Lotto Probability Draw Pattern Mathematics
Lotto Probability Draw Pattern Mathematics is the special naming convention description, proposed by the Tinkermen Lotto Report for a type of mathematical probability model, which specifically outlines the sample space structure for many lotteries that are played throughout the world.
It was originally believed to be determined in Europe and migrated to the United States sometime during the 1970s when lotteries first began to become popular. It has most often been known and described by lotto math enthusiasts as ‘Decades Analysis’.
Depending on the type of research scope undertaken by the publishing author, the mathematical model for lotto probability draw pattern mathematics can be accomplished and produced in a variety of different ways and methods. For the purposes of description within this article, the abbreviated terminology of Draw Pattern Mathematics (DPM) will be used.
This article outline will generally discuss one of the specific mathematical model types, based on the statistical model, which was first researched and produced by the Tinkermen Lotto Report in 2002 and validated by Lotto People Magazine.
“This is a Mathematical Discovery in Lotto, it proves
that Lotteries are not completely Random events”
What best describes the phenomenon of Draw Pattern Mathematics (DPM), is although lotteries are made up of many different numbers from independent random draws, winning lottery number combinations specifically tend to form into different groups and pool sizes, just like when it rains and lands naturally on the ground due to the natural law of physics.
Winning lotto number combinations tend to do this in much the same way, based on the natural flow of mathematics and the law of large numbers. Some groups of past winning number combinations tend to form much larger groups than others, even though the numbers are each selected randomly during the drawings.
When we look at each particular lottery currently available at the Tinkermen Lotto Report, we can see from these examples below that based on their Matrix Structures, each lottery will have its own total amount of draw pattern group types:
Mega Millions 92 different draw patterns
Powerball 92 different draw patterns
California Super Lotto 51 different draw patterns
Euro Millions 51 different draw patterns
Lotto America 68 different draw patterns
Lucky for Life 51 different draw patterns
The background for Draw Pattern Mathematics (DPM) can first be traced back to the theory of probability, which is the foundation for Statistics and Combinatorics that are mainly used to calculate the different draw pattern group sizes and the overall number of combinations possible.
A combination is the combined selection of all of the possible number of items from a particular group or set. A probability math formula is often used to calculate the total number of combinations that are possible.
As an example, given you have three different color items of Red, White & Blue and you only select two of those items at a time, there would be three different total color combinations possible that could be drawn overall using a probability formula.
Red & White
Red & Blue
White & Blue
Using a probability math formula often called a factorial operation, it would be calculated as:
3 * 2 * 1 / 2 * 1 =
6 / 2 =
3 total possible color combinations
Similarly, a deck of 52 playing cards selecting only five cards for any hand, can be calculated using the same probability formula:
52 * 51 * 50 * 49 * 48 / 5 * 4 * 3 * 2 * 1 =
311,875,200 / 120 =
2,598,960 total possible five-hand combinations
Individual Poker hands can also exhibit draw patterns, sub-draw patterns and different combinations of group types just as lotteries do
Lotteries throughout the world can be calculated in much the same way using the same type of probability formulas. Depending on the lotteries overall game configuration and the total amount of numbers that are selected from the total amount of numbers to be drawn from will give you the number of combinations possible. Let's take a look at just five of them:
Pick five numbers from 1 to 70 & 1 Mega number from 1 to 25
(70 * 69 * 68 * 67 * 66 / 5 * 4 * 3 * 2 * 1) * 25 =
(1,452,361,680 / 120) * 25 = 302,575,350 total combinations possible
Pick five numbers from 1 to 69 & 1 Powerball number from 1 to 26
(69 * 68 * 67 * 66 * 65 / 5 * 4 * 3 * 2 * 1) * 26 =
(1,348,621,560 / 120) * 26 = 292,201,338 total combinations possible
California Super Lotto
Pick five numbers from 1 to 47 & 1 Mega number from 1 to 27
(47 * 46 * 45 * 44 * 43 / 5 * 4 * 3 * 2 * 1) * 27 =
(184,072,680 / 120) * 27 = 41,416,353 total combinations possible
Pick five numbers from 1 to 50 & 2 Lucky Stars numbers from 1 to 12
(50 * 49 * 48 * 47 * 46 / 5 * 4 * 3 * 2 * 1) * (12 * 11 / 2 * 1) =
254,251,200 / 120 * 132 / 2 =
2,118.760 * 66 = 139,838,160 total combinations possible
Pick five numbers from 1 to 52 & 1 Star ball number from 1 to 10
(52 * 51 * 50 * 49 * 48 / 5 * 4 * 3 * 2 * 1) * 10 =
(311,875,200 / 120) * 10 = 25,989,600 total combinations possible
Using the same type of probability formulas from above, we can also calculate for each individual draw pattern group type within a lottery, for all of the different groups for each particular lottery.
