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An Analysis of Bookie Lottery: Odds and Payouts, Special Software
By Ion Saliu, Founder of Lotto Mathematics
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Published in September, year of grace 2010; last update February 2019.
First captured by the WayBack Machine (web.archive.org) on January 12, 2020.
I started off this topic incidentally in July this year, on the previous message board. It was my response to a discovery by a loyal member of my online communities and knowledgeable user of my lotto software: Attila David.
Since I decided to close the old message board, I relocated material from it to my new vBulletin forums. (That forum was also closed in 2014.) The thread, remembered by quite a few members, was entitled: "Lotto Strategy Error: Pairs, Triples, Quads, Quints".
New lotto software was requested and I responded by writing and offering new lottery software: "Breaking Lotto Combinations into Pairs and Triples". The new software at that time was named BreakDownNumbers.exe.
Attila David had written in-house software that reported the skip of every pair of a lotto drawing. To my surprise, some lotto pairs skip over 100 draws, even 200 draws... how about more than 300 drawings sometimes! My lotto software (Report6.exe in the Bright6 package) does similar reports, but it only shows the lowest skip of a (sub)group of lotto numbers. That's the minimum level of the respective lottery filter.
For your info, these are the filter names in my lotto software and their corresponding subgroups of numbers –
~ TWO, representing the lotto pairs;
~ THREE, representing the lotto triples;
~ FOUR, representing the lotto quadruples.
I noticed in Attila's reports that 4 to 8 pairs, in each draw, had skips larger than 80. So, I surmised it would be a good lottery strategy to set the minimum level of the TWO filter to 80. Let the sequential lotto generator Lexico6.exe generate all combinations for that filter setting. I used in my test a results file (real draws) from Romania's 6-49 lotto game.
In other words, the program eliminated ALL pairs that came out in the last 80 draws. That is, it generated only combinations with pairs that skipped over 80 draws. The data file with the results in Romania 6-49 lotto generated 6 combinations that passed the restriction (filter). Setting the filter to 100 doesn't generate anything. Does it mean the next draw will have short skips for all pairs? Possible...
I noticed also pairing skips above 200. Obviously, there should be even more triples with skips longer than 200 draws. Therefore, setting the THREE_1 filter to a minimum of 200 would be pretty safe. However, only one lotto combination was generated!
That first test failed. Actually, we didn't have all correct lotto results at that time. We noticed that only 5 lotto pairs had skips larger than 80 in the next drawing. Obviously, such a filter setting (TWO_1_minimum = 80) cannot be successful each and every lottery drawing!
Then, another loyal member of my previous forums, Adam, came up with another idea.
“Here is the idea I'm thinking of trying out, however I got no software to implement it. Nearly anything is worth trying when it comes to shooting for a jackpot.
I would like to be able to break combinations I generated for lotto-6 after some preliminary filtering into lotto pairs and triples. Then be able to strip them of duplicate ones. Finally make all 6-number combinations that might come from them. For instance quite a simplistic example where it could be done by hand: I got 1 6-number combination that would be broken into 15 pairs and 20 triples which finally could be turned into regular 6/49 combos.”
It made a lot of sense. An output of multiple lotto combinations will, most likely, have duplicate subgroups. We can control costs better by generating the subgroups first (pairs, trips, quads), and then purging the duplicates. Thus we will play only unique groups of numeros. That's exactly what my new lotto software, BreakDownNumbers.exe, does.
Next, it was my turn to inquire on new lotto software. I wanted to expand the concept from pairs to triples and quadruples. As I said, I wanted:
“Lotto software to plot the skip of every pair, draw by draw, as in Attila David's software. But that should be only the first vertical bar of the report. Next to it should be the triples with the skips, and then the quads.
That's what I started to do. The concept is easy, but it takes attention to detail.
First, do the pairs report and save the results in an array or to a disk file. Second, do the triples report and save the results in an array or to a disk file. Third, do the quads report and save the results in an array or to a disk file.
