What is a Wheel?
Wheels, wheeling systems, or lottery systems are means to organize lottery tickets in a way that a win is guaranteed, given that certain conditions are met.
The Lucky Gene concentrates (for now) on Abbreviated Wheels, which ensure that the win can be achieved with the least number of tickets.
In a lottery game, the players choose numbers organized on bets or tickets.
The size of a bet may or may not be the same with the count of the numbers drawn by the lottery organization.
For example, in a Lotto 6/49 game the size of the bet is the same as the size of the draw: 6; that is,
a bet may contain 6 numbers from 1 to 49 and a draw is made of 6 numbers from 1 to 49.
In other games, like Keno games, the size of the bet and the draw differ; a player may bet 3 numbers, while the draw may be made of 20 numbers.
A win may be obtained when the numbers in a bet and the numbers in a draw, as sets, intersect.
If all the numbers in a bet are within the numbers drawn, that is usually called a jackpot, the maximum prize that can be won.
Most lotteries have additional, smaller prizes. For example, in a Lotto 6/49 game, there may be wins for prizes of 5, 4, 3, or 2 numbers matched.
Continuing with the Lotto 6/49 game example, let us assume that a player wants to play 10 favourite numbers.
The number of combination of 10, taken 6 at a time, is 210. The player may buy 210 tickets, or may organize the 10 numbers on random bets,
or may use a lottery wheeling system to organize the 10 numbers on bets. For example,
the abbreviated wheel that allows choosing 10 numbers and organizes them on 7 tickets,
has a minimum guarantee of 4, if 5 numbers drawn are within the 10 favourite numbers.
That is, if 5 numbers are correctly guessed, the wheel guarantees at least one prize of 4.
The number of tickets is reduced from 210 possible combinations to 7, reducing the number of tickets by a factor of 30.
Abbreviated lottery systems are studied by the field of combinatorial coverings.
A covering design C(v,k,t,m,=b) is a pair (V,B), where V is a set of v elements (called points) and B is a collection of b k-subsets of V (called blocks),
such that every m-subset of V intersects in at least one member of B in at least t points.
When applied to lottery, in form of an abbreviated wheel:
- v: total numbers in the design; amount of numbers you choose to play the wheel
- k: size of a block or bet
- t: minimum guarantee
- m: amount of numbers that must be guessed correctly in the draw
- b: number of blocks or bets or tickets
Wheel C(10,6,4,5,=7) describes the wheel with 10 chosen numbers designed for a Pick 6 lottery.
The wheel guarantees at least one prize of 4 matches if 5 officially drawn numbers are within the group of 10 chosen numbers.
Finally, the number of bets generated is 7, reduced from a total of 210 possible combinations of 10 taken 6 at a time.
The coefficient of reduction is 30.
Many wheels on The Lucky Gene are accompanied by Tables of Wins, which show all the wins that can be accomplished with the wheel,
for certain numbers guessed, together with a measure of chance for the specific wins.
For example, going back to the C(10,6,4,5,=7) wheel for Lotto 6/49, this is an example of a table of wins:
Some of the wheels available are balanced, that is, each favourite number appears on bets the same number of times.
How to Use the Wheels
To use a wheel, you need to first select a lottery game or a Pick type. The Pick type is the size of the bet.
If you select a game, the bet size can be found from the game’s matrix. As mentioned before, the size of the bet and the size of the draw are not necessarily the same.
The Lottery Wheels page is organized on a system of tabs, guiding each step.
On the first tab, Choose a Wheel, you will see a list of wheels with their characteristics:
Numbers to Choose (favourite numbers), Tickets Generated (the number of bets in the wheel), the Guarantee number1 if number2
(number1 being the minimum prize match and number2 being the count of numbers that need to be guessed correctly in the draw), and the coefficient of reduction. If a lottery
game is selected,
the odds of guessing correctly number2 is also displayed.
The first tab also offers a Search Wheels Panel which allows you to filter the available wheels. For example, if you are interested in wheels with at most 10 tickets,
you can select Tickets generated to be less than or equal to 10, and then press the Search button.
Once you click the row of a wheel, you may choose to display the wheels details, which may contain a table of wins and allows you to download the wheel's blocks.
You can also go to the next tab, Pick Your Numbers, where you can select your favourite numbers, or have them randomly generated.
