Illinois Lotto Odds Calculator

› Illinois Lotto

Calculate Lotto Odds

Balls to be drawn: Total number of prize levels:
From a pool of: Tick to include bonus balls:
Bonus balls to be drawn: Prize levels that involve
matching a bonus ball:
Bonus ball name:
Odds for Popular Lotteries:

Calculated Odds
Numbers Matched Odds (Rounded) Show Working Out +
6 Main Numbers (Jackpot) 1 in 20,358,520 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
1
Calculate:
20,358,520 ÷ (1 × 1) = 20,358,520
5 Main Numbers + Extra Shot 1 in 3,393,087 Show/Hide ›

The odds for this prize level are directly influenced by the Extra Shot. Since the Extra Shot 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 = 3,393,087
6
Calculate:
20,358,520 ÷ (0.0217 × 6 × 46) = 3,393,087
5 Main Numbers 1 in 75,402 Show/Hide ›

The odds for this prize level are indirectly influenced by the Extra Shot. Even though this prize level only involves matching 5 main numbers, the fact that you can also match 5 main numbers and a Extra Shot means the odds of matching 5 main numbers alone are increased. Since the Extra Shot 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 = 75,402
270
Calculate:
20,358,520 ÷ (0.9783 × 6 × 46) = 75,402
4 Main Numbers + Extra Shot 1 in 30,161 Show/Hide ›

The odds for this prize level are directly influenced by the Extra Shot. Since the Extra Shot 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 = 30,161
675
Calculate:
20,358,520 ÷ (0.0435 × 15 × 1,035) = 30,161
4 Main Numbers 1 in 1,371 Show/Hide ›

The odds for this prize level are indirectly influenced by the Extra Shot. Even though this prize level only involves matching 4 main numbers, the fact that you can also match 4 main numbers and a Extra Shot means the odds of matching 4 main numbers alone are increased. Since the Extra Shot 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 = 1,371
14,850
Calculate:
20,358,520 ÷ (0.9565 × 15 × 1,035) = 1,371
3 Main Numbers + Extra Shot 1 in 1,028 Show/Hide ›

The odds for this prize level are directly influenced by the Extra Shot. Since the Extra Shot 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
19,800
Calculate:
20,358,520 ÷ (0.0652 × 20 × 15,180) = 1,028
3 Main Numbers 1 in 72 Show/Hide ›

The odds for this prize level are indirectly influenced by the Extra Shot. Even though this prize level only involves matching 3 main numbers, the fact that you can also match 3 main numbers and a Extra Shot means the odds of matching 3 main numbers alone are increased. Since the Extra Shot 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 = 72
283,800
Calculate:
20,358,520 ÷ (0.9348 × 20 × 15,180) = 72
2 Main Numbers + Extra Shot 1 in 96 Show/Hide ›

The odds for this prize level are directly influenced by the Extra Shot. Since the Extra Shot 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 = 96
212,850
Calculate:
20,358,520 ÷ (0.0870 × 15 × 163,185) = 96
2 Main Numbers 1 in 9 Show/Hide ›

The odds for this prize level are indirectly influenced by the Extra Shot. Even though this prize level only involves matching 2 main numbers, the fact that you can also match 2 main numbers and a Extra Shot means the odds of matching 2 main numbers alone are increased. Since the Extra Shot 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 + 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)!
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
0.9130 × 15 × 163,185
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(52-6-6+2) ÷ (52-6) = 0.0870
6! ÷ (2! × (6-2)!) = 15
46! ÷ (4! × (46-4)!) = 163,185
20,358,520 = 9
2,234,925
Calculate:
20,358,520 ÷ (0.9130 × 15 × 163,185) = 9
1 Main Numbers + Extra Shot 1 in 23 Show/Hide ›

The odds for this prize level are directly influenced by the Extra Shot. Since the Extra Shot 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 - 1
52 - 6
× C(6,1) × C(52-6,6-1)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 1 (balls to be matched from the main pool)
52!
6! × (52 - 6)!
6 - 1
52 - 6
×
6!
1! × (6 - 1)!
×
46!
5! × (46 - 5)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,1) = 6! ÷ (1! × (6-1)!)
C(52-6,6-1) = 46! ÷ (5! × (46-5)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
20,358,520
0.1087 × 6 × 1,370,754
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(6-1) ÷ (52-6) = 0.1087
6! ÷ (1! × (6-1)!) = 6
46! ÷ (5! × (46-5)!) = 1,370,754
20,358,520 = 23
893,970
Calculate:
20,358,520 ÷ (0.1087 × 6 × 1,370,754) = 23
Extra Shot Only 1 in 17 Show/Hide ›

The odds for this prize level are directly influenced by the Extra Shot. Since the Extra Shot 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 - 0
52 - 6
× C(6,0) × C(52-6,6-0)
Substitute:
n for 52 (number of balls in the main pool)
r for 6 (balls drawn from the main pool)
m for 0 (balls to be matched from the main pool)
52!
6! × (52 - 6)!
6 - 0
52 - 6
×
6!
0! × (6 - 0)!
×
46!
6! × (46 - 6)!
Expand:
C(52,6) = 52! ÷ (6! × (52-6)!)
C(6,0) = 6! ÷ (0! × (6-0)!)
C(52-6,6-0) = 46! ÷ (6! × (46-6)!)
! means 'Factorial' eg: 52! = 52 × 51 × 50 ... × 1
Note: 0! = 1
20,358,520
0.1304 × 1 × 9,366,819
Simplify:
52! ÷ (6! × (52-6)!) = 20,358,520
(6-0) ÷ (52-6) = 0.1304
6! ÷ (0! × (6-0)!) = 1
46! ÷ (6! × (46-6)!) = 9,366,819
20,358,520 = 17
1,221,759
Calculate:
20,358,520 ÷ (0.1304 × 1 × 9,366,819) = 17

Approx. Overall Odds: 1 in 4

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 drop down 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 drop down 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" drop-down menu at the bottom of the form to quickly input the variables for your chosen lottery and auto-display the odds table.