Usually, when performing these deeper levels of draw pattern mathematics calculations are attempted, a Matrix Structure is first created to sort out analytically what groups of numbers are needed to be calculated.
Here are two different examples below of draw pattern group types, taken from the California Super Lotto. One of them has many numbers of combinations possible and one of them has a lot fewer number of combinations possible.
Quinto Twenty Draw Pattern (CSLP example)
This is an example of a Quinto Twenty draw pattern group type’s past draw.
This particular Quinto Twenty draw pattern group type has only been drawn one single time as a winning draw number combination in the California Super Lotto’s past 20+ year history because it's such a small draw pattern group type and it only has 6,804 total possible number combinations.
Its structure is made up of all five of the main numbers that are selected from the 1 thru 47 group of numbers, that all five of the numbers are just from the numbers from 20 thru 29.
Viewing its Matrix Structure, we can determine what numbers need to be used to be calculated. Here we see in the Matrix, that we have only one row of numbers to be calculated and all 5 of the numbers are from 20 to 29 and 1 Mega number from 1 to 27 are to be multiplied together to get the total number of combinations possible.
Using the same type of probability formula’s from above, we can calculate this particular draw pattern group type like this. There are a total of 10 different numbers possible to be drawn from over five spaces i.e. 20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
(10 * 9 * 8 * 7 * 6 / 5 * 4 * 3 * 2 * 1) * 27 =
30,240 / 120 = 252 * 27 = 6,804 total combinations possible
The mathematical calculations for this or any type of draw pattern can be simplified like this excel spreadsheet example
In order to obtain the Frequency Draw Rate, to know how often this particular draw pattern group type should be drawn over time, we divide the total number of combinations possible, for this particular Quinto Twenty draw pattern from the overall total amount of numbers possible for the type of lottery and we multiply times 100.
6,804 / 41,416,353 * 100 = 0.016%
Double Twenty Draw Pattern (CSLP example)
This particular draw pattern group type has been drawn hundreds of times in the California Super Lotto’s past 20+ year history. Its structure is more complex and made up of just two of the main numbers selected from the 1 thru 47 group of numbers, that two of the numbers are from 20 thru 29 and with no other double number combination.
Viewing its Matrix Structure, we can determine what numbers need to be used to be calculated. Here we see in the Matrix below that we now have multiple rows of numbers to be calculated. In the third column, we have two of the Double Twenty numbers from 20 to 29 and 3 other numbers from different groups of numbers and 1 Mega number from 1 to 27 that are to be multiplied together to get the total number of combinations possible.
Using the same type of probably formulas from above, we can calculate this more complicated draw pattern group type like this, because any configuration of these 4 different sub-group draw pattern group types may come up as winning draws for the lottery.
If you’re wondering where did we get the number 45 in the third column it’s explained like this. We know this type of draw pattern has two of the numbers are going to be a Double Twenty, or two different twenty number combinations over two of the possible five spaces available from the 1 to 47 main group of numbers selected during the draw.
We calculate and determine that number like this:
(10 * 9) / (2 * 1) =
90 / 2 = 45
In order to obtain the Frequency Draw Rate, to know how often this particular draw pattern group type should be drawn at over time, we divide the total number of combinations possible for this particular Double Twenty draw pattern from the overall amount of numbers possible for the type of lottery and we multiply times 100.