The most difficult task is to place the three reports in a single one. Thus, you can see that draw #1 had 5 pairs with skips larger than 80, had 4 triples with skips larger than 150, and had quads with skips larger than 500 (or so; I don't know the exact results yet for trips and quads).
The winning reports in Bright6 only show the shortest skip for pairs, trips, quads, etc.
There are skilled programmers here, to be sure. I'd be happy if someone beat me in this regard and come up with software like I am talking about here.”
The same Attila David was the first to write such lotto software. But, then again, Attila doesn't write commercial software. He doesn't even compile his programs to standalone executables. But the reports of his new lotto software looked correct. Attila even sent me the source code (in C). I was taken by some surprises after my return from Romania this past July. All of a sudden, among other things, I needed a new car. I spent a long time with that chore... The lotto software that I wanted to write was pushed to the back burner.
Today, however, I was able to write the new lotto software to my liking. The new program is named PairsTripsQuads6.EXE ~ version 1.0 ~ September 2010. The report looked exactly like I wanted... and then I upgraded them. I'll show screenshots only for the latest versions.
I noticed quite a few situations when the quads (the FOUR filter) were larger than 10000, even 20000. I did another test using the quad as the lotto strategy. Again, I ran Lexico6.exe with this filter setting: FOUR-1_minimum = 10000. The run takes longer than the TWO case. It took 2 hours for my adequately fast PC to generate 772 6-number combinations. I didn't generate the combos to disk, so we was unable to break the 6-number lines into pairs, trips, or quads. But it should be an easy task for anybody.
I know, many will start strategizing right away. I think now that choosing TWO_1_minimum = 80 was too tight. It is very important that more than half of the subgroups (e.g. pairs) should pass the filter setting. The occasions are rare when 8 of the 15 lotto pairs in a draw satisfy that filter setting (TWO_1_minimum = 80). If more than half of the subgroups pass the filter setting, chances are good that we get at least one of the winning subgroups.
From what I saw (cursory look), I noticed that FOUR-1_minimum = 10000 occurs in quite a few lotto drawings. In a good number of cases, at least 8 of the quads of each draw show levels above 10000.
And, of course, a strategy is better when we combine filters. And, finally, this type of lotto strategy is better suited for bookie lotteries.
I nicely upgraded PairsTripsQuads6.exe. In fact, there is a new program, named LottoGroupSkips6. It analyzes ALL 6 number groups in a lotto-6 game: Ones, pairs, triples, quadruples, quintets, and the sextet. Incidentally, these 6 parameters should also serve as filters in a lotto program that generates 12-number combinations while working with a 6-number lotto results file.
Here is the beginning of a report:
Look at a draw like #3. The quints can be over 200000 in 4 out of 6 (over half). The sextet is over 9 million; Quad is over 1000 (minimum) and Trip is over 100 (minimum). Could be a very good strategy not only for bookie lotteries!
The lotto programs belong to software category 5.2 on this Web page: Lottery Software: Utilities, Tools, Lotto Wheels.
I created a new program for 5-number lottos: LottoGroupSkips5.exe. It analyzes all 5 number groups in a lotto-5 game: Ones, pairs, triples, quadruples, and the quintet. Incidentally, these 5 parameters should also serve as filters in a lotto program that generates 10-number combinations while working with a 5-number lotto results file.
An important clarification: ONES in LottoGroupSkips5 is calculated differently from the ONE filter in Bright5.exe. ONE filter in Bright5 adds 1 (+1) and deducts 1 (-1) from each number in a lotto draw. The ONES in LottoGroupSkips5 is identical to Any1 (in the MD filter section of Bright5; also in MDIEditor and Lotto WE).
The last parameter (Quintet) does not appear in Bright5.exe. There is a filter in MDIEditor and Lotto WE named Past Draws (right bottom corner on the input form).
Here is the beginning of a report:
The lotto-5 program belongs to software category 5.2 on this Web page:
Lottery Software: Utilities, Tools, Lotto Wheels.
The new lotto generating program is named Combine6-12.exe. The programs are bundled in a package named Bright12.exe. I left in the bundle all the programs incorporated in Bright6. I thought it convenient to do some lotto calculations or combination generating in the same interface, instead of hunting in different software packages.
