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Lottery wheeling (also known as lottery system, lottery wheel, lottery wheeling system) is an entertaining strategy of playing the lotteries, widely used by individual players and syndicates to secure wins provided they hit some of the drawn numbers. It allows playing with more than one ticket and more numbers than those drawn in the lottery. If the lottery is pick 6, then a wheeling system can be used in playing with 7 or more numbers. If the lottery is pick 5, then a wheeling system can be used in playing with 6 or more numbers. For example, in a pick 5 lottery, a lottery system can have 9 numbers and a guarantee of 3 if 3, meaning that the player will get a 3-win whenever three of his/her 9 numbers are among the five numbers drawn. In a pick 6 lottery, an example will be a system with, say, 12 numbers and a guarantee of 4 if 5, meaning that the player will get a 4-win whenever five of his/her 12 numbers are among the six numbers drawn. A lottery wheeling system acts as a single ticket in terms of a particular guarantee, but it allows playing with a set of numbers of size larger than the size of the set of numbers drawn in the lottery. For instance, a single ticket in a pick 6 lottery guarantees a 4-win if four of the player's numbers are drawn. A lottery system with, say, 10 numbers and the same guarantee would require at least 20 tickets to be played, so it will be a well-structured set of 20 tickets, giving the same guarantee, that is, a 4-win if 4 of the player's 10 numbers are drawn. Wheeling systems allow the players to play as many numbers as they wish in a well-organized and balanced way. The term "wheeling" comes from the way some systems are constructed; it is a reference to their cyclic nature. This could be illustrated on the following simple wheel construction example, a pick 6, 9 numbers, 4 if 5 guarantee system in 3 combinations, played on the numbers 1-9 (the player can substitute any 9 numbers instead). It can be observed that this wheeling system has three groups of numbers, A = 1 2 3, B = 4 5 6, and C = 7 8 9, and the tickets are formed by the cyclic shifts of the grouping AB (the first ticket); the other two are BC and CA (tickets 3 and 2 respectively). It is easy to check that if any 5 of the 9 numbers are drawn, then there will be at least one ticket with 4 of the numbers in it, thereby providing the stated guarantee of a 4-win if 5 of the 9 numbers are drawn. The checking can be done by looking at the possible distributions of the 5 numbers drawn among the three groups, and observing that there are always two groups that contain either all 5 or 4 of the 5 numbers drawn. Since any two groups are combined in a ticket, there will always be a 4-win or a 5-win, that is, the minimum guarantee is as stated. Difficulties greatly increase in constructing systems with more numbers and combinations. In mathematics, the study of these objects falls within the branch of combinatorial design. Players are usually interested to have a certain guarantee in the minimum possible (or minimum known) number of tickets. A lottery wheeling system has a basic guarantee (as in the examples above), but it also has other, secondary guarantees, which can be observed from the table of wins for the system, as described in works of the popular lotto systems researcher, professor Bluskov.〔 Iliya Bluskov, "(Combinatorial Systems (Wheels) for Pick-5 lotteries, including Euromillions and the Mega lotteries )", Lotbook Publishing, 2011.〕〔Iliya Bluskov, "(Combinatorial Systems (Wheels) for Pick-6 lotteries )", Lotbook Publishing, 2012.〕 The probability of hitting the jackpot varies between the different lotteries. The popular US lotteries have odds ranging from the astronomical 1 in about 258.91 million in the double pick multi-state lottery Mega Millions to the fairly good 1 in about 170 thousands in the pick 5, 31 number, Wisconsin Lottery Badger 5. Wheeling systems are usually intended to provide a minimum guaranteed number of wins if some of the drawn numbers are captured in the set of the player's numbers. Lottery Wheels were introduced in the 1970s and have, over time, become a popular method of playing. Several "spin off" methods have since become popular, with mixed acceptance. From a mathematical standpoint 'wheeling' has no impact, positive or negative, on the expected value of any given ticket. Wheeling systems do have some value for lottery players, not in some hyped up "beat the lottery" way, but in terms of providing a steadier stream of wins compared to playing a randomly chosen selection of the same number of tickets. Getting some smaller wins while waiting for a larger one seems to be an attractive option for syndicates.〔 "(What is a Lottery Wheeling System? )" 〕 Lottery systems are often mis-sold as a part of various lottery strategy related products, usually bundled with lottery prediction software, and various other "tools" which are supposedly "improving the odds", "guaranteeing profits", etc., generally, the type of get-rich-quick-schemes. These are often based on some mathematically incorrect assumptions and claims, Gambler's Fallacy or plain misunderstanding or misrepresentation of important probability facts; some of the claims in one of the popular books of this type, Lottery Master Guide of Gail Howard,〔 Gail Howard, "(Lottery Master Guide )", Smart Luck Publishers, 2003. 〕 are discussed in.〔 Leah Brown, "(An Analysis of Lottery Master Guide )", Brigham Young University, 2003. 〕 A fairly exhaustive list of such products and honest reviews and criticism about each of them is compiled at.〔 "(Lottery System Reviews )" 〕 Another list, which includes only books, can be found at.〔 "(Top 15 Lottery Books )" 〕 Most of the available lotto strategies books can be found at Amazon.com, on search for Lotteries, or through the branching: Books › Humor & Entertainment › Puzzles & Games › Gambling › Lotteries .〔 "(Lotteries (Amazon.com) )" 〕 == Full Wheel == Full Wheel includes all combinations that can be generated from a set of numbers a player picks, and therefore guarantees a first tier prize if all of the drawn numbers are within the player's set of numbers; it also guarantees a number of lower tier prizes. The only drawback with full wheels is they become fairly expensive with increasing the size of the set of the player's chosen numbers. A player who wishes to play a full wheel with 10 numbers in a pick 6 lottery game will have to play 210 combinations, while a full wheel with 15 numbers in the same lottery will require 5005 combinations! In a famous occurrence, a Polish-Irish businessman named Stefan Klincewicz bought up 80% 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.〔Rebecca Fowler, "(Irish syndicate reveals the painstaking method for beating the odds )", The Independent, 1996.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lottery wheeling」の詳細全文を読む スポンサード リンク
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