Mega-Sena Odds Calculator

Mega-Sena is Caixa Econômica Federal’s flagship 6-from-60 draw. Defaults: Tickets 1, Ticket Price 5 (reais), Jackpot 20,000,000, Main Matches 6. There is no Bonus Matches field: sena is six dezenas, not a Powerball. Calculate and you should see Jackpot Odds 1 in 50,063,860, which is 1/C(60,6). Jackpot Chance on one volante is about 2.00×10^−8. Jackpot EV at the R$20 million default is about −R$4.60, because 20,000,000/50,063,860≈R$0.40 of expected jackpot against a R$5 stake. Expected Jackpot Return is those 40 centavos.

Raise Tickets to 10 if you filled ten independent games on the same concurso. Chance becomes 1−(1−p)^10≈2.00×10^−7. EV scales to about −R$46.00. A bolão that splits 100 games should enter 100 so the book’s expected loss is visible before anyone talks about “quase ganhou.” Price stays R$5 per simple game. If you marked a sena of 7 dezenas, that is C(7,6)=7 simple games: put 7 in Tickets at R$5, not 1 at R$35, unless you deliberately want EV on the bundle as a single outlay.

Jackpot is the estimated rateio for sena in reais. Paste the current concurso estimate from Caixa, especially on Mega da Virada, when the pool is a different species of headline. A R$20 million Wednesday is ordinary; a New Year special in the hundreds of millions of reais is when jackpot-only EV can approach or cross zero before you account for tens of thousands of shared winners. This engine assumes one winner. Mega da Virada’s social reality is the opposite: many teimosinhas and bolões chasing the same six numbers.

Main Matches defaults to 6 (sena). Set it to 5 to price a quina: about 1 in 154,518 for exactly five of the six drawn dezenas. Set 4 for a quadra, about 1 in 2,332. Those are hypergeometric cells, not Caixa’s published prize names with extras. Caixa also sells teimosinha (repeat the same game across concursos) and surpresinha (machine pick). Repeat is still independent trials: ten consecutive Wednesdays is Tickets=10 against ten draws only if you model one draw at a time or treat them as n=10 with the same p.

Read Jackpot Odds as the sena combination count, This Prize Odds as the Main Matches cell, Chance as 1−(1−p)^n for sena, and EV as n·(J·p−price) in reais. Do not add Lotofácil or Quina rules into this form. Mega-Sena is 6/60, R$5, Wednesday and Saturday, sometimes extra concursos, since 1996.

Mega-Sena began in March 1996 as Caixa’s modern national jackpot, sold at casas lotéricas with the familiar green volante. You mark six dezenas from 01 to 60. Draws are typically Wednesday and Saturday; Caixa adds extra concursos around holidays and always builds Mega da Virada for 31 December, the New Year’s Eve draw that has become a Brazilian ritual on a scale that ordinary Wednesdays cannot touch. The product is not a franchise of US Mega Millions. It is a 6/60 pari-mutuel sena whose rateio is a percentage of sales, rolled when nobody hits six.

Casas lotéricas are the social infrastructure: fluorescent light, printed volantes, bolões taped to the counter, teimosinha boxes ticked so the same game rides several concursos. Palpites come from dreams, licence plates, children’s ages, and statistical folklore about dezenas atrasadas. None of that changes C(60,6)=50,063,860. The calculator exists to put that number next to the R$5 price and the advertised sena, including when a TV presenter is shouting about Mega da Virada.

Prize tiers below sena are culturally named: quina (5), quadra (4), and sometimes extra lower bands depending on the current rules. This page’s Main Matches field is the mathematical overlap with the six drawn numbers, which maps cleanly onto sena/quina/quadra for the jackpot-style hypergeometric, without modelling Caixa’s exact rateio percentages. There is no supplementary ball in Mega-Sena. Do not look for Bonus Matches.

Mega da Virada concentrates tickets, headlines, and sharing risk. A pool of several hundred million reais can make jackpot-only EV look less terrible per volante, while the probability of multiple winners explodes because half the country bought a game. This calculator will not estimate the number of winners. It will tell you that p never budged. If two bolões hit, each ticket’s share is J/2 and EV halves on the prize term.

Compared with Lotofácil (15/25, frequent 11–15 hits) and Quina (5/80, daily), Mega-Sena is the slow, expensive jackpot. R$5 is the simple-game floor; marking more than six dezenas multiplies cost combinatorially. Use this page for sena combinatorics and jackpot EV, not as a substitute for Caixa’s concurso results or as a claim that a particular dezena is due.

The sena of Mega-Sena is calculated as six unordered dezenas from sixty, Caixa Econômica Federal's flagship draw since March 1996, not a franchise of United States Mega Millions. Combinations: C(60,6) = 60 × 59 × 58 × 57 × 56 × 55 / 720. The falling product is 36,045,979,200; divide by 720 to obtain 50,063,860. Jackpot probability is 1 / 50,063,860, about 2.00 × 10^−8, or one in 50,063,860. Wednesday and Saturday are the ordinary concursos; Mega da Virada on New Year's Eve is the same six-from-sixty experiment with a larger advertised rateio. No supplementary ball and no Powerball multiply this identity.

Hypergeometric scores on six draws from sixty with a six-spot volante are P(exactly m) = C(6,m) × C(54, 6−m) / 50,063,860. A quina, five of six, is 6 × 54 / 50,063,860 = 324 / 50,063,860, about one in 154,518. A quadra, four of six, is 15 × 1,431 / 50,063,860 = 21,465 / 50,063,860, about one in 2,332. Exactly three is about one in 101. Those last cells explain why television graphics of “acertos” feel common while the sena remains a fifty-million event.

Independent simple games give at-least-once chance 1 − (1 − p)^n. Ten volantes sit near 2.00 × 10^−7. One thousand simple games in a Mega da Virada bolão still have only about 2.00 × 10^−5 chance of at least one sena if the numbers do not collide inside the pool. A seven-dezena play expands into C(7,6) = 7 simple tickets; convert it to seven games before quoting probability. Those seven six-subsets are disjoint as jackpot events, so the union probability is exactly 7p.

Expectation uses the default R$5 (or $5) simple stake and a $20 million advertised sena: 20,000,000 / 50,063,860 − 5 ≈ 0.400 − 5 = −$4.601 per game. Ten games: about −$46.00. Jackpot-only breakeven with one winner is 5 × 50,063,860 = $250,319,300. Mega da Virada estimates can enter that region; ordinary Wednesday pots do not. If ten winners share a $500 million headline, the prize term drops by ten and expected value returns deeply negative. Expected jackpot return at the $20 million default is only about forty cents against a five-dollar stake.

Assumptions: uniform six-subsets of sixty, independent simple tickets unless a multiple-dezena card has been expanded, one sena winner, no quina or quadra cash in the expectation, R$5 simple price, and no Lotofácil 15/25 or Quina 5/80 leaking into the sixty-ball formula. Teimosinha across draws is repeated independent trials with the same p, not a lucky streak.