I wrote also one of my best ever Web pages dedicated to lottery software strategies. It is the most thorough presentation of a lotto software package. Please read: Lotto Strategy, Software: 12-Numbers Combinations in 6-Number Lotto Games.
After I succeeded to write that complex lotto software that generates 12-number combinations based on data files (real drawings) in 6-number lotto games... I expanded the concept to pick-5 lotto games. I finalized complex lotto software that generates 10-number combinations based on data files (real drawings) in 5-number lotto games. The 10-number lotto combinations are then wheeled to 5 numbers with a special 10-number lotto wheel (˜3 of 5 minimum guarantee).
The new lotto generating program is named Combine5-10.exe. The programs are bundled in a package named Bright15.exe. I left in the bundle all the programs incorporated in Bright5. I thought it convenient to do some lotto calculations or combination generating in the same interface, instead of hunting in different software packages.
Why Bright15? Well, 5 + 10 = 15. Remember also, B15 is a vitamin extremely beneficial to humans. It is known as the vitality or longevity vitamin.
Please visit the Web page dedicated to this new lotto 5 software package: Lotto Strategy, Software: 10-numbers Combinations Wheeled to 5-number Lotto Games.
I thought it might be of interest to those of you who play 6/49. I've found the following filter settings quite promising:
Quads: 200
Quintets: 2,500
Sextets: 50,000
You have to let the program run for quite some time, for example for the night. Chances are good that you will have generated 10-15 combinations by the morning.
I already uploaded the update (the entire Bright12 and Bright15 packages). They can be downloaded immediately by the registered members of my software download site.
Again, as I wrote about before, Attila David thought that he wanted a clustering program like the shuffle option in my Combine6.exe (in Bright6). Attila wanted the program to generate square clusters or matrices. That works only with lotto games where the largest number is a perfect square (25, 36, 49, 64). Of course, there are only two viable options: 6-by-6 = 36 and, especially, 7-by-7 = 49.
I did write that lotto program easily. I only had to delete lots of statements from Combine6-12. I did a better job at testing. That's how I discovered the errors in Combine6-12.exe and Combine5-10.exe. The program only works with the 6 / 49 lotto game and nothing else. The filters are the same as in Combine6-12.exe, except for the ONES (Singles) filter. That's because we must play all 49 lotto numbers in the game. This new lotto program, Cluster49-7.exe, appears to be really faster compared to the shuffle generating in Combine6.exe.
For now, I'll post here a few clusters generated by Cluster49-7 for the SEXTET set to 200000 (two hundred thousand). I'll do some more testing and then package everything in a Bright49. There is only one new program, really. But, again, it is convenient to have other programs handy. Besides, I wanna make it harder for some registered users who are too generous with my efforts (they share with friends my software!)
23 28 38 36 4 39 44
37 8 17 43 31 15 42
12 33 6 11 40 29 30
18 49 9 45 35 1 13
21 47 2 22 3 20 7
26 48 16 10 41 14 46
32 19 24 34 5 25 27
35 28 39 38 47 9 26
17 7 19 45 40 11 34
10 24 14 12 1 18 44
46 15 29 4 30 20 23
8 5 49 16 27 32 21
48 36 43 33 6 3 25
22 42 13 41 2 37 31
48 17 20 4 10 33 37
44 41 26 38 24 29 39
49 5 47 42 13 31 6
35 8 36 23 22 7 3
16 14 9 43 34 27 11
40 15 46 21 1 19 25
32 18 45 2 12 30 28
22 39 7 20 40 17 21
30 38 13 9 14 37 49
19 1 26 5 18 31 41
27 42 28 3 32 16 25
45 35 33 2 23 12 4
29 6 8 15 43 34 46
24 44 48 47 36 10 11
I succeeded to write that complex lotto software that generates 7-by-7-number matrices (perfect squares) based on data files (real drawings) in 6 / 49 lotto games.
