Advanced Wheeling

by Robert Perkis / Lotto-Logix cr2000

Over many years of working with wheels (covering designs) I've come up with some theories that may prove useful to some members of the lottery community. None of this is to say, "I'm right and you're wrong." and if you're sure I'm wrong you might not fully appreciate what I'm trying to communicate. Contained within every six number combination are found the following prize winning opportunities . . .

20 ways to make a 3 number winning ticket
15 ways to make a 4 number winning ticket
06 ways to make a 5 number winning ticket
06 ways to make 5 plus a bonus number into a winning ticket
01 ways to make a 6 number winning ticket

This is powerful enough, that any two tickets with all twelve numbers different form a 3if5in12number2combination wheel and of course cover 3if6in12n2c as well. Three tickets with all eighteen numbers different cover better than 80 percent of the combinations necessary to guarantee a 3if6in18n prize if all six of the winning numbers are to be found among the 18 being wheeled.

As wheels grow larger to capture better prizes and/or to bring more numbers into play, combinations form that contain some of the same sub-combinations as other combinations in the wheel.

Here are the pointer numbers for a simple 4if5in9n3c wheel...
1-2-3-4-5-6 4-5-6-7-8-9 1-2-3-7-8-9 notice how the three
sub-combinations 1-2-3, 4-5-6, 7-8-9 are all used twice in this balanced wheel. If you were to have the three winning numbers 3-6-7 you could not win, that's why this is called a 4if5 wheel. On the other hand if you had any combination of 5 of the 9 numbers on the wheel you would be 100% guaranteed one 4 number winning ticket and if you had all 6 of the winning numbers among the 9 not only would you have a guaranteed 4 number win, you would also have about 65% coverage of what it takes to guarantee a 5# win. Not bad for three tickets.

Anyway the point was the three redundant sub-combinations in this little wheel. As wheels grow these tend to multiply to the point where we're buying a lot of redundant coverage for little prizes we're not all that interested in winning.

I used to have a lottery program called LottoMan by Scott Piel one of the first to actually make wheels on the fly from scratch. On an old computer you could actually watch the percentage of coverage grow as combinations were tested. What caught my eye, was how at first the combinations covered a big percentage of what was necessary to cover, at 80-90% coverage a wheel had far fewer combination then the wheels I was using from books and lotto software.

I mean, I was seeing 90% coverage of 4if6in18n in only 24 combinations when 42 are required for 100%. Unfortunately the program could not be stopped at that ideal point and continued the build by throwing random combinations at the problem which would result in a bloated wheel of about 60 combinations.

Still I realized even back then, 90% coverage at 2/3rds the cost to play was the direction I wanted to go.

[side note] Yes, anytime you play fewer tickets your overall odds of winning are lower when computed by the simple process of dividing your number of tickets into the total number of combinations. I personally believe you are best off buying the most efficient coverage your budget allows to get the most bang for your buck.

Remember the 4if5in9n2c wheel above, well here it is at the front of a 4if6in12n6c wheel. . .

01-02-03-04-05-06 04-05-06-07-08-09 01-02-03-04-05-06

01-04-09-10-11-12 02-05-06-10-11-12 03-07-08-10-11-12

The larger wheel has been front loaded with a smaller tighter wheel at no additional cost (abet possible a fraction of a few points less efficient in some prize tiers) yet with much greater potential for those who rank their numbers from most likely to least and put them on the wheel in that order.

In the same sense, I found within the area of savings by playing wheels of 80-90% coverage rather then the bloated 100% wheels, there was room to add a combination here and there to turn clusters of combinations into stand alone quality wheels within the larger wheel.

Now sure, you might say any collection of combinations you find within a wheel will test out to percentages of coverage and be called an open-cover wheel, just as above I showed you how any two or three tickets form a 3if wheel. The difference is the quality and efficiency of coverage of the wheels within wheels. Just as I found you can put the 4if5in9n3c wheel into the 4if6in12n6c wheel, you can put two of those 4if6in12n6c wheels into a 3if6in24n wheel and still achieve 95% of 3if6in24numbers coverage in only 15 combinations!

Many wheels these days are made by putting a 3if3 wheel next to a 3if4 wheel to make an overall 3if6 cover because if all six winning numbers fall among those being played, at least 3 must fall onto the 3if3 or if not then 4 must fall onto the 3if4 half of the wheel. This is wonderful strategy if you want to win a 3# prize. If you want to do better, then all the numbers must fall onto one side or the other. Even though it is always slim odds to find all the winning numbers on a small wheel, you have a better chance of it happening when they are of equal size and strength, rather then a small 3if3 standing alone from a 3if4 with no numbers in common to both sides.

Despite the obvious value of open cover wheeling (playing a high percentage of coverage by eliminating some redundancy at a reduced cost to play) some experts insist even the smallest hole in a cover is a sure bet to lose the prize. I always have to wonder why they play if they are that unlucky. On the other hand, it is also possible to make a wheel that operates on sort of an either/or principle. Where you have say a 5% chance of a 5# win or an 85% chance of winning a 4# prize if all six winning numbers are among those being played and if the 10% chance of a loss kicks in you win 10 or more 3# prizes as a consolation instead, all for a 3rd less then playing a 100% 4 if wheel. Not to mention all the times you will get a 4# and some 3# wins.

Because of the time it takes to educate people, most lotto products won't tell you the advanced options you have to get the most efficient coverage for your playing dollar. And yes, the most likely return on a 3if wheel with or without multiple wheels within wheels is some 3# tickets. And yes, in both cases it is possible to get lucky and do better, but in the case of wheels within wheels you put targets of known quality in there on purpose. In the case of front loading, your skills pay off when proven correct, rather then diluted across a balanced wheel. You have to play in the way that's best for you, provided you are aware you have choices. To learn more about wheeling start here...

Philippe Coustaux's Wheeling: get the only thing you have to remember to do is give your wheel a name ending in .txt (ie: 46126.txt) so you can find it in the same directory.
http://Philippe Coustaux's wheeling repository

Nick Koutras' Wheel builders and techniques

The Lottery Institute

John Rawson's CoverMaster wheel builder Fantastic Wheeling Program

Download the Temp.Doc for CoverMaster (browser download only) 39k

Return to Lotto-Logix Wheeling

Good luck to you.

All rights reserved copyright Lotto-Logix 1998-2002