How Big is a 'Full' Lotto Wheel?

A "Full" Lotto wheel covers every possible Jackpot combination in a set of numbers.  The more numbers you want to cover, the more combinations you must have to cover them.

For a small set of numbers, the full coverage does not have to be very large.  For example, to cover 8 numbers in a Pick-6 game you need just 28 combinations; for 9 numbers you need 84 combinations, and so on.

For larger sets of numbers, full coverage gets out of hand.  It gets impractical and very expensive.  You can have millions of combinations.

This article shows you how impractical a Full wheel is, if you want to play all possible combinations in a typical Lotto game.

For an example, we'll take a Pick-6 game with 49 numbers.

A game of this kind has 13,983,816 possible combinations.

Here is what you'll get, if you want to play every combination.

If you want to make a Full wheel with 13,983,816 combinations, consider how much space you will need -- on your PC's disk, and in your RAM memory.

In a text file, each combination in this range:

1 2 3 4 5 6
...
4 5 6 7 8 9

... takes 13 bytes.

And each combination in the range:

10 11 12 13 14 15
...
44 45 46 47 48 49

... takes 19 bytes.

A full wheel containing all 13,983,816 combinations will require about 270 megabytes of storage on your hard disk.

There are methods for file compression, but ultimately if you are going to "do something" with the file, such as viewing or printing it, you'll need to get it into its pure text form.  You'll have to handle a file that is 270MB in size.  That can be bigger than most other files in your PC.

If you want to view or print that file with your 13,983,816 combinations, you'll need to use it in typical application software.  For example, you'll need to open that file in a wordprocessor or spreadsheet application, like Microsoft Word or Excel.

Word or Excel does not do well in reading a file of that size.  You'll spend plenty of time waiting, while Windows works out what to do in your PC's RAM and what else to do, if necessary, in your PC's hard disk swap file space.

You'll see lots of hourglasses on your monitor screen.  A 270 megabyte text file is not a trivial thing.

Now we'll consider your printout of 13,983,816 combinations.

Consider the printed page.  Suppose you print 4 combinations across per line, with 70 lines per page.  That will give you 280 combinations on each page.  You'll need (13,983,816/280) a stack of 49,943 pages.

A ream of paper (500 pages) is 1.5 inches high.  If you print single-sided on each sheet of paper, your printout will be about 12.5 feet high. If you can do it on a duplex printer you'll have a stack just over 6 feet high.

You would also have to consider your printing cost, because you will have to pay for your paper and your laser toner or inkjet cartridges.  You're going to use about 100 reams of paper if you print single-sided.  At a cost of $4.00 per ream, that's $400.00 cost for your paper alone.  If your laser toner cartridge lasts for 4,096 pages, you'll be replacing 12 cartridges, at a cost of about $50.00 each.  That's another $600.00 cost for your cartridges.

If your printer outputs at a speed of (say) 10 pages per minute, it will be printing continuously, night and day, for a total of 83 hours.

Now you have your printout.  You have 13,983,816 combinations printed on 49,943 sheets of paper.

If your pages are printed single-sided, your stack of paper is 12.5 feet high.

You have to decide what you're going to do with it.

Suppose you can't afford to play all 13,983,816 combinations.  You want to choose some of them, by marking them with a 'highlighter' pen.  You'll be working with your pen in a stack of pages 12.5 feet deep, if they are printed single-sided.

Instead of a paper printout, perhaps you'd rather view the combinations on a screen display, assuming your PC application can handle a 270MB file.  On your PC monitor, you can view perhaps 100 combinations per screen.  You'll be scrolling through thousands of screens.  It would take many hours, working with your keyboard's Page Up and Page Down buttons, or with your mouse scroll wheel.

Now let's consider what happens when you play all of those 13,983,816 combinations.

Somehow you'll need to get the combinations marked on your game's Lotto playslips.

The UK 6/49 game's playslip has 7 panels.  That is, each playslip takes 7 combinations.

