There are two sides to winning lotto. Prediction is one side and Wheeling is the other, sort of a Ying Yang thing.
In Why We Lose Part 1 we learned how Prediction of exclusively "Hot" "Average" or "Cold" numbers virtually guarantees we will lose in 99 out of 100 tries or worse.
A mathematician will tell you every combination has an equal chance to win in every drawing and this is true. What is also true, is lottery combinations can be grouped into populations of different sizes. These groups represent a percentage of the total combinations and from them combinations are expected to be drawn as often as their percentage of the whole suggests.
In other words. If a combination is a member of a group that consists of one percent of the combinations a combination from this group is expected to be drawn 1 time in 100 draws. This draw can take place no times and then twice in the next 100 draws, or be drawn twice this 100 draws and not be drawn in the next 100 draws.
Playing combinations that have a chance of winning 1 time in 100 draws, but could be drawn in any one of them is vastly different from combinations that has a chance of being drawn in almost every draw. Albeit, when the 1 in 100 draw comes up you have a better chance of winning because the population is smaller.
While you can't escape all things being equal, you can decide whether to have a chance in every draw or to have already lost in 99 out of 100 draws before the first ball is drawn.
In Part 2 we're going to learn how some popular forms of lottery wheeling also reduce your chances of winning in much the same way.
The modern form of lotto has been played in europe and the former U.S.S.R. far longer then in the U.S.A. Before the arrival of the personal home computer, mathematicians made lottery wheels or "cover designs" to guarantee prizes when prediction proves correct.
Back in those days the object was to win a jackpot and if not a jackpot, then multiple prizes and if not multiple prizes at least to win something. Naturally the object was also to keep playing costs as low as possible.
Due to the high cost of full wheels, abbreviated wheels were developed to guarantee lower tier prizes depending on how many of the winning numbers fell among those being wheeled.
Other types of wheels were developed: Pair wheels, Triples wheels, Group wheels, Pivot wheels, Compound wheels, wheels that walked around the coverage requirements of lower tier prizes and took a direct shot at the jackpot or higher tier prizes when stringent conditions were met.
Occasionally highly skilled lottery wheel makers would start with one of the specialty wheels and manage to build a valid abbreviated wheel around it to be played at roughly the same cost as the abbreviated wheel alone. Of course all wheels have the potential of playing above their guarantee; not all have a higher tier prize covered if the numbers are loaded with the internal specialty wheel in mind.
When the U.S. caught lottery fever in the mid-eighties and early nineties it coincided with the advent of the personal computer.
Computers could be run for days, even weeks, grinding out wheels by by brute force testing every possible combination against every other. It was a time of great promise for lottery players that resulted in ultimate betrayal. For you see the high winning potential wheels were replaced by wheels that saved a couple of bucks.
Not only were the internal specialty wheels missing, many of the new wheels were what we now call "split" into two parts.
The smallest possible wheel is actually one combination.
Within each 6 number combination there are . . .
20 ways to combine 3 numbers.
15 ways to combine 4 numbers.
6 ways to combine 5 numbers.
6 ways to combine 5 numbers plus bonus.
1 way to win a jackpot.
15 ways to combine 4 numbers.
6 ways to combine 5 numbers.
6 ways to combine 5 numbers plus bonus.
1 way to win a jackpot.
The way splitting works is by the wheel maker constructing two wheels.
The smallest split wheel is two combinations. Like this . . .
01-02-03-04-05-06 | 07-08-09-10-11-12
Both halves can be considered 3if3, 4if4, 5if5 and 6if6 wheels because if 3 or more of the 6 winning numbers lands on either side you would be guaranteed a 3-number win or better. However, if 3 or 4 winning numbers are evenly divided among both sides there can be no winner.
Clearly even 4 winning numbers could produce a 3-number or 4-number win on either side, though it cannot be guaranteed.
When 5 of the winning numbers fall among the 12 a 3-number win is guaranteed and when 6 winning numbers fall among the 12 two 3-number prizes are guaranteed.
