Preface

Why this came to be

There's nothing much to say why I am writing this report in one single page except that I want the information and discoveries I wish to share written in an organized manner rather than on different blog posts. This report also serves as my journal or documentation of the many information I have discovered while studying statistically this type of lottery. If you are interested how this blog was conceived, you can read Why I Created This Blog on one of the pages here with the same title.

Studies I made used simple methods, basic arithmetic mainly counting, adding, and calculating percentages. What made it complicated is that I had to deal with a large volume of data, faced with a challenge on how to calculate numbers in one click. Equipped with a programming skill, the first digital tool I used was MS Access - a database program. Unfortunately, time outdated my computer and software had become unaffordable. Eventually, I switched to Excel. Macbook replaced my notebook which made me switch to Numbers (a Mac spreadsheet app). For the reason that I wanted to share my data live on this blog, I switched to Google Sheets. Unlike any database program, the use of a spreadsheet program was more of a challenge: large volume lags the sheets; you can not automate everything; studying how the built-in functions work and how to formulate them can be brain excruciating. Nevertheless, in the end, it was all fun and self-rewarding.

To make this report comprehensive even to the ordinary mind, I tried not to use technical terms but not to avoid to mention them totally, just so to express that I know what I am really talking about Statistically speaking. I also made up some terms specifically for this report. Do not worry; everything will be explained.

Do I have the right to write this stuff? Maybe, I don't. I am simply an Accountant by profession with some programming skills and with a nerdy passion for numbers. In the entire report, after this preface, I will be using We instead of I simply for art's sake.

Warning: This is a long read! The rich information may overwhelm you; so, pace your reading and be patient.

Part I

A Few Words

just about what this is

No foreword :-)

This part may not interest you, so just skip anytime. I won't mind. However, if you wish to learn a little about Math, Statistics, this type of lottery, and how I measured everything, you are most welcome. Just to prove that I make sense out of it. Let's begin your journey.

[ This report is a work in progress; so, bear with me. From time to time, come again to check if there has been updates. ]

About

What to expect in this report

This report is about a statistical study of the collected drawing results of a lottery system 6/58. It aims to find out ~

The odds of winning a lottery system 6/58. Are chances either to win or to lose? Are top winning numbers guarantee sure wins?
If probability data reveal better chances of winning or otherwise. Various probability measures were calculated to find out if numbers of probability can aid in chances of winning.
How often forms and patterns are repeated. If such significantly exist, do they guarantee better chances of winning?

At the end of every chapter, there are some exercises on how to apply the statistics without the aid of a computer or any spreadsheet software.

What Covers The Study

The study includes:

Statistical and probability data based on actual lottery results. Initially, the studies covered results from 2015 - 2018. Later studies included data until 2022. This is a progressive report, therefore, data may include lottery results from the most recent ones;
Creation and collection of measured data;
Analyses of statistical data, findings and observations.

This report classifies two types of probability: general and current. General probabilities, set as standards, are based on all actual results beginning from 2015 until 2022 (and in some cases, up to the present). Current probabilities, with the aim to capture what's currently trending, are based on the most recent draws which may cover 6 draws, 21 draws, 33 or 60 draws.

Outline

This report is presented in four parts.

Part I. Brief information about the lottery system 6/58, and the math applied in measuring statistics or probabilities;
Part II. Setting of the probability standards in interpreting lottery data;
Part III. Trending probabilities – the significance of what's trending;
Part IV. How to use the Lotto Calculator, a spreadsheet app that aids you in combining your numbers based on cohesive probability factors.

General info: The first part is an overview about what the lottery system 6/58 is; the mathematical methods that I used to come up with probability data; and a vocabulary of new terms that I made up for the purpose of this study;
The standards
The trends: coming soon...
The spreadsheet app: coming soon...

Data Sampled In The Study and Scope

For the study of this lottery system 6/58, results from Ultra Lotto 6/58 of the Philippines were used. The results cover the period 8 February 2015 (its very first drawing) up to, as much as possible, the current date. For other players in other countries, so long as your lottery system method of drawing use the tumbler method, the information here may still serve useful for adapting it to a similar system in your area. Otherwise, if you want to use your own draw results, you can just download the tools provided here and replace the results with that of your local lottery’s.

OVERVIEW

Brief general and mathematical facts

This section presents general information about the lottery system 6/58 and the mathematical facts that go with it. The Overview that follows ~

States general information about the lottery;
Explains the mathematical methods used in this study;
Calculates the probability of winning from a lotto system 6/58 based on all possible combinations;
Calculated an example of calculated margin of error to determine the reliability or sampling confidence of the probability data.

What Is A Lottery System 6/58?

A lottery system 6/58 is a lottery system wherein six numbers are drawn from numbers 1 to 58. The first six numbers drawn make the official winning numbers. The method of drawing the six numbers vary. It can be digital or traditional. The usual traditional method of drawing the numbers use a tumbler. This tumbler contains 58 pingpong balls numbered 1 to 58. Each pingpong ball is of the same size, shape, and weight with precision of up to ten decimal points or longer.

