8/18/2012

Grand Lotto 6/55 When Do Leapers Leap?

A lotto number may take some time to win again. If that is the case, the number leaps at least 2 draws before it wins again. In contrast, a skipper skips only 1 draw whereas a leaper leaps 2 or more draws.

My previous post states that a repeater occurs at 52% probability. At 49%, a skipper occurs. In all other cases, a leaper occurs around 31%. If you notice, adding up the percentages exceeds 100%. The reason for that is that a repeat, a skip, and a leap can occur all at the same time from one lotto drawing.

Frequency of lotto numbers winning again after 2 draws
LeapersFreq%Ratio
356100%
019154%2
113438%3
2308%12
310%356

The table above reveals that a 2-draw leap occurs at 46% or a ratio of once every 2 draws. A 2-draw leap means that a lotto number may win again after 2 draws. Two leapers from one draw is rare (8%); while 3 leapers from one draw is nearly impossible. The chance that a number may not win again after 2 draws is 54%.

The next table reveals the probability of a winning lotto number emerging from the last 4th draw or a number winning again after 3 draws. At 35%, yes, it is possible. However, it is more often that it doesn't emerge from there (65%).

Frequency of lotto numbers winning again after 3 draws
LeapersFreq%Ratio
355100%
022965%2
110229%3
2236%15
310%355

Likewise, the probability a number from the last 5th draw to win again is 38% (a number winning again after 4 draws). However, more often than that, at 62%, it can come from other previous results.

Frequency of lotto numbers winning again after 4 draws
LeapersFreq%Ratio
354100%
021962%2
111934%3
2154%24
310%354

Let's look at another set of data. This time, a 5-draw leap, which occurs at 31%. A number from the last 6th draw can win again after 5 draws.

Frequency of lotto numbers winning again after 5 draws
LeapersFreq%Ratio
353100%
024569%1
19828%4
293%39
310%353

Based on all the data above, it is more often that only 1 number comes from a previous draw result. Very seldom that the jackpot takes 2 numbers from the same draw. Also notice that the non-occurrence of a leap occurs more than its occurrence. The reason for that is that the jackpot numbers do not come only from the 3rd to 6th previous draw. It can also emerge from the last 1st draw (repeater), last 2nd draw (skipper), and beyond the 6th draw.

In a nutshell

So far, we covered only the possibility of jackpot numbers coming from the last 6 draws – repeats (from the last draw), skips (from the 2nd last draw), and leaps (from the 3rd to 6th last draws). It is also possible that numbers from much earlier draws can win again.

Only one number usually emerges from any previous draw result. The occurrence of a repeat is as often as its non-occurrence. Likewise, the occurrence of a skip is as often as its non-occurrence. In the case of a leap (2 to 5 leaps), its non-occurrence is more often than its occurrence. That means that a leap is not concentrated only from the last 6 draws.

8/10/2012

Grand Lotto 6/55 Frequency Of Skippers

If a repeater is a number that wins again on the next draw, a skipper does not; but instead, wins again after the next draw. There is one draw apart.

The table below shows how frequent a number skips and how many numbers usually skip.

Frequency of Skippers
SkippersFreq% Recur
352100%
018051%2
113338%3
2329%11
372%50
400%0


How often does a skip occur? A skip occurs every, but not exactly, 3 draws. Based on 352 draw results, 49% of those has skippers. On the other hand, as frequent as a number skips, jackpot numbers do not contain any skipper (51%).

How many numbers usually skip? At most, 38% of all the jackpot numbers contain 1 skipper. There were only a few times (9%) that the winning results contain 2 skippers or 3 skippers (2%).

When do skippers usually recur? If today the jackpot has a skipper, the next draw contains again another skipper (see first item below with 0-85). Half that probability, a skipper may not recur until after 1 to 3 draws.

Skips Recurrence
Draws Freq
172
085
140
221
315
45
54
61
71
80

A view from another angle

The idea of repeats and skips may sound confusing, and, perhaps, unnecessary. To give you a clearer understanding, let me illustrate.

