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# Florida Lotto Probability

Topic closed. 8 replies. Last post 5 years ago by RJOh.

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New Member
Gainesville, FL
United States
Member #121734
January 16, 2012
8 Posts
Offline
 Posted: January 22, 2012, 7:47 pm - IP Logged

Florida Lotto is a 6 ball, 53 number Lottery.
It's Odds are:

Hits = 1     1 in 8.8
Hits = 2     1 in 91.9
Hits = 3     1 in 1171.3
Hits = 4     1 in 19521.7
Hits = 5     1 in 478280.8
Hits = 6     1 in 22957480

There are around 104 drawings per year; so you could expect to Hit 1 ball on your quick pick about once a month ... 2 about once a year ... 3 about once a decade ... 4 about once a generation ... 5 once in a lifetime and 6 in the midst of the next ice age.

mid-Ohio
United States
Member #9
March 24, 2001
19900 Posts
Offline
 Posted: January 23, 2012, 11:48 pm - IP Logged

Where did you come up with those odds calculations?

possible combos of 6/53 numbers = 22957480
MATCHES     ODDS
6/6      1 : 22957480
5/6      1 : 81410
4/6      1 : 1416
3/6      1 : 71
2/6      1 : 9
1/6      1 : 2

My odds calculations show you can expect to match one on every other QP or 1:2 or get a free ticket once a month or 1:9.

* you don't need to buy more tickets, just buy a winning ticket *

New Member
Gainesville, FL
United States
Member #121734
January 16, 2012
8 Posts
Offline
 Posted: January 24, 2012, 6:07 pm - IP Logged

C(53,Hits)/C(6,Hits)
Essentially, Make 2 lists ... one with all possible combinations using 53 numbers, in the other, all possible combinations using 6 numbers.  Then divide the list counts.

You get a slightly better result if you do: 1/(1/53 + 1/52 + 1/51 + 1/50 + 1/49 + 1/48)  = 1 in 8.4, but I prefer the picking entries in a great big list method.

 Hits Odds Combos in 53 Combos in 6 Hits = 1 1 in 8.8 53 6 Hits = 2 1 in 91.9 1378 15 Hits = 3 1 in 1171.3 23426 20 Hits = 4 1 in 19521.7 292825 15 Hits = 5 1 in 478280.8 2869685 6 Hits = 6 1 in 22957480 22957480 1
New Member
Gainesville, FL
United States
Member #121734
January 16, 2012
8 Posts
Offline
 Posted: January 24, 2012, 6:22 pm - IP Logged

* THat which happens most *
* is most likely to happen again *

is unlikely in a lottery.

New Member
Gainesville, FL
United States
Member #121734
January 16, 2012
8 Posts
Offline
 Posted: January 24, 2012, 7:00 pm - IP Logged

I don't know if you're a coder; but these are my visual basic routines -- p is permutations, c is combinations.

' P(n,k) = n! / (n-k)!
Public Function p(ByVal n As Double, ByVal k As Double) As Double
Dim i As Integer

p = 1

For i = ((n - k) + 1) To n
p = i * p
Next
End Function

' C(n,k) = P(n,k) / k!
Public Function c(ByVal n As Double, ByVal k As Double) As Double
Dim i As Integer

c = p(n, k)

For i = 2 To k
c = c / i
Next i
End Function

I'd really like to know if I've got any of this wrong.

mid-Ohio
United States
Member #9
March 24, 2001
19900 Posts
Offline
 Posted: January 24, 2012, 7:21 pm - IP Logged

I don't know if you're a coder; but these are my visual basic routines -- p is permutations, c is combinations.

' P(n,k) = n! / (n-k)!
Public Function p(ByVal n As Double, ByVal k As Double) As Double
Dim i As Integer

p = 1

For i = ((n - k) + 1) To n
p = i * p
Next
End Function

' C(n,k) = P(n,k) / k!
Public Function c(ByVal n As Double, ByVal k As Double) As Double
Dim i As Integer

c = p(n, k)

For i = 2 To k
c = c / i
Next i
End Function

I'd really like to know if I've got any of this wrong.

nCr=n!/[(n-r)!*r!]

I used the above formula to get my results which are the same posted on state websites that I've visited so I assume they are correct.

*Permutations aren't the same as a combinations.  Permutations include all the different possible arrangements of numbers in a combination.

