Quina Odds Calculator

Quina is Caixa’s 5-from-80 daily lottery. Defaults: Tickets 1, Ticket Price 2.50, Jackpot 5,000,000, Main Matches 5. No Bonus Matches field: five dezenas, no extra ball. Calculate: Jackpot Odds 1 in 24,040,016, which is 1/C(80,5). Jackpot EV at R$5 million is about −R$2.29 (expected sena-equivalent return ≈R$0.21 against R$2.50). Main Matches=5 is the quina itself — Caixa uses the same word for the game and for hitting all five.

Drop Main Matches to 4 to price a quadra: about 1 in 64,107. Main Matches=3 is a terno, about 1 in 866. Main Matches=2 is a duque, about 1 in 36. Those names are Caixa’s; the numbers are hypergeometric. Daily cadence means you can burn through Tickets=7 in a week of one-game nights without noticing. Set Tickets to how many independent 5-number games you hold on the concurso you are modelling, not how many days you have been playing in your life.

Price is R$2.50 for a simple five. Marking 6 dezenas is C(6,5)=6 simple games (R$15); 7 is C(7,5)=21, and so on, up to Caixa’s current maximum. Convert those to Tickets at R$2.50 each. Jackpot is the estimated 5-acertos rateio. Paste the concurso figure. Daily games have smaller typical jackpots than Mega-Sena; using Mega-Sena’s R$20 million default here would be a lie about Quina’s pool.

A counterintuitive check: Mega-Sena is 6/60 with C(60,6)=50,063,860, Quina is 5/80 with C(80,5)=24,040,016. The 80-ball field looks harsher; the jackpot combination count is actually easier than Mega-Sena. What is hard is the sparse 5-hit on a huge urn, plus a R$2.50 price that still cannot be justified by a R$5 million daily pool. EV does not care that eighty numbers “feel” worse than sixty.

Read Jackpot Odds as C(80,5), This Prize Odds as the Main Matches cell, Chance as 1−(1−p)^n, EV as n·(J·p−price). Do not paste Lotofácil’s 15/25 or Mega-Sena’s 6/60 into this form. Quina since 1994 is five from eighty, daily, Caixa.

Quina started on 13 March 1994, two years before Mega-Sena, as Caixa’s five-number game on an 80-dezena volante. It is the daily habit: casas lotéricas stamp a cheap R$2.50 ticket on a weekday evening when nobody is waiting for Saturday’s Mega-Sena. The name is the prize: quina means five hits. Lower bands — quadra, terno, duque — keep the counter noisy. There is no Powerball and no supplementary. This calculator’s missing Bonus Matches field is historically correct.

Because the game is daily, folklore about dezenas atrasadas runs hotter than on twice-weekly Mega-Sena. The barrel does not remember Tuesday when it spins on Wednesday. C(80,5) is 24,040,016 every concurso. Teimosinha repeats the same five numbers across days; that is independent trials with identical p, which the Tickets field can mimic only if you are modelling one draw’s card count, not a superstition about accumulated destiny.

Compared with Mega-Sena, Quina is combinatorially easier at the top prize (24 million vs 50 million) and culturally smaller in jackpot. People still call it “harder” because eighty numbers look endless and because five correct dezenas on that field feel sparse. Both intuitions are about psychology; the binomial coefficient is the referee. Lotofácil, sitting on the same shelf, is a different geometry entirely: 15/25 with a 3.27 million jackpot and a designed 11-acertos drip.

Bolões on Quina exist but are less mythic than Mega da Virada. Rateio is pari-mutuel. Multiple winners on a modest daily pool hurt more, percentage-wise, than on a Virada monster. This EV assumes one winner. Use Caixa’s published estimate as Jackpot, not a fantasy migrated from Mega-Sena.

Use this page to keep 5/80 arithmetic honest, to convert 6–N dezena cards into C(N,5) simple games, and to stop ranking Caixa products by “how big the urn looks.” Eighty balls and five draws is 24 million tickets. Sixty balls and six draws is 50 million. The daily R$2.50 line is still a negative jackpot-EV product at a R$5 million default.

The five-acertos prize of Quina is calculated as five unordered dezenas from eighty, Caixa's daily game since 13 March 1994, two years older than Mega-Sena and combinatorially a different object. The binomial coefficient C(80,5) equals 80 × 79 × 78 × 77 × 76 / 120. The falling product is 2,884,801,920; divide by 120 to obtain 24,040,016. Jackpot probability is 1 / 24,040,016, about 4.16 × 10^−8, or one in 24,040,016. Eighty balls look endless, yet C(80,5) is smaller than Mega-Sena's C(60,6) = 50,063,860. Psychology says “harder because the urn is huge”; the binomial referee says the five-hit on eighty is easier at the top prize than the six-hit on sixty. No extra ball multiplies this identity.

Hypergeometric scores on five draws from eighty are P(exactly m) = C(5,m) × C(75, 5−m) / 24,040,016. A quadra, four of five, is 5 × 75 / 24,040,016 = 375 / 24,040,016, about one in 64,107. A terno, three of five, is 10 × 2,775 / 24,040,016 = 27,750 / 24,040,016, about one in 866. A duque, two of five, is 10 × 67,525 / 24,040,016 = 675,250 / 24,040,016, about one in 36. Exactly one is unpaid as a jackpot and still common. Those names are Caixa's; the numbers are hypergeometric.

Independent simple games on one concurso give at-least-once chance 1 − (1 − p)^n. Seven nightly games in a week sit near 2.91 × 10^−7. A six-dezena card covers C(6,5) = 6 of the five-subsets inside those six numbers; if the five drawn dezenas all lie in your six, you hit, and the six jackpot indicators are disjoint, so chance equals 6p exactly. A seven-dezena card covers 21 five-sets; a ten-dezena card covers 252.

Expectation uses the default R$2.50 stake and a $5 million advertised five-acertos pool: 5,000,000 / 24,040,016 − 2.50 ≈ 0.208 − 2.50 = −$2.292 per simple game. Ten games: about −$22.92. Jackpot-only breakeven with one winner is 2.50 × 24,040,016 = $60,100,040, far above a typical daily estimate. Expected jackpot return at the default is about twenty-one cents. Daily cadence lets a player burn through tickets without noticing; the formula does not accumulate destiny across concursos. Teimosinha is independent trials with identical p.

Assumptions: uniform five-subsets of eighty, independent simple tickets unless a multiple-dezena card was expanded, one winner, no terno or quadra cash in the jackpot expectation, R$2.50 price, and no Lotofácil 15/25 geometry pasted into C(80,5). The slogan that Quina is harder than Mega-Sena fails the binomial test; the economic hardness is a small daily pool against a $2.50 stake, not eighty versus sixty.