Today, lottery companies use air-pressurized tumbler to ensure that no hands intervene with the drawing of the lottery results.

In the Philippines, this type of lottery is called Ultra Lotto. Lottery companies from other countries may call it some other names. Whatever, it is called, the names are irrelevant.

Ultra Lotto 6/58 is being managed by Philippine Charity Sweepstakes Office (PCSO), a Philippine government agency. Drawing of results use an air-pressurized tumbler. Only one tumbler is used. This tumbler contains 58 pingpong balls numbered 1 to 58. The first six balls drawn determine the six winning numbers. Winning numbers are in no particular order.

How To Play Ultra Lotto and How To Win It

To play Ultra Lotto system 6/58, you pick six unique numbers from 1 to 58. Your six numbers can be in any combination and order. Using a bet card, you mark the card corresponding to your six numbers. A lotto operator feeds the card to a computer to generate a ticket. Printed on this lotto ticket are the six numbers you are playing. You can play as many tickets as you like. Each set of six numbers played costs ₱20.

Under the Aquino regime, PCSO taxed the price of each lottery ticket increasing it to ₱24. The Duterte administration moved it back to ₱20.

How You Win The Game

If the six numbers you played are the same numbers drawn during the official drawing of the lottery, you win the jackpot prize. If there are more than one winner, the winners share the jackpot prize equally. You can win a smaller prize if you matched only 3, 4, or 5 numbers. The order the balls are drawn is irrelevant.

Probability of Winning A Lottery System 6/58

Permutations vs Combinations

In Statistics, there is a difference between permutations and combinations. In permutations, the order of the numbers is significant. In combinations, the order of the numbers is irrelevant. In permutation, ABC is not the same as CBA. In a combination, ABC is just the same as ACB, BCA, BAC, CAB, CBA. For the reason that Ultra Lotto system 6/58 disregards the order of numbers, we are only after all possible combinations.

Number of All Possible Combinations

To determine the number of all possible 6-number combinations that you can make from numbers 1 to 58, use the Combination formula.

The other way to write it is —

C(n,k) = n! ÷ [(n - k)! k!]

which you read it as —

n choose k equals the factorial of n divided by all over the factorial of n minus k times the factorial of k. In other words, find all possible combinations of k objects from n items.

Let's substitute the formula with lotto 6/58.

C(58,6) = 58! ÷ [ (58 - 6)! × 6! ]

Let's read —

58 choose 6 = the factorial of 58 divided by all over the factorial of 58-6 times the factorial of 6.

The result is — 40,475,358 possible combinations all in all.

In Excel and Google Sheets, the function to find the number of combinations is COMBIN(n,k); eg COMBIN(58,6).

Odds Of Winning

Therefore, your chance or probability of winning a system 6/58 lottery is 1:40,475,358 or 0.00000247%. By playing two combinations, you double your chance. To increase your odds of winning to 1%, you need to play 404,754 combinations; this will cost you ₱8,095,080.

Margin of Error

Margin of Error (MOE) expresses how close statistics to truth. It is usually expressed with plus or minus. Let's calculate the margin of error for one of our probability findings.

The lotto numbers 01 - 58 were grouped into six such as: 1s, 10s, 20s, 30s, 40s, 50s. Based on 324 lotto results, 318 revealed that there's always 1 winning number that would come from each group.

Let's calculate its margin of error.

Margin of Error Formula

The formula to calculate the margin of error is ~

MOE = z √ {[p ( 1 - p )] / n }

where ~

n is sample size
p is sample proportion expressed in percentage
z is the confidence level (which is usually 95% expressed as 1.96; if 99%, 2.58)

You can read the formula as ~

The square root of p times 1 minus p divided by n multiplied by z equals MOE

Let's substitute the formula with our figures above.

Sample size n is 324, which is the number of draw results.
Proportion p is 318 or 98.15% probability (318 divided by 324).
Confidence level z is 99% expressed as 2.58 (this is constant based on a standard table).

So, how true is the 98.15% probability that there's always 1 winning number that would come from each group mentioned above? Let's calculate the margin of error.

MOE = 2.58 √ {[ 98.15% ( 1 - 98.15% )] / 324 } = plus or minus 1.93% or 2% rounded off.

This means that the statement mentioned above is 96% to 100% true (98.15% plus or minus 1.93%)

Quantiles

Grouping the lotto numbers with related attributes

Quantiles divide probability data into equal groups, such as a group of four, five, six or ten. If grouped into four, each group is called a quartile. If five, quintiles. If six, hextiles.

Lotto system 6/58 draws 6 winning numbers. If we are going to group the lotto numbers into 6 groups, is it possible that each winning number would come from each group?