Commercial wheel makers realized they could scale this up to any size by combining a 3if3 wheel with another 3if3 wheel to make a 3if5 wheel or combining a 3if3 with a 3if4 wheel to make a big 3if6 wheel.
As this trick usually shaves off a few combinations, commercial wheel makers competed to make wheels using the fewest possible combinations. Their potential customers would learn to judge the wheel quality and in turn the overall quality of the lottery system or software by the minimum number of combinations necessary to guarantee a 3# prize.
The most famous wheel of this type plays all Pick-6, 49 numbers on a 3if3of6in22 numbers 77 combinations wheel combined with a 3if4of6in27 numbers 86 combination wheel placed side by side to form a 3if6in49 number 163 combination wheel.
If your lottery goal is to play 163 tickets per draw for a 100% guaranteed 3-number win, this wheel is for you.
Unfortunately there is a devilish problem with these split wheels.
To have any chance what-so-ever of winning a jackpot all the winning numbers must fall on one side of the split or the other.
How often this can be expected to occur is exactly as often as probability tells us to expect a draw that is all odd or all even or all high or all low. In other words 1 in 100 draws. As we are playing both sides, that reduces the odds to 1 in 50 draws.
Split wheels come in all sizes. This means you must not only beat the odds of having all the winning numbers on your wheel, but when you do, you have a 1 in 50 or 2 in 100 shot at having all the winning numbers on one side. YOU CAN NOT WIN A JACKPOT IF YOU DO NOT HAVE ALL THE WINNING NUMBERS ON ONE SIDE OF A SPLIT WHEEL! This means 49 draws out of 50 you can not win. This is why we lose!
How to recognize a split wheel.
Most split wheels are easy to spot. Take this basic 3if6in24 wheel.
1 2 3 4 6 9
1 2 5 9 10 12
1 2 7 8 9 11
1 3 5 6 7 12
1 3 6 8 10 11
1 4 5 8 11 12
1 4 7 8 9 10
2 3 4 5 8 10
2 3 4 7 11 12
2 5 6 7 10 11
2 6 7 8 11 12
3 5 7 9 11 12
3 7 8 9 10 12
4 5 6 7 8 9
4 6 9 10 11 12
13 14 15 20 21 22
13 14 16 17 18 20
13 19 20 21 22 23
14 15 17 19 23 24
14 16 17 21 22 24
14 17 18 21 22 24
15 16 18 19 23 24
end 3if6in24 numbers 22 lines
1 2 5 9 10 12
1 2 7 8 9 11
1 3 5 6 7 12
1 3 6 8 10 11
1 4 5 8 11 12
1 4 7 8 9 10
2 3 4 5 8 10
2 3 4 7 11 12
2 5 6 7 10 11
2 6 7 8 11 12
3 5 7 9 11 12
3 7 8 9 10 12
4 5 6 7 8 9
4 6 9 10 11 12
13 14 15 20 21 22
13 14 16 17 18 20
13 19 20 21 22 23
14 15 17 19 23 24
14 16 17 21 22 24
14 17 18 21 22 24
15 16 18 19 23 24
end 3if6in24 numbers 22 lines
This wheel consists of a 3if3of6in12 numbers 15 combinations or lines combined with a 3if4of6in12 numbers 7 lines for an overall guarantee of 3if6in24 numbers 22 lines.
The split is easy to spot and avoid as one group of numbers is 01-12 and the other 13-24.
Naturally the mathematicians will tell you this wheel is just fine because all combinations have a equal potential to be drawn in the next drawing -- without telling you the odds of getting all the winning numbers on one side or the other is only 1 in 50 on those rare days when all 6 winning numbers are among the 24.
To disguise the obvious flaw in the wheel, commercial wheel makers randomize the numbers while retaining the split matrix like this . . . same wheel matrix with randomized pointer numbers.
