# South Africa Lotto Odds Calculator

› South Africa Lotto

## Calculate Lotto Odds Round Odds:

 Balls to be drawn: Total number of prize levels: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 From a pool of: Tick to include bonus balls: Bonus balls to be drawn: Prize levels that involvematching a bonus ball: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 From the remaining: From a separate pool of: Bonus ball name: Bonus Ball Cash Ball Extra Ball Euro Number Free Ball Hot Ball Jolly Ball Lucky Ball Lucky Star Mega Ball Plus Ball Powerball Super Ball Star Ball Thunderball Extra Shot Odds for Popular Lotteries: ---- Choose a Lottery ---- Australia Set For Life California SuperLotto Plus EuroMillions Eurojackpot Florida Lotto Irish Lotto Lotto America Mega Millions Powerball South Africa Lotto South Africa Lotto Plus 1 South Africa Lotto Plus 2 South Africa Powerball South Africa Powerball Plus SuperEnalotto UK Health Lottery UK Lotto

Calculated Odds
Numbers Matched Odds Show Working Out +
6 Main Numbers (Jackpot) 1 in 20,358,520.000 Show/Hide ›

The odds for this prize level are not influenced by any 'Bonus Balls' and only the variables associated with the main ball pool are required to calculate the correct odds. The following formula is therefore used (Please note: calculations have been rounded):

 C(n,r)
 C(r,m)
×
 C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
 C(52,6)
 C(6,6)
×
 C(52-6,6-6)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 6 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 6! 6! × (6 - 6)!
×
 46! 0! × (46 - 0)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,6) = 6! ÷ (6! × (6-6)!)
C(52-6,6-6) = 46! ÷ (0! × (46-0)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 1 × 1
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
6! ÷ (6! × (6-6)!) = 1
46! ÷ (0! × (46-0)!) = 1
 20,358,520 = 20,358,520.000 1
Calculate:
20,358,520 ÷ (1 × 1) = 20,358,520.000
5 Main Numbers + Bonus Ball 1 in 3,393,086.667 Show/Hide ›

The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
 r - m n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(52,6)
 6 - 5 52 - 6
× C(6,5) × C(52-6,6-5)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 6 - 5 52 - 6
×
 6! 5! × (6 - 5)!
×
 46! 1! × (46 - 1)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,5) = 6! ÷ (5! × (6-5)!)
C(52-6,6-5) = 46! ÷ (1! × (46-1)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 0.0217 × 6 × 46
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(6-5) ÷ (52-6) = 0.0217
6! ÷ (5! × (6-5)!) = 6
46! ÷ (1! × (46-1)!) = 46
 20,358,520 = 3,393,086.667 6
Calculate:
20,358,520 ÷ (0.0217 × 6 × 46) = 3,393,086.667
5 Main Numbers 1 in 75,401.926 Show/Hide ›

The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 5 main numbers, the fact that you can also match 5 main numbers and a Bonus Ball means the odds of matching 5 main numbers alone are increased. Since the Bonus Ball is also drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
 n - r - r + m n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(52,6)
 52 - 6 - 6 + 5 52 - 6
× C(6,5) × C(52-6,6-5)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 5 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 52 - 6 - 6 + 5 52 - 6
×
 6! 5! × (6 - 5)!
×
 46! 1! × (46 - 1)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,5) = 6! ÷ (5! × (6-5)!)
C(52-6,6-5) = 46! ÷ (1! × (46-1)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 0.9783 × 6 × 46
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(52-6-6+5) ÷ (52-6) = 0.0217
6! ÷ (5! × (6-5)!) = 6
46! ÷ (1! × (46-1)!) = 46
 20,358,520 = 75,401.926 270
Calculate:
20,358,520 ÷ (0.9783 × 6 × 46) = 75,401.926
4 Main Numbers + Bonus Ball 1 in 30,160.770 Show/Hide ›

The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
 r - m n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(52,6)
 6 - 4 52 - 6
× C(6,4) × C(52-6,6-4)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 6 - 4 52 - 6
×
 6! 4! × (6 - 4)!
×
 46! 2! × (46 - 2)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,4) = 6! ÷ (4! × (6-4)!)
C(52-6,6-4) = 46! ÷ (2! × (46-2)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 0.0435 × 15 × 1,035
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(6-4) ÷ (52-6) = 0.0435
6! ÷ (4! × (6-4)!) = 15
46! ÷ (2! × (46-2)!) = 1,035
 20,358,520 = 30,160.770 675
Calculate:
20,358,520 ÷ (0.0435 × 15 × 1,035) = 30,160.770
4 Main Numbers 1 in 1,370.944 Show/Hide ›

