Combinatorial Distribution

Reply #12

JADELottery — Sat, 02 Dec 2006 09:07:33 GMT

Yes, however, if you add a little Quantum Fog to the combinatorial set of {01, 10, 20, 30, 40, 49} you'll get more coverage.

Reply #11

johnph77 — Sat, 02 Dec 2006 09:02:38 GMT

Absolutely. And if you were to reduce them to the most common occurances in each column, you'd wind up playing 01-10-20-30-40-49 - the numbers most likely to appear in each column. But that combination has as much chance of hitting than any of the others.

gl

j

Reply #10

JADELottery — Sat, 02 Dec 2006 08:07:17 GMT

As stated before, good idea. It's the same place I started when I came up with the idea for JADE LSG. I'm sure there are many other possible ways of deriving a wheel or using as a lottery number selection method.

Reply #9

johnph77 — Sat, 02 Dec 2006 03:34:08 GMT

Yes, it was deleted. It was mine, but needed further work.

The 6/49 position frequency chart as I had first developed it - it is exactly as you had published it in your original post:

...............................6/49................................

..........A........B........C........D........E........F......Total

..1....1712304..............................................1712304

..2....1533939...178365.....................................1712304

..3....1370754...326370....15180..... [ More ]

Reply #8

JADELottery — Sat, 02 Dec 2006 00:44:22 GMT

Well, there was something there... guess it was deleted.

Reply #7

JADELottery — Sat, 02 Dec 2006 00:43:00 GMT

That is a good idea. Basically, JADE LSG does something like that when creating a wheel algorithmically; tweaked for line count(play count).

Reply #6

JADELottery — Fri, 01 Dec 2006 15:35:29 GMT

Graph for 6/49, shows symmetry by color; red, green, and blue are symmetric with each other.

Reply #5

JADELottery — Wed, 29 Nov 2006 13:00:24 GMT

Yeah, back in about the 1988-89 time frame, I went the long way to arrive at that equation, but worth it.

Reply #4

johnph77 — Wed, 29 Nov 2006 12:57:13 GMT

TY.

It is - http://www.johnph77.com/math/ls.html.

Personally, I'm not too good with graphs and charts, but I can do tables.

And thanks for the formulas - nicely done. Although the formulas used to generate the spreadsheet that resulted in those tables were different the results are the same. Nice to have confirmation using a different approach, though. All the data in those tables was originally confirmed by programming - going through the matrices and doing an actual count of all inst... [ More ]

Reply #3

JADELottery — Wed, 29 Nov 2006 06:13:07 GMT

Great job. Your second link is probably mistyped, but I got there anyway.

I tend to think in formulae or code and can setup tables and graphs in my mind's eye. It keeps things more compact for me. I posted the code for others to copy and paste for personal use.

Reply #2

johnph77 — Wed, 29 Nov 2006 05:42:11 GMT

http://www.johnph77.com/math/lf.html

Positional frequencies for all lottery matrices from 2/2 to 7/100.

http://www.johnph77.com.math/ls.html

Sum charts for all lottery matrices from 2/2 to 7/100 plus Pick 2 through Pick 6.

gl

j

Reply #1

JADELottery — Tue, 28 Nov 2006 16:08:07 GMT

Here is some Visual Basic code for the functions. Excel has it's own factorial, permutation, and combination functions.

Factorial VB code

Function Fact(n) As Double

If (n < 1) Then

Fact = 1

Else

Fact = n * Fact(n - 1)

End If

End Function

Permutation VB code

Function Perm(n, r) As Double

If (n < r) Then

Perm = 0

Else

Perm = Fact(n) / Fact(n - r)

End If

End Function

Combination VB code

Function Comb(n, r... [ More ]

Combinatorial Distribution

JADELottery — Tue, 07 Nov 2006 17:38:41 GMT

Combinatorial Distribution

Factorial - n! = n * (n -1) * (n - 2) * ... * 3 * 2 * 1 , and 0! = 1

Permutation - P(n,r) = n! / (n - r)!

Combination - C(n,r) = P(n,r) / r!

Combinatorial Distribution - D(n,r,c,z) = C(z - 1, c - 1) * C(n - z, r - c)

n - total number of items

r - number of items in a combinatorial or permutational set

c - column number of the distribution

z - item number of the distribution

Example distribution of 49