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for n/N + 1/M lotto games
Lottery Wheels Abbreviated Lottery Wheels Lottery Wheel Checker Lottery Wheel Analyzer 4-Number Wheels 5-Number Wheels 6-Number Wheels Full Wheel with Fixing
for n/N lotto games
Full Wheel with Fixing
for n/N + 1/M lotto games
United States Lotteries

Lottery Wheels

What is a Lottery Wheel?

A Lottery Wheel is simply a combinations generator. It generates a set of combinations of a group of numbers so that if certain conditions are met, the generated numbers will guarantee a win. Many players have a set of numbers to play such as birthdays and ages of their loved ones, historycally hot or cold numbers of a certain game, etc. However, in many cases, these set of numbers would be greater in number than those played by the lottery game. For instance, a player may have ten favorites to play a 6-number lottery game. These numbers can be combined at random and played in two or more tickets, but a lottery wheel will combine the ten numbers systematically and generate two or more tickets that will guarantee a certain winning.

There is one thing that should be clear here. A lottery wheeel does not increase your chance of winning the lottery per se. The chance of winning is always increased by playing more than one ticket, whether wheeled or not; that is, the more number of tickets you play, the better will be your chance of winning. Nevertheless, if the winning numbers are in the group of your favorite numbers, at least one of the tickets generated by a lottery wheel will be a winner of either the jackpot or lesser prizes while randomly combining the numbers may not result in any winner.

Types of Lottery Wheels

Basicaly there are two types of lottery wheels:
1. Full Wheels, and
3. Abbreviated Wheels

Both these types of wheels can be designed to incorporate some fixed numbers (also called key numbers), which will appear in all the generated numbers.

Some people also refer to simple "number pickers" as wheels, while others define various tools as balanced, filtered, and optimized wheels. The idea behind these tools is to extract a few combinations from those generated by a full wheel in such a manner that some optimum parameters such as sums, ranges, distribution of the numbers are satisfied.

Full Lottey Wheel

A Full Wheel is simply a generator of all the possible combinations of a set of numbers into group of n numbers, where n is usually the game number (the number of numbers played in the game). For 6/49 lotto, n is 6. Since all the combinations of the set are played, a full wheel guarantees a winning equal to how many of the numbers in the set are winning numbers; if all the winning numbers are in the set then it guarantees a jackpot (and several lower prizes as well).

The drawback of these wheels is that the number of combinations generated are too many, thus too expensive. For example, all the possible 6-number combinations of a set of 10 numbers is 210; for a set of 20 numbers it is 38,760. Our combinations calculator and generator for n/N lottery games is actualy Full Wheel for n/N lottery games. And that is where the above figures are obtained from. Also, the combinations calculator and generator for n/N + 1/M lottery games is the Full Wheel for for n/N + 1/M lottery games.

Full Lottey Wheel with Fixed (Key) Numbers

This wheel is similar to the above except that some of the numbers are fixed. Fixing some numbers means that those numbers will appear in all the generated lottery tickets, and thus reducing the number of plays generated. The guaranteed wins in this case are equal to the sum of winning fixed numbers and the winning other selections.

The number of tickets generated will depend on how many numbers are fixed. For example, for 6-number combinations of a set of 10 numbers where three of them are fixed, there will be 35 combinations; for a set of 20 numbers with 3 fixed there will be only 680. Please see our Full Lottey Wheel with Fixed Numbers for n/N lottery games as well as Full Lottey Wheel with Fixed Numbers for n/N + 1/M lottery games.

Abbreviated Lottey Wheel

An Abbreviated Lottey Wheel generates a combination that is much less in number than that generated by full wheels to guarantee wins other than the jackpot. The design of an abbreviated wheel itself is not a simple matter; there is no formula for it and is mostly a result of iterations and trials and errors. In fact, in mathematics, it is called Covering Design and belongs to a branch of mathematics called Combinatorics.

Since we have recently developed several tools and wheels, they will be dealt with in separate pages. Please see,

Abbreviated Wheels - contains notations, description and selection of abbreviated wheels
Lottery Wheel Checker - tool to check the validity of an abbreviated wheel
Lottery Wheel Analyzer - enter your own wheel to see what it would guarantee
6-Number Lottery Wheels - List of abbreviated wheels with an interactive and friendly genertor.

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