Abbreviated Lottery Wheels
An Abbreviated Lottery 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.
There are hundreds of abbreviated wheels and each is represented mathematically by
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 represented 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.
So, if we use such a wheel on the ten numbers 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, the result 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 if the winning lotto numbers contain any four of the ten numbers, then at least one of the four plays listed above will have
We have recently added abbreviated wheels to all US nulti-number games in this web site. All non-US lottery games can use the general
abbreviated wheels available at BetStarter.com. If you have your own lottery wheel, you
can check its validity at the wheel checker page,
or analyze it at the wheel analyzer page.
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.
Abbreviated Lottery 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 guaranteed wins, or smaller number of plays generated.
• About Lottery wheels
• Full Lottery Wheels
• US multi-number games
• Lottery odds calculator
• Description and classification of United States lottery games
• List of US-state lottery games
• List of US Multiple-state lottery games