Lotofácil Odds Calculator

Lotofácil is Caixa’s 15-from-25 game: you mark fifteen numbers, Caixa draws fifteen numbers, and the jackpot is matching all fifteen. Defaults: Tickets 1, Ticket Price 2.50, Jackpot 1,500,000, Main Matches 15. There is no Bonus Matches field. Calculate: Jackpot Odds 1 in 3,268,760, which is 1/C(25,15). That is wildly softer than Mega-Sena’s 1 in 50 million. Jackpot EV at R$1.5 million is about −R$2.04 (expected jackpot return ≈R$0.46 against a R$2.50 stake). Do not confuse “easier jackpot” with “positive EV.”

Lotofácil is designed so you match many numbers. Set Main Matches to 11: This Prize Odds are about 1 in 11.4 for exactly eleven of the fifteen drawn numbers. Twelve is about 1 in 60; thirteen about 1 in 692; fourteen about 1 in 21,792; fifteen is the 3.27 million jackpot. Caixa typically pays from 11 acertos upward. The probability of at least 11 exact-or-better on a 15-number card is about 10.6%, roughly 1 in 9.4. That high hit rate is the product, not a glitch.

Tickets counts independent 15-number games. In the real product you may mark 16 to 20 numbers, which Caixa expands into C(k,15) simple games: 16 numbers → 16 games (R$40), 17 → 136 (R$340), 18 → 816 (R$2,040), 19 → 3,876 (R$9,690), 20 → 15,504 (R$38,760) at R$2.50 each. If you bought a 16-number volante, enter Tickets=16 at Price=2.50, not Tickets=1 at 40, unless you want EV on the bundle as one line. Those 16 games are not independent random 15-sets; they are all 15-subsets of your 16, so they are positively correlated on the jackpot. The engine treats tickets as independent, which slightly mis-models a system card’s joint hit probability.

Jackpot is the 15-acertos rateio in reais. Paste the concurso estimate. Price is R$2.50 per simple fifteen. Main Matches should stay in 11–15 if you care about paid bands; setting 8 will still compute a hypergeometric cell that Caixa does not pay as a jackpot.

This is not Mega-Sena and not Quina. Fifteen numbers drawn from twenty-five is a dense grid. Use Tickets for how many 15-sets you actually hold, including expanded 16–20 plays converted to C(k,15), then read Chance as 1−(1−p)^n under the independence assumption.

Lotofácil launched on 29 September 2003 as Caixa’s “easy lotto”: a 5×5 grid of 25 dezenas, fifteen marked by the player, fifteen drawn. The marketing was honest about frequency. Matching eleven is an everyday event on a long enough sample; matching fifteen is still millions-to-one, but millions-to-one in a 3.27 million space, not Mega-Sena’s 50 million. Brazilians treat it as the after-work volante at the casa lotérica, cheaper per hope than Mega-Sena’s R$5 sena and noisier with small prizes.

The option to mark 16, 17, 18, 19 or 20 numbers is the other half of the product. Each extra dezena explodes the number of 15-subsets combinatorially, which is why a 20-number play costs tens of thousands of reais. People still buy them, especially as bolões, because covering more 15-sets raises the chance of 15 acertos and of the 11–14 bands at the same time. This calculator will not expand the grid for you; it will multiply independent tickets. A correlated system is a different probability object.

There is no supplementary ball. Prize bands are 15, 14, 13, 12, 11 acertos (rules have been tweaked over the years; the combinatorics of 15/25 do not change). Teimosinha and surpresinha exist as in other Caixa games. Draws are frequent compared with Mega-Sena’s twice-weekly rhythm; check Caixa’s current calendar rather than assuming Wednesday/Saturday.

Culturally Lotofácil sits next to Mega-Sena and Quina on the same counter, which produces bad comparisons. “I always hit 11 on Lotofácil so Mega-Sena is due” is a category error: P(≥11)≈0.106 on a 15/25 card is designed, while P(sena)=1/50,063,860 is a different sport. This page exists to keep those denominators visible.

Use it to price a 15-acertos jackpot, to see why 11 acertos are cheap, and to convert a 16–20 number volante into C(k,15) tickets before talking about odds. Do not use it as Caixa’s official rateio table or as a claim that a particular grid pattern is hot.

The fifteen-acertos prize of Lotofácil is calculated on an inverted geometry that must not be mistaken for a six-from-forty-nine lottery. Both the player and the barrel choose fifteen-subsets of a twenty-five-set. The number of possible cards is C(25,15), and the symmetry C(25,15) = C(25,10) lets you expand the smaller factorial instead: 25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17 × 16 / 3,628,800 = 3,268,760. Jackpot probability is therefore 1 / 3,268,760, about 3.06 × 10^−7, or one in 3,268,760. You pick many numbers; the draw is also fifteen. That is why hit rates sit in a different universe from Mega-Sena's one in fifty million. Caixa launched this 5×5 grid on 29 September 2003 as the frequent-prize cousin on the same lotérica counter.

Hypergeometric overlap is symmetric: fifteen winning numbers in an urn of twenty-five, fifteen draws for the ticket, so P(|ticket ∩ draw| = m) = C(15,m) × C(10, 15−m) / 3,268,760, and m cannot fall below five because 15 − m cannot exceed the ten non-winning numbers. Matching all fifteen is the singleton 1 / 3,268,760. Matching fourteen is 15 × 10 / 3,268,760 = 150 / 3,268,760, about one in 21,792. Matching thirteen is 105 × 45 / 3,268,760 = 4,725 / 3,268,760, about one in 692. Matching twelve is 455 × 120 / 3,268,760 = 54,600 / 3,268,760, about one in 60. Matching eleven is 1,365 × 210 / 3,268,760 = 286,650 / 3,268,760, about one in 11.4. Summing the paid upper tail m = 11 through 15 gives about 346,126 / 3,268,760 ≈ 0.106, roughly one in 9.4. Among every game in this lecture set, those are the highest ordinary hit rates: the product is designed so eleven acertos are an everyday event on a long sample.

System cards that mark k > 15 numbers cover C(k,15) distinct fifteen-sets inside the k-set. The fifteen-acertos event occurs if the drawn fifteen-set sits inside the marked k, so the probability is C(k,15) / 3,268,760. Sixteen marked numbers cover sixteen games and jackpot chance 16 / 3,268,760 exactly, because those sixteen jackpot indicators are pairwise disjoint. Seventeen numbers cover 136 games; twenty numbers cover 15,504 games at brutal cost. Correlation appears in the eleven-to-fourteen bands, not in the fifteen-acertos indicator.

Expectation at the default R$2.50 simple stake and a $1.5 million fifteen-acertos pool is 1,500,000 / 3,268,760 − 2.50 ≈ 0.459 − 2.50 = −$2.041 per simple card. Jackpot-only breakeven with one winner is 2.50 × 3,268,760 = $8,171,900. Independent simple cards still give at-least-once chance 1 − (1 − p)^n. Lower 11–14 cash would lift total-game expected value; this jackpot lecture omits it on purpose so the 3.27 million denominator stays visible.

Assumptions: uniform fifteen-subsets of twenty-five, one fifteen-acertos winner, R$2.50 simple price, no Mega-Sena 6/60 and no Quina 5/80 reused here, and system cards converted by binomial expansion rather than treated as one magical ticket. Matching eleven on Lotofácil is not evidence that Mega-Sena is “due.” Different binomials, different sports.