The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 4 main numbers, the fact that you can also match 4 main numbers and a Bonus Ball means the odds of matching 4 main numbers alone are increased. Since the Bonus Ball is also drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
 n - r - r + m n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(52,6)
 52 - 6 - 6 + 4 52 - 6
× C(6,4) × C(52-6,6-4)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 4 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 52 - 6 - 6 + 4 52 - 6
×
 6! 4! × (6 - 4)!
×
 46! 2! × (46 - 2)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,4) = 6! ÷ (4! × (6-4)!)
C(52-6,6-4) = 46! ÷ (2! × (46-2)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 0.9565 × 15 × 1,035
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(52-6-6+4) ÷ (52-6) = 0.0435
6! ÷ (4! × (6-4)!) = 15
46! ÷ (2! × (46-2)!) = 1,035
 20,358,520 = 1,370.944 14,850
Calculate:
20,358,520 ÷ (0.9565 × 15 × 1,035) = 1,370.944
3 Main Numbers + Bonus Ball 1 in 1,028.208 Show/Hide ›

The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
 r - m n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(52,6)
 6 - 3 52 - 6
× C(6,3) × C(52-6,6-3)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 6 - 3 52 - 6
×
 6! 3! × (6 - 3)!
×
 46! 3! × (46 - 3)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,3) = 6! ÷ (3! × (6-3)!)
C(52-6,6-3) = 46! ÷ (3! × (46-3)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 0.0652 × 20 × 15,180
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(6-3) ÷ (52-6) = 0.0652
6! ÷ (3! × (6-3)!) = 20
46! ÷ (3! × (46-3)!) = 15,180
 20,358,520 = 1,028.208 19,800
Calculate:
20,358,520 ÷ (0.0652 × 20 × 15,180) = 1,028.208
3 Main Numbers 1 in 71.735 Show/Hide ›

The odds for this prize level are indirectly influenced by the Bonus Ball. Even though this prize level only involves matching 3 main numbers, the fact that you can also match 3 main numbers and a Bonus Ball means the odds of matching 3 main numbers alone are increased. Since the Bonus Ball is also drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
 n - r - r + m n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(52,6)
 52 - 6 - 6 + 3 52 - 6
× C(6,3) × C(52-6,6-3)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 3 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 52 - 6 - 6 + 3 52 - 6
×
 6! 3! × (6 - 3)!
×
 46! 3! × (46 - 3)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,3) = 6! ÷ (3! × (6-3)!)
C(52-6,6-3) = 46! ÷ (3! × (46-3)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 0.9348 × 20 × 15,180
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(52-6-6+3) ÷ (52-6) = 0.0652
6! ÷ (3! × (6-3)!) = 20
46! ÷ (3! × (46-3)!) = 15,180
 20,358,520 = 71.735 283,800
Calculate:
20,358,520 ÷ (0.9348 × 20 × 15,180) = 71.735
2 Main Numbers + Bonus Ball 1 in 95.647 Show/Hide ›

The odds for this prize level are directly influenced by the Bonus Ball. Since the Bonus Ball is drawn from the same pool as the main numbers, the following formula is used (Please note: calculations have been rounded):

C(n,r)
 r - m n - r
× C(r,m) × C(n-r,r-m)
C(n,r) = Odds of correctly choosing r balls from n
n = Number of balls in the main pool
r = Balls drawn from the main pool
m = Balls to be matched from the main pool
C(52,6)
 6 - 2 52 - 6
× C(6,2) × C(52-6,6-2)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 2 (balls to be matched from the main pool)
 52! 6! × (52 - 6)!
 6 - 2 52 - 6
×
 6! 2! × (6 - 2)!
×
 46! 4! × (46 - 4)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,2) = 6! ÷ (2! × (6-2)!)
C(52-6,6-2) = 46! ÷ (4! × (46-4)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
 20,358,520 0.0870 × 15 × 163,185
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(6-2) ÷ (52-6) = 0.0870
6! ÷ (2! × (6-2)!) = 15
46! ÷ (4! × (46-4)!) = 163,185
 20,358,520 = 95.647 212,850
Calculate:
20,358,520 ÷ (0.0870 × 15 × 163,185) = 95.647

Overall Odds: 1 in 38.250

Please note, some lotteries have irregular prize levels, therefore the odds calculated may not be 100% accurate.

### How to use the Lotto Odds Calculator

1. Enter the number of balls to be drawn
2. Enter the total number of balls from which these are drawn
3. Choose the total number of prize levels the lottery has, eg: Match 6, Match 5, Match 4 and Match 3 would be 4 levels
4. If the lottery includes 'bonus' numbers eg: a Powerball, tick the "include bonus balls" box
5. If the box has been ticked, a dropdown menu will appear in a similar style to the original fields. Enter the number of 'bonus' numbers to be drawn, the size of the pool it/they are drawn from, and the amount of prize levels that involve matching the bonus number. Finally, select the name of the bonus number from the remaining dropdown box
6. Click the "Calculate Odds" button to view the odds, or to start again, click Reset.

Alternatively you can choose a lottery from the "Popular Lotteries" dropdown menu at the bottom of the form to quickly input the variables for your chosen lottery and auto-display the odds table.