Let's just say that every day, there is a lotto drawing and you want to find out where the winning numbers may come from. Will one of the winning numbers come from yesterday's draw or a day before that? If from yesterday's draw, a number is repeated. If from the day before that, a number is not repeated, instead, it skips one draw. It's also possible that both a repeater and a skipper exist at the same time. It is also possible that neither can exist.

The illustration that follows uses example lotto numbers. The ones shaded blue are repeaters. Those in red are skippers. The #2 and #8 skip a draw before they win again. The one in yellow is a leaper – it skips 2 (or more) draws before it wins again. Wouldn't it be great if you would have an idea where the next winning number can come from, whether from yesterday or 5 days before that?

Repeats And Skips Illustrated
Draw DateL#1 L#2L#3L#4L#5L#6
Today123456
Yesterday17891011
The other day2712131415
Earlier days3812161718


To repeat or to skip – that is the question. The table that follows groups the repeaters and skippers to illustrate if it is possible that a jackpot result may contain both a repeater and a skipper. Values 11 to 23 mean that there exist both a repeater and a skipper. Values 10 to 30 mean that there exist only repeaters. Values 01 to 03 mean that there exist only skippers. Zero-zero means that neither a repeater or skipper exists. Notice the percentages. They are almost close to each other; not much deviation. That means that there are 4 possible options that are almost equally probable.

Frequency of Repeats and Skips Combined
DrawsFreq Subtotal% Remarks
350 350 100%
00949427%No repeats, no skips
1154
1216
131
2121
223
232 9728%Combination of repeats and skips
1069
2011
304 8424%Only repeats, no skips
0158
0213
034 7521%Only skips, no repeats

Applying repeats and skips to combine numbers

When combining numbers, you can observe these rules based on the factors we just established in relation to repeaters and skippers. To keep it simple, let's assume that there is a lotto 6/55 draw every day.

Option 1
  • Repeat 1 number from yesterday's draw (1 repeater).
  • Repeat 1 number from the draw just before yesterday (1 skipper).
  • Get the other 4 numbers from any time 2 days ago or earlier (4 leapers).
Option 2
  • Repeat 1 number from yesterday's draw (1 repeater).
  • Get the other 5 numbers from any time 2 days ago or earlier (5 leapers).
Option 3
  • Repeat 1 number from the draw just before yesterday (1 skipper).
  • Get the other 5 numbers from any time 2 days ago or earlier (5 leapers).
Option 4
  • Get 6 numbers from any time 2 days ago or earlier (6 leapers, no repeater, no skipper).

1 Thing Leads 2 Another

8/04/2012

Grand Lotto 6/55 Winning Frequency Of Seed Numbers

First, what is a seed number? Seed numbers refer to numbers 1 through 9. Every number has a seed number. For example, the seed number of 11 is 2. The seed number of 17 is 8. The seed number of 30 is 3. The seed number of 68 is 5. To figure out the seed number of a natural number, simply add its digits. For example, 1 + 1 = 2, the seed number of 11. Another example is 2 + 0 = 2, which is also the seed number of 20. The seed number of 68 is 5, arrived at by adding 6 + 8 = 14, then further reduce it to 1 + 4 = 5.

Remember our medians and quantiles? For medians, we group the lotto numbers into two parts: odd and even numbers. We also group them and separate the low numbers from the high numbers. In quantiles, we divided the lotto numbers equally into 5 groups namely: 1 – 11, 12 – 22, 23 – 33, 34 – 44, and 45 – 55. For each grouping that we did, we discovered something meaningful to increase our odds of winning the lotto 6/55.

Here's another quantile – grouping the numbers 1 to 55 according to its seed number.