3,815,100 / 41,416,353 * 100 = 9.21%
The reason one draw pattern from our examples group type has been drawn a lot more times, as actual winning lottery draws than the other, is simply due to the fact that one draw pattern group type has many more number combinations possible bouncing around inside of the lottery ball machine or virtually in a computer program, than the other.
To take a quick look at all of the number of combinations possible for each particular draw pattern group type for the California Super Lotto, view this short 20 second video below or view the mathematics section tab of the database probability report:
Continuing to use the Mega Millions, Powerball, California Super Lotto, Euro Millions and the Lotto America lotteries as examples, one of the main things to understand about draw pattern mathematics (DPM) is that every time a lottery drawing takes place, the winning number combination that’s drawn, will fit within one of the corresponding draw pattern group types for that particular lottery.
This is another example below in this short 11 second video sample history chart, taken from the past draws of the California Super Lotto, of winning lottery number combinations drawn based on their draw pattern group type as they actually occurred over a five-year period from February 2nd, 2016 to June 24th, 2020
Similarly, here are the same type of draw pattern history charts for Mega Millions, Powerball, Euro Millions and Lotto America;
A broader outline of Draw Pattern Mathematics (DPM) includes:
Probability, Statistics, Combinatorics and the Law of Large numbers are used to determine Lotto Mathematics Model Structures
Lotto Mathematics Models are known as Probability Reports
Lotto Mathematics Models prove that many Lotteries, while still random events, are Mathematically Deterministic
Each Lotto Mathematics Model will have a fixed number of grouped draw patterns, that are determined by a Matrix and its Mathematics
"Lotteries are made up of independent random draws which are mathematically deterministic and that lead to probable outcomes over the course of time, due to the law of large numbers"
- John Francis / Edvin Hiltner
One of the most common ways to visually and analytically view Draw Pattern Mathematics (DPM), is to view past winning draw combinations that are actually separated by their corresponding group types. Color coding the past draw pattern group types is used for the best visual analysis.
By looking at past lottery draws that are separated by their different draw pattern combinations, into their respective group types on a spreadsheet, it allows us to see and analyze them more easily.
This also allows us to then name the different grouped draw patterns and add title labels (Alfa Codes) and gives us more of an ability to analyze them with excel formulas to separate all of the past draws in a systematic way.
Each individual group draw pattern can also be formed into its own matrix and properly labeled with a corresponding code (Example CSLP1 stands for California Super Lotto Pattern 1)
Then like we’ve described earlier, once we know the structure of a particular draw pattern matrix, we can then use mathematics to calculate the total number of combinations possible for each grouped Draw Pattern and determine how often it should be drawn as a winning combination over time.
Then lastly as we discussed above, the use of statistics models and analytical analysis viewpoints can then be used to compare the frequency drawing rates for each individual draw pattern against the actual draw pattern percentage rates taken from actual past winning lottery drawings.
So how does knowing about and using Draw Pattern Mathematics (DPM) help us gain any advantage or lower our overall chances of winning a jackpot when actually playing a real lottery, even though the drawings are random?
Part of the answer comes from understanding that 70% of lotto players often choose the fastest and most convenient method of playing the lottery using the common everyday Quick Pick Ticket. We know that based on reviewing quick pick tickets that players are receiving draw pattern combinations that hardly ever or infrequently come up as winning draws.
Let’s look at this example below of a quick pick ticket purchased for the California Super Lotto by the Tinkermen Lotto Report on July 4th 2020. The very first number combination that was randomly generated by the quick pick ticket machine was a Quad Forty draw pattern.
This particular draw pattern has a total of 73,710 possible number combinations, out of 41,416,353 total possible for the California Super Lotto. Its draw pattern frequency rate is 0.18% of the time that it will actually be drawn as a winning lottery combination over time. Based on the law of large numbers that equates to this draw pattern actually being drawn as a winning number combination just about 2 times for every 10-year span that the lottery runs.