1 2 5 9 21 24
1 2 13 15 17 20
1 5 15 20 21 24
1 9 13 15 17 20
2 9 11 15 20 22
3 4 6 7 18 23
3 4 6 8 12 16
3 4 6 10 14 19
3 4 14 16 18 19
3 7 8 12 19 23
3 7 10 14 16 23
3 8 10 12 14 18
4 6 7 8 10 19
4 7 12 14 16 19
4 8 14 18 19 23
4 10 12 16 18 23
5 11 13 17 21 22
6 7 8 14 16 18
6 7 10 12 18 19
6 7 12 14 19 23
6 8 10 16 19 23
11 13 17 20 22 24
end 3if6in24 numbers 22 lines randomized pointer numbers on a split wheel matrix.
1 2 13 15 17 20
1 5 15 20 21 24
1 9 13 15 17 20
2 9 11 15 20 22
3 4 6 7 18 23
3 4 6 8 12 16
3 4 6 10 14 19
3 4 14 16 18 19
3 7 8 12 19 23
3 7 10 14 16 23
3 8 10 12 14 18
4 6 7 8 10 19
4 7 12 14 16 19
4 8 14 18 19 23
4 10 12 16 18 23
5 11 13 17 21 22
6 7 8 14 16 18
6 7 10 12 18 19
6 7 12 14 19 23
6 8 10 16 19 23
11 13 17 20 22 24
end 3if6in24 numbers 22 lines randomized pointer numbers on a split wheel matrix.
See how
1 2 5 9 21 24
1 2 13 15 17 20
1 5 15 20 21 24
1 9 13 15 17 20
2 9 11 15 20 22
do not share lines with any numbers from
3 4 6 7 18 23
3 4 6 8 12 16
3 4 6 10 14 19
3 4 14 16 18 19
3 7 8 12 19 23
3 7 10 14 16 23
3 8 10 12 14 18
1 2 5 9 21 24
1 2 13 15 17 20
1 5 15 20 21 24
1 9 13 15 17 20
2 9 11 15 20 22
do not share lines with any numbers from
3 4 6 7 18 23
3 4 6 8 12 16
3 4 6 10 14 19
3 4 14 16 18 19
3 7 8 12 19 23
3 7 10 14 16 23
3 8 10 12 14 18
There are still two sets of 12 numbers on independent lines to be found in there that never share a line in common. Always look for two groups of numbers that never share lines in common to reveal split wheels. Sometimes they can be even harder to spot.
A further problem with split wheels is most lottery players and their lottery software sort the predicted numbers into numeric order and enter them onto the wheel. This means the basic split wheel will load the lower numbers on one half and the higher numbers on the other half. Assuming an even split between low and high numbers this adds another layer of: no way to win a jackpot in 49 out of 50 draws.
In Why We Lose Part 1 we saw how 16 "Hot" numbers and 16 "Cold" numbers came together to contain all six winning numbers only 3 times in 208 tries. Now imagine those same numbers being loaded onto a 3if6of32 numbers split wheel with "Hot" on one side and "Cold" on the other resulting in no way to win a jackpot what-so-ever.
Pick-5 and Pick-7 are not immune to split wheels. The Pick-5 split wheel combines two 3if3 wheels while the Pick-7 combines two 3if4 wheels for what looks like 3if7 coverage for a tempting price.
On the up-side, 4if, 5if, and 6if abbreviated wheels are immune from being split except for Pick-7 4if7 made of two 4if4 wheels and a few games where bonus numbers may apply to 4# prizes.
When you might want to use a split wheel.
Knowledge is power. Consider a split 3if5of6in20 numbers 20 combination wheel guarantees 2-3# prizes when all 6 winning numbers fall among the 20 numbers.
A 5if6in10 number wheel requires 14 combinations and concurrently covers 3if3. You can play two independent 5if6in10 number wheels in 14 lines each with multiple 4if5 coverage and still have an overall 2-3# prize guarantee if the more likely happens and 3 winning numbers fall on each side when all six winning numbers are among your 20.
The difference is in deliberately playing two independent wheels with numbers chosen for those wheels with combined coverage when played side by side, versus being tricked into playing a split wheel that secretly divides your numbers into two untenable sets.
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