 1/[C(54,5)×C(10,1)]. The main coefficient is 54×53×52×51×50 / 120 = 3,162,510. Times ten claves: 31,625,100. A line hits with probability 1/31,625,100. That is easier than Primitiva's 6/49 times Reintegro (1 in 139,838,160) and harder than Bonoloto's plain 6/49 (1 in 13,983,816). Stake is 1.50 euros, the Sunday premium for a different polynomial.

Combinatorial construction is two independent uniform draws. Five unordered mains from fifty-four, then one clave from ten. Order of the five mains does not matter, so permutations 54 P 5 would overcount by 5! = 120; dividing recovers C(54,5). The clave is not a sixth main ball drawn from the remaining forty-nine. Mixing those stories replaces a factor of 10 with a factor of 49 and invents a game SELAE does not sell.

Hypergeometric mass on the five mains is C(5,k)×C(49,5−k)/C(54,5). Three mains: C(5,3)×C(49,2) = 10×1,176 = 11,760, about 1 in 269 before the clave. Miss the clave and multiply by 9/10, about 1 in 299. Four mains plus clave: [C(5,4)×C(49,1)/3,162,510]×(1/10) = 245/31,625,100, about 1 in 129,082. Five mains without clave: 9/31,625,100. Five mains with clave: the jackpot. Complementary-number classes in the live table are a sequential extra ball, not the 1-from-10 clave.

Independent Sundays do not accumulate pity. Fifty weeks of one line give chance 1−(1−p)^50 ≈ 50/31,625,100, about 0.000158 percent. Expected jackpot count is n p. A syndicate chasing expected count one must buy about 31.6 million lines at 1.50 euros, more than 47 million euros of stake, to chase a 10 million euro working bote.

Expected value against the jackpot alone is n×(J/31,625,100 − 1.50). Ten million over 31.6 million is about 31.6 cents of jackpot expectation against 1.50 euros, so about −1.184 euros per apuesta. That 32 cents looks fatter than Primitiva's default jackpot expectation because the denominator is smaller relative to a 10 million headline, but the stake is also higher. Navidad arithmetic is a uniform draw over printed numbers, typically a 20 euro décimo in a series structure that has nothing to do with C(54,5). Feeding a 400 million Christmas headline into this 5/54 model keeps p at 1/31,625,100 and prints nonsense. Keep Sunday, clave, 1.50 euros, SELAE 1993.