If you have a lottery game selected, this panel will display a representation of the Statistics for the current game.
The statistics may be built based on several past lottery results, or for results withing a certain date range. All statistics are sortable.
Once you select your favourite numbers, you may go next to the Your Tickets tab which will display a downloadable list of bets generated from the
wheel with your favourite numbers.
Here you may find a brief description of the characteristics of the wheel, including high ranking prizes that the wheel won in the past,
displaying the bet number and the date of the win.
You also have the option of swapping between two favourite numbers, to rearrange the numbers on the bets (note that the order of the chosen numbers matters).
If a game is selected, clicking on the row of a bet will popup a box with all the results for which the bet won a prize.
The Results tab is only active if a game was selected. You may search the game’s results for past prizes won by any of the wheel’s bets.
The Try the Wheel tab allows you to predict a result and check it against the current wheel’s bets.
Table of Wins
Many systems on The Lucky Gene have table of wins computed. A table of wins shows what prizes you can win, with a measure of chance.
It also confirms the wheel's minimum guarantee.
For example, for the C(10,6,4,5,=7) wheel for Lotto 6/49, this is the table of wins when 5 numbers are guessed correctly:
The default numbers guessed is the one required by the wheel to win the minimum guaranteed prize, in this case the number is 5,
but you may select other possible numbers guessed.
In the table's header we see all possible matches, that is, possible intersections between the wheel's bets and a combination drawn, as well as Hits and "Out of".
The last column is for Odds or Probability.
The tables are complete and display all possible matches, whether they are prizes in the lottery game or not, including no matches (0 matches).
The table of wins is computed by generating all possible combinations of numbers guessed, 5 in this case with a total of 252 combinations of 5 from 10 chosen numbers,
intersecting them with the wheel's bets and making of record of obtained matches.
Let's look at the first row in the table shown above: Out of a total of 252 combinations of 5 from 10 chosen numbers,
6 combinations (Hits) can result in 2 matches of 5, 4 matches of 4 and 1 match of 1. The Odds column shows
how probable it is to hit this distribution of prizes, dependant on whether 5 out of 10 numbers are guessed correctly.
In Lotto 6/49 a match of 5 is a prize and a match of 4 is a prize as well.
Let's look at the last row in the table: the minimum match that can be obtained is 1 of 4 (the minimum guarantee),
but we can see that in addition to that, we can also have 2 matches of 3 and 4 matches of 2, which in
Lotto 6/49 are valid prizes.
Looking at the Hits or Odds colums, we can see that the most likely matches distribution is the one with 108 Hits.
If we play a wheel with 10 chosen numbers, although the probability is lower, we could guess correctly 6 numbers instead of 5. Let's see what we could win:
We can see that it is possible to win the jackpot and that the least we can win is a configuration of 3 matches of 4 and 4 matches of 3.
A table of wins accompanied by a measure of probability is a good tool for adjusting expectation. First we need to understand how possible it is to guess correctly 5 numbers,
when we play 10.
Then we have a measure of probability based on percentage of Hits out of the total possible combinations. The two combined show us how probable it is to win a certain
configuration of prizes.
A wheel's details, that includes the table of wins, can be displayed in a popup window, or can be displayed in a separate tab or separate window. You may verify the table of wins by using the Try the Wheel tab
to predict a result and compare the wins displayed with the possible matches in the table of wins.
Why Should I Use Wheels?
Using wheels is a personal preference. We made The Lucky Gene available because we prefer to play wheels and we could find no software with a simple interface and the tools we
like searching the results’ history tools, or sorting results to see combinations that have not been drawn yet. We thought others might be interested as well.
Our website allows for choosing numbers and generating tickets in seconds, without the need of writing numbers on paper, or needing to be an advanced Excel user.
By displaying odds and tables of wins, we are offering a realistic approach to playing wheels, without fake promises, relying on mathematical foundations.
The wheels made available here have all been verified for the minimum guarantee.
To our knowledge, our website is the only one offering full and complete table of wins, which can be sorted by matches or by probability.
The tables of wins have been accurately computed. We prefer the full tables of wins rather than abbreviated, for accuracy.
We believe the tools on The Lucky Gene are implemented correctly, however errors are possible. Please do not hesitate to contact us using the Feedback page, should you see an error, or should you wish a feature added.