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 lower-prize 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 3-number 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 lower-prize 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 (non-lottery) 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 no-wins, 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 no-win dry spell. Or, you could see the long no-win 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 short-term smaller wins. With your random combinations, your minor wins will come as series of long dry no-win 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 lower-prize matches.
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Hope it helps.
Joe Roberts

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