Abbreviated Lottery Wheels

What is an Abbreviated Lottery Wheel?

An Abbreviated Lottey Wheel consists of a set of combinations extracted from a full lottery wheel in such a manner that those systematically picked combinations would conditionally guarantee certain winnings other than the jackpot. While it not that hard to find a set of combinations that satisfy the desired conditions, the difficulty in the design of these wheels lies in minimizing those number of combinations. In mathematics, the procedure is called Covering Design and belongs to a branch of mathematics called Combinatorics.

Abbreviated Lottery Wheel Specification

In order to specify abbreviated wheels we use two parameters, namely, the notation which serves as the name or identification of the wheel and the representations which are the indices that will later be replaced the actual numbers you are playing.

The indices go from 1 to how many numbers you want to wheel. For example, the following is a representation of a wheel for 10 numbers,
1, 2, 3, 4, 5, 8
1, 2, 3, 4, 6, 9
1, 2, 3, 4, 7, 10
5, 6, 7, 8, 9, 10
Then when you play your actual numbers each one of these will be replaced by your numbers in the order in which they are listed. If your 10 numbers are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, then replace 1 by 3, 2 by 6, ..., 10 by 30. So, what you actually will mark your play slip with would be
3, 6, 9, 12, 15, 24
3, 6, 9, 12, 18, 27
3, 6, 9, 12, 21, 30
15, 18, 21, 24, 27, 30

And now let's see the notation used to identify this wheel.

Abbreviated Lottery Wheel Notations

In general, abbreviated wheels are denoted as

C(v,k,t,m)=b
In English, it reads as
"Covering of v sets of numbers combined into groups of k to guarantee at least a t if m numbers are correct, resulting in b plays."

Since there is no standard notation for the rest of us, we shall, in this website use the following notation to represent an abbreviated wheel:

"K-V, T if M in B", which means
"For a game of K numbers, V numbers are wheeled to generate B combinations that will guarantee T correct if M numbers match."

For example, a wheel identified by
C(10,6,3,4)=4
or, by our notation as
6-10, 3 if 4 in 4
would be a wheel that generates 4 plays of a 6-number game from 10 numbers to guarantee at least a 3 if any 4 of the winning numbers are among the ten numbers. In fact this wheel is nothing else but the one listed above. So, if the winning lotto numbers contain any four of the ten numbers, then at least one of the four plays listed above will have three correct.

Choosing a Lottery Wheel

There are several ways to wheel your favorite numbers ranging from a couple of plays up to all the possible combinations (Full Wheel). To choose a lottery a lottery wheel, first you need decide how many numbers you want to wheel, how many to guarantee, and if what condition is satisfied. For example, if you want to wheel 10 numbes, you may choose the following 2 combinations:
1, 2, 3, 4, 5, 6
5, 6, 7, 8, 9, 10
which is a "6-10, 3 if 5 in 2" wheel that guarantees 3 if 5 or more of the winning numbers match your ten numbers. Or, you may use a Full Wheel to generate all the 210 combinations that guarantees as many winners as your matches, including the jackpot.

In fact, in between these two extremes, there are several wheels to choose from that depend on the values of T and M. You'll have to spend more for higher guarantees (T) and lower conditions (M). If you want to guarantee a 4 if 5 match, you'll need 7 plays; if you want to guarantee a 5 if 5 match, you'll need 50 plays. To see the effect of the match M, you need 4 plays for 3 if 4, and 15 plays for 3 if 3. Obviously, "if M" actually implies "if M or more". You can find the list at our 6-Number lottery wheels page.

Finally, note that there is no unique abbreviated wheel for a given combination. For instance, you'll find wheels on the internet for a 6/49 lottery game to generate plays that guarantee a three by using all the 49 numbers. I have seen "6-49, 3 in 168", "6-49, 3 in 167", and "6-49, 3 in 163" (there is no 'if' since they cover all the numbers). The difference between these wheels is the number of plays to be generated, otherwise they all have the same purpose and result. In these situations the one that claims the minimum number of plays is the best since it is the least expensive. Whether it is a true claim or not is another question.

You can check your lottery wheel or analyze it at
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

Abbreviated Lottey Wheel with Fixed Numbers

Just as it was done for Full Wheels, some numbers may be fixed in an abbreviated wheel as well. Although this sets more stringent conditions, it will result in either better guarateed wins, or smaller number of plays generated.