The Canada National 6/49 slip has 10 panels.  Florida's former 6/49 slip had 5 panels.

Marking 13,983,816 combinations would require this many playslips:

UK:  1,997,688 playslips,
Canada:  1,398,382 playslips,
Florida:  2,796,764 playslips.

If your software will print the playslips for you at 10 seconds per playslip, it will take this long:

UK:  231 days,
Canada:  162 days,
Florida:  323 days.

Review those times again.  With one printer, you would be printing playslips continuously for months.  You would probably want to do it on multiple printers.

Now at last you have your playslips.  What do they look like?

At a thickness of 0.1mm per playslip, you have a stack of playslips this high:

UK:  655.4 feet,
Canada:  458.8 feet,
Florida:  917.6 feet.

Now it gets really interesting.

The player takes his stack of playslips to his local lottery outlet.  He is ready to play them.  The ticket agent now begins inserting the playslips, one at a time, into the slot in the lottery's computer terminal.  He prints out a lottery ticket for each playslip, and hands the ticket to the player.

How long will it take to play those playslips?

At a rate of one playslip per 6 seconds (600 per hour), the lottery ticket agent will be inserting playslips into the terminal continuously for:

UK:  3,329 hours,
Canada:  2,330 hours,
Florida:  4,661 hours.

There are 168 hours in a week.  If the player divided the playslips into 10 stacks, and took them to 10 separate lottery ticket terminals:

In the Canada game, those 10 lottery ticket terminals would be going 24 hours a day for 9.7 days.

That's 10 separate lottery terminals, working around the clock, for 9.7 days -- and at each terminal, the ticket agent inserts a new playslip every 6 seconds, continuously, 24 hours a day.

That's for the fastest game.  The other two games would take longer.

During that time, 10 lottery terminals are continuously being used for one person's playslips.  If other players arrive with their playslips, it will take even longer.

People are not going to wait in line for 9.7 days to play.  And it's unlikely those lottery ticket agents would enjoy their jobs during that time.

One more thought.

Back to the printed list of combinations.

We have printed out our 13,983,816 combinations, 4-across per row, 70 rows per page.  Each page has 280 combinations.  We have 49,943 pages.  At a thickness of 1.5 inches per ream (500 sheets), our printout is 12.5 feet tall.

We are now standing in front of our stack of paper, 12.5 feet high.

Somewhere inside that stack of paper, somewhere, is the winning combination the game will draw on Saturday night.

That's why lottery players use filtering in their combinations.

With filtering, the idea is pick out the desired combinations during the wheeling, not afterwards.

For example, if a player's budget is for 20 combinations, it makes no sense to make a full wheel and then manually select those 20 combinations from it.  Here's why it makes no sense to do it that way.  First, the player has gone through the time and effort to produce 13,983,816 combinations.  Then he has selected just 20 of them and rejected 13,983,796.  That's not a productive process, nor even a logical one.

It's far better to reduce those combinations "up front" through filtering methods.  It has the same outcome -- to get a final set of combinations the player wants to keep.

When you use software filtering, you decide on the kinds of combinations you want to play.  The software does the rest of the work for you.  It scans the full set of combinations.  If a combination meets your criteria, the software keeps it for you.  If the combination does not meet your criteria, it is simply not produced.  At the end, you get your set of combinations at the playing cost you have decided on.

Filtering your combinations down from 13,983,816 to just 20 does not give you 'better' combinations.  Your chances of winning a prize with them are the same as with any other set of 20 all-different combinations.

Filtering, like wheeling, is not any kind of 'prediction' tool.  With filtering, as with wheeling, the idea is to get a known amount of prize coverage for your numbers, for a known amount of playing cost.

Filtering is a tool for the convenience of players who enjoy tracking and playing their game.  With a few mouse clicks you have combinations inside your budget, customized as you like them for the next draw, and stored so you can check them later for winners.

Filtering software does the heavy work.  You simply use menus to choose the kinds of combinations you want to keep.

CDEX