The new lotto generating program is named Cluster49-7.exe. The programs are bundled in a package named Bright49.exe. I left in the bundle all the programs incorporated in Bright6.exe. I thought it convenient to do some lotto calculations or combination generating in the same interface, instead of hunting in different software packages.
Please read the Web page dedicated to this 6-49 lotto software package: Special Lotto Software: 7-by-7-Number Combinations in Lotto 6 / 49 Games.
From there, registered members can download the Bright49 lotto software.
1 ball correct 4/1
2 balls correct 40/1
3 ball correct 375/1
4 balls correct 3750/1
5 balls correct 50,000/1
39 Ball Game – 7 numbers drawn
1 ball correct 3/1
2 balls correct 29/1
3 ball correct 199/1
4 balls correct 1599/1
5 balls correct 14,999/1
42 Ball Game – 6 numbers drawn
1 ball correct 6/1
2 balls correct 56/1
3 ball correct 573/1
4 balls correct 7461/1
5 balls correct 7,461/1
45 Ball Game – 6 numbers drawn
1 ball correct 5/1
2 balls correct 54/1
3 ball correct 575/1
4 balls correct 6,500/1
5 balls correct 100,000/1
45 Ball Game – 7 numbers drawn
1 ball correct 4/1
2 balls correct 35/1
3 ball correct 300/1
4 balls correct 3,000/1
5 balls correct 30,000/1
49 Ball Game – 5 numbers drawn
1 ball correct 7/1
2 balls correct 89/1
3 ball correct 1,299/1
4 balls correct 22,499/1
5 balls correct 99,999/1
49 Ball Game – 6 numbers drawn
1 ball correct 6/1
2 balls correct 58/1
3 ball correct 650/1
4 balls correct 8,000/1
5 balls correct 150,000/1
49 Ball Game – 7 numbers drawn
1 ball correct 5/1
2 balls correct 38/1
3 ball correct 329/1
4 balls correct 4,500/1
5 balls correct 50,000/1
59 Ball Game – 6 numbers drawn
1 ball correct 7/1
2 balls correct 85/1
3 ball correct 1,250/1
4 balls correct 17,000/1
5 balls correct 150,000/1
59 Ball Game – 7 numbers drawn
1 ball correct 6/1
2 balls correct 55/1
3 ball correct 600/1
4 balls correct 7,500/1
5 balls correct 75,000/1
I made a comparison between the Bet365 bookie (one of the largest betting operators in the world) and the 6/59 lotto game of New York State Lottery (NYSL). It is the only jackpot game with 2 tickets for $1. But, please read the warning after this payout table.
• 1 of 1 in 6 from 59 bookie odds: 1 in 9.83
• Bet365 pays 8/1, 81% fairness (i.e. 19% house edge)
• 1 of 6 in 6 from 59 lottery odds: 1 in 2.62
• NYSL pays 0, 0% fairness (i.e. 100% house edge)
• 2 of 2 in 6 from 59 bookie odds: 1 in 114.07
• Bet365 pays 100/1, 87% fairness (i.e. 13% house edge)
• 2 of 6 in 6 from 59 lottery odds: 1 in 10.26
• NYSL pays 0, 0% fairness (i.e. 100% house edge)
• 3 of 3 in 6 from 59 bookie odds: 1 in 1625.45
• Bet365 pays 1300/1, 80% fairness (i.e. 20% house edge)
• 3 of 6 in 6 from 59 lottery odds: 1 in 48.08
• NYSL pays 1, 2% fairness (i.e. 98% house edge)
• 4 of 4 in 6 from 59 bookie odds: 1 in 30,341.73
• Bet365 pays 25,000/1, 82% fairness (i.e. 18% house edge)
• 4 of 6 in 6 from 59 lottery odds: 1 in 1,089.92
• NYSL pays 30, 3% fairness (i.e. 97% house edge)
• 5 of 5 in 6 from 59 bookie odds: 1 in 834,397.67
• Bet365 pays 250,000/1, 30% fairness (i.e. 70% house edge)
• 5 of 6 in 6 from 59 lottery odds: 1 in 72,207.49
• NYSL pays 1600, 2% fairness (i.e. 98% house edge).