But for every 1 million lottery players that buys a quick pick ticket, for each and every draw, that equates to 18,000 lotto players being generated this type of draw pattern group type. That’s 18,000 combinations, for just this one single example, that could of had a better chance at possibly winning a lottery jackpot, as a more favorable draw pattern number combination. Other draw pattern group types can often come up at draw rates as high as 6 to 9 percent of the time, giving the lotto player more chances and more often to have the same type of lottery combination as the winning combination drawn.
With a better perspective on what insights Draw Pattern Mathematics (DPM) offers and what a lotto probability mathematical structure model report contains, this now leads us to the next step in better understanding what number combinations to actually play.
Many lottery mathematics book authors, strategy websites and math enthusiasts around the world have written extensively on using their particular insight and knowledge to lower a player’s overall chances/odds of winning a jackpot.
This is most often accomplished using a combination of techniques, or what’s commonly known as ‘Number Filtering Techniques’ that can include:
Wheeling Numbers, Hot Numbers, Cold Numbers, Odd/Even Number Analysis, Sum, Backtracking, Mirror Numbers, Date Sum, Root Sum, Hit Sum, Sector Analysis, Positional Tracking and as we’ve briefly touched on earlier, Frequency Analysis.
These filtering technics all aim at doing the same thing, by eliminating specific numbers and groups of numbers and number combinations that are the least likeliest to come up as part of a lotteries winning jackpot drawing. The Tinkermen Lotto Report aims at doing the same thing.
Our Philosophy is simple...
'Create a community discussion that advocates the playing of the lottery, using the most convenient online mobile technologies.
While incorporating a predictable game playing strategy, of using favorable number combinations, so that more people can actually win the lottery'
Something new has recently come about that makes using the knowledge obtained from understanding Draw Pattern Mathematics (DPM) much more convenient and easier to use, with the advent of the internet and the modern mobile lottery ticket purchasing app.
This change now allows the public more opportunities to more easily incorporate a lottery playing strategy when selecting lottery number combinations to play from the internet or on their mobile playing device.
The Tinkermen Lotto Report currently attempts to do this in two particular ways, through public education and through offering correct draw pattern predictions and generated number combinations that are specific within those predictions. We start out the process by offering the public six different lotto games to choose from.
As an example, by clicking on and selecting a particular lottery, we offer precise generated number combinations that fit within particular Draw Pattern group types for draw patterns most due or are drawn more or less frequently.
After a particular draw pattern prediction has been selected by a player, the lotto player is able to create as many lottery number combinations as they want to use to play with by clicking on the GENERTE button.
The Tinkermen Lotto Report has been online and making draw pattern predictions for six different lotteries including; Mega Millions, Powerball, Euro Millions, Lotto America, Lucky for Life and the California Super Lotto for about two years now using the knowledge of Lotto Probability Draw Pattern Mathematics. We currently have an overall correct prediction rate of over 90% for all six of the major lotteries combined that we currently make draw pattern predictions for before each draw.
In closing, Draw Pattern Mathematics (DPM) has been known about by lottery math enthusiast for literately decades. But the public has been choosing to play the game of lotto at a high percentage rate (70%), using quick pick tickets.
This has given us another statistical number concerning lotteries that is seldom discussed or written about, which on average is that around 10 to 15 lottery jackpots are being won each and every year for every major lottery throughout the world.
The Tinkermen Lotto Report and others within the industry feel that if the majority of lotto players changed how they viewed and played the game of lotto using a Draw Pattern Mathematics (DPM) playing strategy, this might actually change the total number of jackpot winners each and every year.
That question still remains to be seen by the majority of lottery math enthusiast and lottery strategy websites like the Tinkermen Lotto Report, Lottery Codex, Lotto Rainbow and many others based on the internet that promote using a lottery playing strategy using favorable number combinations as opposed to playing quick pick tickets.
We wish everyone the best of Luck in Life & Lotto & please don't forget to try our special Extended Lotto Reports that give players even deeper insights into a lottery's draw pattern behavior over time.
- The Tinkermen Lotto Report