Minimum bet
- Input
- Quina, 5 dezenas
- Expected output
- 1 em 24.040.016
Only 5 matches required, but out of a pool of 80 numbers.
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Quina odds
On Quina you mark 5 to 15 numbers inside the range of 1 to 80. On the minimum bet of 5 numbers, the top-tier chance is 1 in 24,040,016, the result of C(80,5). Needing only 5 matches sounds easy, but the pool of 80 numbers weighs far more heavily on the final math than it first appears.
Only 5 matches required, but out of a pool of 80 numbers.
The maximum allowed covers C(15,5) simple games in a single ticket.
Quina's lowest tier already pays out from a two-number match.
With a simple 6-number bet, the odds of hitting the jackpot are 1 in 50,063,860. Marking more numbers raises the probability in proportion to the games covered.
On the minimum 5-number bet, the top-tier chance is 1 in 24,040,016, the exact result of C(80,5).
Because Quina's pool of numbers is much bigger, 80 versus Lotofácil's 25. A larger pool drags the odds down more than needing fewer matches can make up for.
By simple combination, C(80,5): it counts every possible group of 5 numbers out of 80 and divides one group by the total.
Marking the maximum 15 covers 3,003 games and brings the chance to about 1 in 8,005, a sizeable improvement over the minimum 5-number bet.
| Hits | Odds | Probability |
|---|---|---|
| 5 | 1 in 24,040,016 | 4.16e-6% |
| 4 | 1 in 64,107 | 1.56e-3% |
| 3 | 1 in 866 | 0.12% |
| 2 | 1 in 36 | 2.81% |
The odds use the standard hypergeometric model of lotteries: the chance of matching exactly k numbers combines the drawn and the not-drawn numbers within the game's universe.