Lottery Wheel with Fixed Numbers for n/N + 1/M Games
This is a full lottery wheel similar to the one for the common n/N games but applies to such games as the US Powerball and Mega
Millions, denoted as n/N + 1/M , where the numbers are selected from two sets -- 4, 5, or 6 from the first set and one from
the second set. The tool generates all the combinations of a selected set of numbers into groups of n + 1, with the option
of fixing some selections. Fixed numbers are those numbers that the user wants to appear in all generated plays. Such
a system guarantees a jackpot if all the conditions are satisfied.
This combinations generator is divided into two parts - Preview and Generation, which function independently.
The Preview part is intended for analizing the scenarios and expected outcomes of the combinations of a set of numbers before
they are generated. The generation part lists the plays based on the user's selections. If you are a first time user of this tool
you may first read the usage instructions provided further below.
Both the preview and the generator are initially set up for a 5/59 + 1/39 game, which is the US Powerball. You can
change the game type by entering the values of n, N and M in the right box below.
Once you have determined how much to spend and selected your numbers, you can generate the combinations with following
tool. Click on a number to select it, click on a selected number to fix it, click on a fixed number to unselect it.
Every time you click, the total combinations to be generated will be displayed at the bottom. Note that you can fix only one number in the
second set since one is to selected, and if you fix a number there, you cannot have other selections. The 'Generate' button opens
a new window with the generated numbers. Becasuse of the time and computer resources involved to generate these combinations, this
lottery tool can generate only up to 100,000 combinations.
If no numbers are fixed, the generated plays will be all the possible combinations of the selected numbers, which will be
exactly the same as our other utility - Combinations Generator (for n/N + 1/M games).
If some numbers are fixed, then the plays will be generated by combining the fixed numbers with all the possible combinations
of the rest of the selected numbers.
The purpose of fixing some numbers is to reduce the number of plays generated. This results in lower cost, but
at the expense of reduces chance of winning. For instance, the combinations of 8 regular and 5 extra numbers in a 5/59 + 1/39 game
will result in 280 plays; but if 2 of the regular numbers are fixed, the number of plays becomes 100. This utility allows you to
fix upto upto n - 1 regular numbers, that is, one less than the numbers to be selected for game. Obviously, you cannot fix more
than one in the second set, moreover, if you fix one, you cannot have other selections.
A jackpot is guaranteed if the fixed numbers are all winning numbers, plus if all the other winning numbers are among the
selected numbers. All other scenarios, such as what happens if you get 2 of the fixed and 2 of the other selected, can be viewed
by manipulating the 'what if..' situations in the 'Preview' section as demonstrated below.
Let us suppose that we want to play all numbers that are divisible by 7 of a 5/59 + 1/39 game, that is, 7, 14, 21, 28, 35, 42, 49, 56
(a total of 8) of the regular numbers, and 7, 14, 21, 28, 35 (a total of 5) of the extra ball numbers.
To preview the scenarios, select 8 and 5 from the drop-down numbers on the Preview panel and click "Show Scenario".
The total number of plays to be generated will be shown as 280 and a list of IF conditions will be listed. Now, we can view the
'what if' situations to see how the 280 tickets would fare. For example, clicking on the 'If 4 + extra ball correct' line will list
that 4 of our plays(tickets) will match 4-of-5 + Ball, 16 will match 4-of-5, 24 will match 3-of-5 + Ball, and so on. If all of
the winning numbers are divisible by 7 (click on 'If 5 + Extra Ball correct' line), then it will be celebration time.
Now let us see the effect fixing 2 of our numbers. On the Preview panel select 2 as the numbers to fix, and then click the button.
In this case there will be only 100 plays to be generated all of which, as you'll see later, will contain the 2 fixed numbers.
Here, the scenarios options listed will involve how many of the fixed numbers and how many of the other selected numbers are
winners. For example, if 2 of the fixed numbers and 2 of the other selected numbers are winners (withoout ball), then 20 of the 100
tickets will match 4-of-5, 60 will match 3-of-5, and so forth.
Thegeneration part shouldn't pose any problem except how to select and fix the desired numbers. To select a number,
just click on it. To fix a number, click on an already selected number. To unselect a number, click on an already
fixed number. Thus, a cycle of clicks on a number will select, fix, and unselect it, respectively.
At this point, you can select the 8 numbers of our example and see the outcome. Also, you may fix 2 numbers, say,
7 and 35, and click "Generate". Observe that all the generated combinations will contain 7 and 35.
This full wheel generator can be used for any multi-number lottery game, with two sets of numbers, as long as the total numbers
to select from (both N and M) do not exceed 99, and n is 10 or less. This, we hope, will cover any such type
of lottery game in the world.