Lotto Numbers 1 - 55 Grouped According To Seed Numbers
123456789
123456789
101112131415161718
192021222324252627
282930313233343536
373839404142434445
464748495051525354
55

Now, take a look at the data below. Notice that the frequency of winning of each seed number does not significantly deviate from the rest, except between the highest and the lowest values. It appears that any seed number is as good as any other. The occurrence of multiples, however, tells us something more significant – singles occur more than doubles. However, if you're going to add up all the double occurrences, this sums up to 351, which means that nearly every draw, a double emerges. The problem is that we can not exactly pinpoint which seed number will double.

Winning Frequency of Seed Numbers
Seed#Freq%1x2x3x4x
351532
1 271 77% 139 54 7 1
2 221 62% 140 34 5 0
3 240 68% 145 43 4 0
4 242 68% 144 40 6 1
5 197 56% 118 26 9 0
6 231 65% 149 32 6 0
7 238 67% 136 45 4 0
8 240 68% 147 36 7 0
9 244 69% 147 41 5 0

Eliminating the lower probability

Let's explore further the occurrence of multiple seed numbers. Yes, it is possible for two jackpot numbers to emerge from the same seed number. For example, from the jackpot numbers 4 – 5 – 25 – 26 – 38 – 53, the seed number 8 occurs twice (26 and 53). But how often does this occur? Examine the next table of data.

Occurrence of Multiple Seed Numbers
MultiplesFreq%
Singles (non-multiple) 54 15%
Doubles 189 53%
Triples 52 15%
Double-doubles 73 21%
Triple-doubles 5 1%
Quadruples 1 0%
Mix * 20 6%

There are only 54 instances (15%) when all the jackpot numbers emerge from different seed numbers, for example, 123456, wherein no two seed numbers are the same (non-multiple, singles). A high probability is that 300 out of 354 draws, the jackpot numbers contain multiple seed numbers. The most common are doubles (53%) wherein 2 numbers have the same seed numbers, for example, 123455. Rare instances, other than the singles, are double-doubles (for example, 122355) and triples (for example, 122235).

* A mix occurs when the jackpot numbers contain doubles and triples. Note. The total percentage exceeds 100% because of the occurrence of mix multiples.

Combining lotto numbers

Therefore, when combining numbers, make sure that there exist 2 lotto numbers that belong to the same seed number – a mix of singles and one double. From time to time, you may opt for all singles (no multiples), triples, or double-doubles.

1 Thing Leads 2 Another

8/02/2012

Grand Lotto 6/55 Line Groups Probability

Is it possible that jackpot numbers come from a specific number group?

In Statistics, there is a term called quantiles, wherein the data are divided equally into, not just two equal parts (called median), or 4 equal parts (called quartiles); but, also 5, 6, 10, or even 100 parts. If we apply the same idea to lotto, can we see something good? Let's find out.

I grouped the lotto 6/55 numbers into 5 equal parts as follows: (1 to 11), (12 to 22), (23 to 33), (34 to 44), and (45 to 55). What I want to find out is that if there are instances when the jackpot numbers come from only one group; if not, what are the groups where the jackpot numbers usually emerge from? The data below reveals the answer.
Line Groups
1 - 11
12 - 22
23 - 33
34 - 44
45 - 55
410
399
419
409
427

Based on the preceding data, the jackpot numbers are fairly distributed among the 5 groups. That means that the winning number can come from any group.

On another angle, let's look at the table below. This is something more interesting.
Line Groups
Number of groups
Frequency
%
1
0
0%
2
11
3%
3
95
28%
4
180
52%
5
58
17%
Total
344
100%

What follows are what the data reveals

  • Jackpot numbers do not emerge from only one group. 
  • Jackpot numbers come from 4 groups most of the time. 
  • In rare instances, jackpot numbers can emerge from 3 groups or 5 groups. 
  • Very seldom, that jackpot numbers emerge from 2 groups only. 
Therefore, when you combine your numbers, they should come from 4 groups. In rare instances, you may consider 3 or 5 groups; but, never from 1 or 2 groups only.

The information just revealed eliminated more lotto combinations that have low probability chances.

1 Thing Leads 2 Another