Lottery Wheeling
Encyclopedia
Lottery wheeling is a method of arranging lottery ticket numbers in a way that will allegedly improve chances to win multiple-tier lottery prizes. Wheeling was designed for players who wish to play more numbers than the set required for a lottery ticket. Using mathematical formulae based on combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

 it generates tables that would give either full or partial coverage of all possible combinations of numbers a player selects for a lottery draw.

The probability of hitting the jackpot in a popular lottery is quite low. Most popular US lotteries have odds
Odds
The odds in favor of an event or a proposition are expressed as the ratio of a pair of integers, which is the ratio of the probability that an event will happen to the probability that it will not happen...

 ranging from 1:176 million in Mega Millions
Mega Millions
Mega Millions is a US multi-jurisdictional $1 lottery game. Since it replaced The Big Game in May 2002 , Mega Millions' advertised jackpots have started at $12 million, paid in 26 yearly installments , increasing when there is no jackpot winner...

 to 1:11 million in the Michigan lottery
Michigan Lottery
The Michigan Lottery offers numerous on-line and scratch-off games, giving players a wide variety of prize possibilities. Initiated under the authority of Public Act 239 in 1972, the games collect funds to support Michigan’s public school system.- History :...

 to mention a few. Wheeling systems are intended to optimize the winning chances on smaller lottery prizes, rather than the jackpot
Jackpot
-Comics:* Jackpot , the name of several comic book characters* Jackpot Comics, a 1941 American comic book from MLJ Publications* Jackpot , a 1979–1982 British comic book-Film and television:* The Jackpot, a 1950 comedy...

. If some of the numbers a player wheels are present among the lottery's winning numbers, he will receive some of the lottery's second-tier prizes.

Full and Abbreviated Wheels are perhaps the most popular among different types of lottery wheels .

Full Wheel

Full Wheel includes all combinations that can be generated from a set of numbers a player picks. It is designed for the players who wish to obtain maximum coverage of numbers. If all of lottery winning numbers are in the group a player selects, he will win the lottery jackpot as well as additional prizes. If he only has some of the winning numbers in his set, he will be guaranteed to have multiple prizes.

In a famous occurrence, a Polish-Irish businessman named Stefan Klincewicz bought up almost all of the 1,947,792 combinations available at the Irish lottery. He and his associates paid less than one million Irish pounds while the jackpot stood at 1.7 million pounds. The syndicate did have a ticket with the winning numbers. However, so did two other players, and the jackpot was split three ways. With the "Match 4" and "Match 5" prizes, though, Klincewicz's syndicate made a small profit overall.

It is generally believed that full wheels are quite costly. A player who wishes to play with 10 numbers in the Pick 6 lottery game will get 210 combinations in a full wheel while to wheel 15 numbers in the same kind of lottery will give him 5005 combinations.

Abbreviated Wheel

An Abbreviated Wheel is an economical alternative for a Full wheel. Although it won't include all possible combinations of the chosen numbers, it will guarantee at least one winning ticket if a certain amount of numbers drawn fall within the wheeled number set.

A number of combinations in Abbreviated Wheel are significantly reduced compared to the Full Wheel. For example, Abbreviated Wheel for 8 numbers will only require 7 combinations. If 4 of the 6 winning numbers are among the 8 numbers player wheels, he will have at least one successful combination matching 4 winning numbers.

Filtered Wheel

Filters can reduce number of combinations in a Full or Abbreviated Wheel. For example, a filter can be set to remove combinations with all odd numbers, to include one or more player's favorite numbers in every combination, to balance the amount of odd and even numbers within the combination, etc.

Key Number Wheel

Key Number Wheel is a special case of Filtered Wheel. One or more numbers special to a player will appear in every combination of the Key Number Wheel. A player who wishes to win with a Key number wheel will need to match some of the numbers he plays with the winning numbers drawn.
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