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Anastasios Tampakis
©1999-2007
Wheel types / Definitions
What is a wheel?
Most people are aware of wheels and their usage. In short, a wheel is an organized set of pointer tickets. The user of a wheel has to assign a number to each pointer and then substitutes all pointers with his assigned numbers. The result is the the tickets to play. Depending on the type of wheel, we can have minimum cost and maximum exposure to a specified prize division (minimal wheels), or other constructions with varying properties.
Definitions
A minimal wheel can be defined as C(n,k,t,m)=b or LD(n,k,t,m,L)=b (the letters and the order can be seen differently elsewhere), where
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n=the total balls we want to wheel
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k=the ticket size (e.g. a 6 ball game has k=6)
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t=the prize division we want to guarantee a win
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m=the condition that has to be met, in order to guarantee the t prize division win; m defines the least number of balls from our n set that must be correct.
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L=the lowest percentage of prizes t achieved, when the m parameter is met. If L=1 (or 100%), it can be omitted.
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b=the total tickets required to play.
For example, C(10,6,4,5)=7 means we need 7 tickets for a 6 ball lottery, when we select 10 numbers to guarantee at least 1-4# prize win (L=1 here) when we match at least 5 balls correct from our 10 selected. Of course, the L parameter does not limit the wheel to only one hit. In many cases, we can have multiple wins, but we are guaranteed to have at least one. Also, here we do not count possible lower division wins that can occur; for example, besides the 1-4# prize we might have additional 3# prizes (multiple hits). A quality minimal wheel can provide many opportunities for multiple hits.
In minimal wheels, we are interested in reducing the cost (tickets required) and still guarantee a prize win. For other types of wheels (not minimal), the above definition does not provide a good description of the wheel's quality.
Types of wheels
There are several types of wheels available:
- Full wheels (or System wheels)
- Close-cover wheels [minimal Abbreviated]
- Open-cover wheels [minimal Abbreviated]
- Partial (or banker/key) wheels [minimal Abbreviated]
- Box/Straight wheels
- Other types of wheels
Full wheels (or System wheels)
These are the most expensive to play, but they guarantee a jackpot prize in case he have all winning numbers among our selected numbers. In simple terms, a full wheel covers all possible tickets that can be generated, using our selection of numbers. Lotto Architect offers complete support to full wheels.
These are much cheaper to play, compared to full wheels. They belong to the Abbreviated wheels category, and they are the most well known representative. Close-cover wheels are wheels that have their L parameter >=1. So, we are always guaranteed to win the P prize specified (if the M condition is met of course!). Almost all minimal wheels available have L=1, as this offers the least possible tickets required to guarantee the specified prize. The close-cover wheels displayed in this web site belong to L=1 category. Also, note in abbreviated wheels, we cannot have the prize guaranteed equal to the ticket size. This means, we cannot guarantee a 6 prize win for a 6 ball game. This is only possible using a full wheel. However, an abbreviated wheel offers some chances to hit the jackpot as well, although reduced. Lotto Architect provides full support to close-cover wheels. See here a list of all close-cover wheels included.
These are even more cheaper to play, compared to close-cover wheels. They belong to the Abbreviated wheels category as well and they are wheels that have their L parameter <1. The lower the L is, the fewer tickets required to play. It is much preferable to use an open-cover wheel to ensure a predetermined chance to hit the specified prize instead of removing tickets (filtering) from the relevant close-cover abbreviated wheel, to reduce the tickets to a specified amount. The open-cover wheels included in the database of Lotto Architect have the L value to 0.99 (99%), 0.98 (98%), 0.95 (95%), 0.90 (90%), 0.80 (80%) and 0.50 (50%) and they are highly optimized using Wheel Generator 1.4 optimization system, to ensure maximum exposure and multiple hits output. Also, Lotto Architect is the first software available worldwide that offers high quality open-cover wheels. Lotto Architect provides full support to open-cover wheels. See here a list of all open-cover wheels included.
Partial (or banker/key) wheels (minimal)
These wheels are even cheaper to play compared to the relevant close-cover or open-cover wheels. In short, in a partial wheel (also called a banker or key wheel), we define some numbers (the banker or key numbers) that should be in every ticket of our wheel. In case we hit the banker numbers, we are guaranteed the prize specified. Also, even if we do not hit all the banker numbers, depending on the construction of the wheel, we might still have good chances to win on lesser divisions. These wheels can also be considered to belong to the Abbreviated wheels category, as they are essentially close/open-cover wheels with the special property of banker numbers. This type of wheels will be supported in the next version of Lotto Architect.
These are totally different wheels and can be used only for Pick style games (e.g. Pick 3). We choose a wheel to play based on the playing style we prefer. If we play boxed, then a box wheel should be used, otherwise straight wheels is the option to go. Lotto Architect offers full support for both types of wheels.
The above wheel categories are the major wheels available for Jackpot & Pick games. There are other types of wheels as well (e.g. Matrix wheels) with several special properties. Also, there are other constructs that have a different design in mind (not minimal). Such wheels can be based on e.g. triple hits (organize numbers in groups) and they almost always require more tickets than the minimal ones but if some certain conditions hold, they are rewarding. Lotto Architect provides full support to matrix wheels. Other types of wheels can be designed and used within the program.