Lottery Wheeling vs Random Number Combinations
By Joe Roberts / CDEX Lottery Director
Q. I assume when you wheel your odds of winning the bigger prizes get much
better. But do you give up something so you have more losing tickets in the
long run?
A. Wheeling does not affect your odds of winning any prize. Its main job
is to give you a known match for a known cost. It's sometimes called a
"conditional win guarantee". The key word there is "conditional".
Sometimes it gets left out, so that the remaining words "win guarantee"
sound like a sure win. There is no such thing, neither with the wheel nor
without it.
What a typical wheel of good design does is this. If you match a stated
minimum amount of the game's winning numbers, then you have a stated
likelihood that one or more of your wheeled combinations will have a stated
size of winning match. For example, a typical wheel could stated something
like this:
"The game will draw 6 winning numbers. If you match any 5 of them, you will
have at least one combination that contains 4 winning numbers in it, and you
can be 100 percent sure of having it."
Or ...
"The game will draw 6 winning numbers. If you match any 4 of them, you will
have at least one combination that contains 3 winning numbers, and you can
be 90 percent sure."
There are many variations of wheels. You could visit some of the wheeling
sites listed in the newsgroup's FAQ, and get a pretty good idea of the
variety of wheels that are available.
There are two practical values to wheeling. One is that you know in advance
what your matching requirements are, what size of prize you'll see if you
fulfill those matching requirements, and what your cost will be. The second
value is in the spacing of your wins at the lower prize levels, giving you
some control over your playing budget.
When you play a set of combinations that were made at random, you probably
do not cover every possible lowerprize match for the cost you are
outlaying. In other words, you can expect to have some missing matches
(called "holes"). If you happen to match the game's winning numbers, you
may not have any prize in your combinations. For example, you might not
have all of the possible 3number sets present in your random combinations.
You matched all 6 winning numbers in your full set of numbers, but you might
see no more than 2 winning numbers in any combination. Where those "holes"
exist in your combinations, there's no prize for that drawing. Those
"holes" are compensated for by your having duplicated matches of your other
numbers, so if you happen to match those other numbers you'll have duplicate
prizes for that drawing. The trouble is, you can't predict which numbers
the game is going to draw, so you don't know (with the random combinations)
if the drawing will hit one of your "holes" or one of your duplicates.
If you put those two pieces together  "holes" and duplicates in the
matches  it means that you will tend to win multiple lower prizes spaced
farther apart in time. On the other hand, a well designed wheel contains
more balanced coverage of the matches. With it, you will tend to win single
lower prizes more often.
In all cases, for any given set of numbers that you play, and for the same
amount of combinations you make with them, the _total_ matches you will see
over a long period of time will be the same for both the random combinations
and the wheeled ones. That's _total_ matches, over a long time. They
come smaller and more often with wheeling. They come larger and less often
with random combinations.
Note that the above only applies to your lowerprize matches. Your Jackpot
chances are not affected in any way by either set of combinations  random
or wheeled.
So the "benefit" to wheeling goes something like this. If you hope to get a
big win, you must expect to be into the game for a long time (a _very_ long
time). You'll have to play fairly consistently, over a series of draws.
Until you get a major win, you'll have a net cash outgo  not income 
because your minor wins will _not_ offset your expenses until you see that
major prize. Any minor wins you receive, gives you cash you can replay. As
that happens you will outlay a proportionately lower amount of your own
cash, freeing the remainder for other (nonlottery) investment or other use
as you see fit.
It is confusing as can be, unless you try to visualize it like this:
When you play random combinations, you must expect longer periods of
nowins, followed by some multiple minor win (say, two or three matches in
the same draw). You can't help it. It's determined by the amounts of
"holes" and duplicates in your combinations. You cannot know just _when_
that multiple win will occur. It could occur on the next drawing, and then
be followed by the long nowin dry spell. Or, you could see the long nowin
dry spell run on for many drawings, eventually followed by some distant
multiple win in one drawing. Obviously if the former happens you can begin
with a slight cash windfall which you can budget for future play. But if
the latter happens you will go through a long period of no money coming back
to you, meaning that you must make the full and continuous cash outlay on
your part. You can't assume which of those effects you'll see, with your
random combinations.
Now contrast it with the wheeled combinations, for the same set of numbers.
You will see smaller wins, occurring more often. At any point in time, you
know more closely  not perfectly, but better  what your cash outlays
will be.
Either way  random or wheeled  you will see the same total cost and the
same total amount of prizes over a long time, perhaps over a span of several
years. But with the wheeled combinations, your minor wins will come to you
as a succession of relatively shortterm smaller wins. With your random
combinations, your minor wins will come as series of long dry nowin spells
punctuated by larger wins.
Keep this timing effect in the same view with your playing goal. You won't
make money in Lotto with minor wins. All they can do is offset your cost
toward the big win. Your goal is a major win like the Jackpot or large
second prize. With that goal you have to expect to be in the game for the
long term, probably for years. Suppose a set of combinations gives you back
20 percent on your play, from minor wins. Over the long term you will be
outlaying 80 percent of your cost toward a big win. Consider how you will
have to outlay that 80 percent  meaning, how you will get the 20 percent
on return from minor wins.
With the wheeled combinations, your cost will be a more steady 80 percent
than with the random combinations. To illustrate it, with the wheeled
combinations you might outlay something close to 80 percent of your playing
cost in each year for three years. With the random combinations, you might
outlay 100 percent of your playing cost in two of the three years, with just
40 percent in the other year. The point is, with random combinations you
cannot know in advance what cost will occur in any of those three years.
(There is a way to calculate your average cost, by running a 'matching
validation' test on the random combinations, but there would be little point
in doing it. You would know your average cost, but you still couldn't
predict the actual cost in any year.) So if you have other ideas for your
ready cash besides playing the Lotto (and one hopes you do), then you can
manage the cash more closely with the wheeling.
For USA players there is also some benefit in your net taxable income from
wins, with wheeling. There are some benefits where prizes are paid on the
parimutuel, although they are slight.
The bottom line is, it does not cost you any more to wheel your numbers than
it does to put them into the same quantity of random combinations. Your
Jackpot chances are identical, either way. The difference is in the more
balanced coverage of lowerprize matches.
  
Hope it helps.
Joe Roberts
CDEX
