Odds and Prizes for MegaSena Lottery
How to Calculate MegaSena Probabilities
MegaSena is the national lottery of Brazil and is operated by the Caixa Econômica Federal Bank. It's the largest lottery in Brazil and tempts players with huge prizes. The structure of the game is different from that of lotteries in the US, Canada, and Europe. It has some similarities to keno. During the official lottery drawing, 6 numbers are selected from between 1 and 60. If you match all 6 you win your share of the grand prize, and if you match 5/6 or 4/6 you can win a smaller prize.
What makes MegaSena different from lotteries such as Powerball, Mega Millions, Canada's 6/49, EuroMillions, UK Lotto, Oz Lotto, and other games is that players can select 6 to 15 different numbers per board. The more numbers you select the better your odds of winning, but also the higher the cost of the board. The cost is proportional to how many groups of 6 there are. For example, if you pick 9 numbers, there are 84 different groups of 6, so the cost of the board is 84 times the base price. Your probability of winning depends on how many numbers you choose to play, which makes the calculations a little more difficult. See table below. In this respect, MegaSena is similar to the Philippines UltraLotto.
A common question asked by MegaSena lottery players is whether it is better to buy a single board with multiple numbers, or to spend the same amount of money on separate boards with fewer numbers. The answer is the probabilities.
Cost of Buying More Than 6 Numbers
Numbers per Board
 Number of Groups of 6
 Price Increase Factor


6
 1
 1

7
 7
 7

8
 28
 28

9
 84
 84

10
 210
 210

11
 462
 462

12
 924
 924

13
 1716
 1716

14
 3003
 3003

15
 5005
 5005

The table above shows the price increase factor for every extra number you buy. The price increase factor is equal to the number of groups of 6. If you choose K numbers, there are
K(K1)(K2)(K3)(K4)(K5)/720
different groups of 6. For example if the base price of a MegaSena lottery ticket with 6 numbers is $2, then a board with 15 numbers costs 5,005 times that amount, or $10,010. If the base price is $3 per board, then a board with 9 numbers costs $3 × 84 = $252.
Probability of Matching X out of 6 Numbers, Playing N Numbers
The probability of matching X out of 6 numbers (where X = 4, 5, or 6) by playing N numbers (where N = 6, 7,... 15) is given by the combinatorial formula
[(54 choose NX) * (6 choose X)] / (60 choose N)
where (A choose B) = A! / [B!(AB)!]. For example, to compute the probability of matching all 6 numbers when you play only 6 numbers in MegaSena you let X = 6 and N = 6. This gives you
[(54 choose 0) * (6 choose 6)] / (60 choose 6)
= 1 / (60 choose 6)
= (6*5*4*3*2*1) / (60*59*58*57*56*55)
= 1 / 50063860
= odds of 1 in 50,063,860
≈ 0.0000000199745
The probability of matching 5/6 numbers when playing 9 numbers in MegaSena is
[(54 choose 4) * (6 choose 5)] / (60 choose 9)
= [316251 * 6] / 14783142660
= 459 / 3575990
≈ 0.000128356
≈ odds of 1 in 7,791
The table below summarizes the MegaSena lottery odds for all the possible plays and wins.
Odds of Matching 4/6
 Odds of Matching 5/6
 Odds of Matching 6/6
 Overall Odds
 

Buying 6 Numbers
 1 in 2,332
 1 in 154,518
 1 in 50,063,860
 1 in 2,298

Buying 7 Numbers
 1 in 1,038
 1 in 44,981
 1 in 7,151,980
 1 in 1,014

Buying 8 Numbers
 1 in 539
 1 in 17,192
 1 in 1,787,995
 1 in 523

Buying 9 Numbers
 1 in 312
 1 in 7,791
 1 in 595,998
 1 in 299

Buying 10 Numbers
 1 in 195
 1 in 3,973
 1 in 238,399
 1 in 185

Buying 11 Numbers
 1 in 129
 1 in 2,211
 1 in 108,363
 1 in 122

Buying 12 Numbers
 1 in 90
 1 in 1,317
 1 in 54,182
 1 in 84

Buying 13 Numbers
 1 in 65
 1 in 828
 1 in 29,175
 1 in 60

Buying 14 Numbers
 1 in 48
 1 in 544
 1 in 16,671
 1 in 44

Buying 15 Numbers
 1 in 37
 1 in 370
 1 in 10,003
 1 in 34

MegaSena Prizes
Currently, 35% of MegaSena lottery ticket sales are put into the jackpot, 19% is put into the second tier prize for matching 5 out of 6, and 19% is put into the third tier prize for matching 4 out of six. The jackpot is split evenly among winners who have 6 out of 6, and the lower tier prizes are also paid on a parimutuel basis  meaning the prize fund is divided evenly among the winners. Since there is a higher probability of matching 4 out of 6 than 5 out of 6, there are more winners for the third tier prize and thus the payout is less than the second tier prize.
The rest of the income from lottery ticket sales is distributed among special MegaSena games. 22% of it funds a drawing held after every five regular MegaSena drawings, and 5% of it funds a very special endofyear drawing offering a huge jackpot.
Is It Worth It to Buy More Than 6 Numbers per Board in MegaSena?
When you play MegaSena, your overall odds of winning any prize do not increase in proportion to the price increase of buying more than 6 numbers for a board. Therefore, you have a lower expected return on investment when you buy more than the basic 6 numbers. If you have money to burn, it is better to buy a separate lotto ticket with 6 completely different numbers.
For example, the 7number board is 7 times as expensive as the 6number board. But your overall odds of winning any prize with a 7number board is only about 2.3 times better, not 7 times better.
The 8number board is 28 times more expensive than the 6 number board, but the overall odds of winning are only about 4.4 times better. The more numbers you buy, the worse the value in terms of overall odds.
However, the jackpot odds do improve proportionally with the price increase.
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