Example
1
This example applies for Expert Lotto 6/49 demo lottery.
The following definitions will be made:
Let A1 and A2 be two sets of numbers, such that:
A1
= 16,17,19,20,33,40,48,49,32
and
A2 = 13,18,35,38,39,26
Also:
- None
of the tickets will contain all six draws taken from one set of numbers
only (A1 or A2).
- Triplets
of successive numbers are to be excluded.
- The
majority of all the possible triplets should be considered (15 numbers
can give rise to 455 possible triplets).
Tickets
following the above rules can be drawn by:
a)
Randomly generating tickets from a pool of 15 number, allowing for a maximum
overlap in 3 numbers, which can then be swapped for the desired numbers
from A1 and A2.
and/or
b)
Full package generation with subsequent step-by-step filtering.
Part
a):
Approximately
32 tickets will cover about 90% of all triplets from 15 numbers, with
a maximum allowed overlap in 3 numbers. Thus, taking the following steps:
- Select
Generator from the Package
menu.
- Enter
30 in the field Tickets to generate, and select Tickets numbers
range to be from 1 to 15. Select the Generate tickets with random
numbers option and select Maximum Overlap to be 3.
Swap generated numbers (1 to 15) for the numbers in A1 and A2, by selecting
Swap Numbers from the package drop
down menu. Save the package contents
to a file named, say model1a.
- Return
to the Generator and select the Generate maximum possible
number of tickets option to generate tickets for all number combinations
(5005 tickets) from the proposed 15 numbers. Save the contents
of the resultant package to a file named template15.
- Using
the Generator again, select the boxes 4, 5 and 6 in the Dummy
numbers list (and ensure that the option for Generate maximum
possible number of tickets is still selected), thus ensuring tickets
will cover all possible triplets (455 tickets). Save them to
file named trips15.
- In
the Generator, now select boxes 5 and 6 in the Dummy numbers
list and create tickets covering all possible quads (1365 tickets). Save
them to a file named, say quads15.
Note: These 4 files will be used for
testing how many triplets (or quads) are to be covered by your bet.
- Load the file model1a
back into the package and use the Successive
Numbers filter to remove triplets of successive numbers (if any).
- Switch
to the Visual Package page,
and click on the numbers from set A1 (or A2) in the table header. Select
boxes ’0’ and ’6’ next to the Remove Match
in button and click on this button. This way a modified set of tickets
will be produced which contains at least 1 and at most 5 numbers from
A1 (or A2). Other box selections can be made to produce different number
combinations. Save the results back into the file named model1a.
- Now
load the template15 file back into the package.
Using the Match Tickets in a File
function remove from the file template15 all tickets
that match tickets in the model1a file in 4, 5 and 6
numbers.
- Again
filter out triplets of successive numbers and also remove tickets with
numbers in either of the sets A1 or A2 from the remainder of the package
(Visual Package).
- Apply
the Shuffle function (from the Package menu) on the tickets remaining
in the package, and then use Match
Tickets in the Package to remove tickets matching in 4, 5 and 6 numbers.
The contents of the package will be reduced to the non-matching tickets.
- Save the rest of the package to the model1a
file with the Append to the end of the file option on.
This
procedure should be repeated until the package is empty.
Part
b):
- Use
the Generator to insert tickets for
all possible number combinations (drawn from the full pool of 49) into
the package.
- Use
the Successive numbers filter
to remove triplets of successive numbers.
- Switch
to the Visual Package page.
- Click
numbers from the set A1 (or A2) in the table header. Select boxes ’0’
and ’6’ next to the Remove Match in button and click
on this button. This way a modified set of tickets is obtained with at
least 1 and at most 5 numbers from the set A1 (or A2). Again, alternative
selections of checkboxes can be made for differing number combinations.
- Apply
the Shuffle function (from the Package menu) on the
rest of the tickets in the package and then use the Match
Tickets in the Package filter to remove tickets matching in 4, 5 and
6 numbers. The contents of the package will be reduced to the non-matching
tickets.
- Save the tickets remaining in the package
to a file named, say model1b.
- Load the template15
file into the package again.
- Apply
the Match Tickets in a File
filter to compare the package with the model1b file and
remove tickets matching in 4, 5 and 6 numbers.
- Repeat
the Visual Package page procedure and remove from the package
tickets matching set A1 (or A2) in the ’0’ and ’6’
number positions.
- Shuffle those that remain in the package,
and then apply the Match Tickets in a Package filter once more
to remove tickets matching in 4, 5 and 6 numbers.
- Append the rest of the tickets in the
package to the end of the model1b file.
- Load
the template15 file into the package and repeat the procedure
as long as any tickets remain in the package.
The
following procedure checks the coverage of triplets and/or quads by your
bet either in the model1a file or in the model1b
file.
Load either the model1a
or the model1b file into the package and use the Match
Tickets in a File filter to compare it with the trips15
and quads15 files. Make sure that the Tag matching
tickets option is selected before using the filter. When the filter
is finished load the file you compared with (trips15 or quads15) into
the package and use the Tagged Tickets
-> Leave (Remove) function to find out how many tickets are covered
by your bet. Usually the bet containing 32 tickets should cover about
95% of all possible triplets and about 45-50% of all possible quads. You
can conclude that guessing 4 numbers means about 90% guarantee of winning
a 4th prize together with several 5th prizes.
You
should be able to easily setup similar procedures depending on your required
win guarantees.