* you don't need to buy more tickets, just buy a winning ticket *

New Member
Gainesville, FL
United States
Member #121734
January 16, 2012
8 Posts
Offline
 Posted: January 24, 2012, 8:15 pm - IP Logged

Ok.  I've put up my thinking; but I also ran a test.  I took the first 100 Lotteries in the Florida Lotto history list and ran them against each other so that each Lottery took the other 99 as Quick Picks.  The results confirm your calculations.  Where did I go wrong?

Quick Pick Results
HitsCountPercentProbability
1404440.851 in 2.4
2117011.821 in 8.5
31181.191 in 83.9
4100.11 in 990.0
New Member
Gainesville, FL
United States
Member #121734
January 16, 2012
8 Posts
Offline
 Posted: January 25, 2012, 7:03 am - IP Logged

Thanks RJOh!
My error is that I thought the probability formula is WaysToWin/TotalCombinations.  The correct formula is (WaysToWin*WaysToLose)/TotalCombinations.  The Permutations and Combinations code I put up are correct and this is the corrected table, now just like RJOh:

Odds

HitsPicks to HitWays to WinWays to LoseTotal Combinations
02.111073757322957480
12.56153393922957480
28.61517836522957480
370.8201621522957480
41415.815108122957480
581409.564722957480
6229574801122957480
mid-Ohio
United States
Member #9
March 24, 2001
19900 Posts
Offline
 Posted: January 25, 2012, 5:06 pm - IP Logged

Thanks RJOh!
My error is that I thought the probability formula is WaysToWin/TotalCombinations.  The correct formula is (WaysToWin*WaysToLose)/TotalCombinations.  The Permutations and Combinations code I put up are correct and this is the corrected table, now just like RJOh:

Odds

HitsPicks to HitWays to WinWays to LoseTotal Combinations
02.111073757322957480
12.56153393922957480
28.61517836522957480
370.8201621522957480
41415.815108122957480
581409.564722957480
6229574801122957480

That's pretty close.  These are some full printouts of the program I wrote some years ago using GWBasic.  I can use different variables to fit the game that I'm playing or the answers that I want.

combination size             6
basic pool size              53
(B) bonus numbers            none
smallest match               0
tickets or chances per draw  1
possible combos of 6/53 numbers = 22957480
MATCHES     ODDS                WINNING COMBOS      EXPECTED WINNERS
6/6      1 : 22957480           1                      0.00
5/6      1 : 81410              282                    0.00
4/6      1 : 1416               16215                  0.00
3/6      1 : 71                 324300                 0.01
2/6      1 : 9                  2675475                0.12
1/6      1 : 2                  9203634                0.40
0/6      1 : 2                  10737573               0.47
______________________________________________________________________________
overall odds are 1 : 1                  1.0 total expected winners
22957480 winning combos = 100 % of possible

combination size             5
basic pool size              59
(B) Bonus pool size          35
smallest match no (B) number 3
largest match with bonus     5
smallest match with bonus    0
tickets or chances per draw  1
possible combos of 5/59 + 1/35 numbers = 175223510
MATCHES     ODDS                WINNING COMBOS      EXPECTED WINNERS
5/5+B    1 : 175223510          1                      0.00
5/5+0    1 : 5153633            34                     0.00
4/5+B    1 : 648976             270                    0.00
4/5+0    1 : 19088              9180                   0.00
3/5+B    1 : 12245              14310                  0.00
3/5+0    1 : 360                486540                 0.00
2/5+B    1 : 706                248040                 0.00
1/5+B    1 : 111                1581255                0.01
0/5+B    1 : 55                 3162510                0.02
______________________________________________________________________________
overall odds are 1 : 31.8               0.0 total expected winners
5502140 winning combos = 3.14 % of possible combos

combination size             6
basic pool size              53
(B) bonus numbers            none
smallest match               3
tickets or chances per draw  1
possible combos of 6/53 numbers = 22957480
MATCHES     ODDS                WINNING COMBOS      EXPECTED WINNERS
6/6      1 : 22957480           1                      0.00
5/6      1 : 81410              282                    0.00
4/6      1 : 1416               16215                  0.00
3/6      1 : 71                 324300                 0.01
______________________________________________________________________________
overall odds are 1 : 67.3               0.0 total expected winners
340798 winning combos = 1.48 % of possible combos

* you don't need to buy more tickets, just buy a winning ticket *

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