Florida Lotto ProbabilityPrevious TopicNext Topic

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.

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.

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.

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

is unlikely in a lottery.

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.

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?

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

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