Dividing the numbers or data into different groups reveal more information as to which numbers win most often. In Chapter 6, the data were divided into six, called hextiles, according to the frequency of winning of each lotto number. In Chapter 7, The Probability of Forms and Patterns, the lotto numbers were grouped by first digits such as 20s, 30s, etc.

Method: Simple Basic Math

Generally, most method used in the studies is simple math such as summation and calculating the percentage. It gets complex, however, when presenting the data on a spreadsheet such as manipulating the database with the use of complex spreadsheet functions and formula.

Frequently Used Terms

Probability: This is either presented in a percentage form (%) or as a ratio (x:y). Sometimes mentioned as probability rate or probability ratio.
Frequency: The number of times an event or something has occurred or recurred. For example, the number of times a lotto number has won.
Winning Frequency: The number of times a lotto number has won in a given period, which could be all-time or from a shorter period.
Instance: The number of times a homogeneous attribute has recurred in every draw. For example, how many odd numbers have won so far; or in other words, present in the entire database of drawing results. This may also be referred to as occurrence or recurrence.
Instance of instance (IoI): The presence or occurrence of homogeneous attributes in a combination of numbers. For example, the number of odd numbers in a combination.
Trend value: Also called trending value or trending score. This refers to the winning frequency of a number within a trending period.
Trend zone: Also referred to as the trending period. A trend zone refers to a certain period that comprises a smaller number of draws where numbers start to trend or cease to trend. In the case of a system 6/58 lottery, a trending period covers 21 consecutive draws starting from the most recent one.
Hot zone: The hot zone refers to the most recent 6 consecutive draws. Also referred to as the winning zone or jackpot zone.
Delimiters: Delimiters are probability indicators that delimits your choices of numbers. With delimiters, numbers with the least probability of winning are removed. Thus, instead of choosing from 58 numbers, your choices become limited to a few.
Probability indicators: Any value that indicates any level or grade of probability. A similar term is probability factors.
Rank: This is presented as an ordinal number such as 1st, 2nd, etc.
Percentile Rank: Presented as %Rank, it is ranking presented in percentage form such as the top 10%.

As you read on, you will encounter terms used specially and differently for this report.

Part II

All-Time Statistics

Setting the Standards

General probability based on all results

In these first set of chapters, all studies were based on all draw results since the time Ultra Lotto 6/58 started, which was in the year 2015 and to cover until portions of 2022; and in some cases, up to the present as shown by the date stamp in Chapter 1. All in all, the mathematical studies covered over 1000 drawing results (and growing) from Ultra Lotto 6/58. The purpose of this all-time statistics study is to establish a set of general probability standards which you may observe when picking the lotto numbers that you wish to play.

Winning Frequency of Each Number

How often does your number win?

Perhaps, the first thing that crosses your mind and eager to find out is: which of the lottery numbers usually win? Let's find out.

In Oct 2022, the probability for each number to win ranges from 8% - 12%. Following is the result from more than 1000 lottery draws. From time to time, the data are updated to give you real-time data, or at least, the most current one, as indicated on the date stamp you see just after this.

Winning Frequency of the 58 Numbers (Data 01)

The above data are arranged from highest frequency of winning to lowest as shown, alongside its probability rate. It is divided into 6 groups (called hextiles in Statistics). The first hextile, which you see on the first page, is the top 10 winning numbers of all time (at least up to the year 2022; or as indicated on the date above). The second top 10 winning numbers are presented on the second page; followed by the next 10 on the third page, and so forth and so on. The figures on the chart are updated from time to time as shown by the date above it. This date indicates up to which draw the data cover.

The figures explained

Lotto# shows the lotto numbers 1 - 58 arranged top to bottom according to each number's frequency of winning.
Win is the frequency of winning, in other words, the numbers of times the number has won so far since the first draw of Ultra Lotto. Just to give you an idea, lotto number 6 has won more than 130 times out of 1076 draws (the highest in March 2023); while the lotto number 37 has won 91 times (the lowest so far in March 2023).
Prob is the Probability Rate in percentage. In March 2023, the highest probability rate was 12.17%; while the lowest was 8.46%. Notice that the probability rates are low. This implies that all the 58 lotto numbers are fairly performing well.

You may have wondered if the top six numbers had won the jackpot before. If the top six numbers that you are seeing are 06 • 14 • 25 • 22 • 13 • 34, these numbers have not made it to the jackpot yet; not even any 5 of the numbers combined. Four of these numbers had won only once. Any 3 of these numbers had won 23 times. If these are the top 6 winning numbers, how come they have not made it to the jackpot? So, we dig further.

Top Winning Numbers

What if you play all the top winning 29 numbers? What are your chances of winning?

Data 02 is the result of that study.

Top 29 Lotto Numbers (Data 02)

Presented above are the top 29 winning numbers based on ultra lotto 6/58 drawing results from 2015 to 2022. For each draw, the presence of the top 29 numbers were determined. These are the results.

Unique combinations from the top 29 made it to the jackpot 20 times (2%).
Any 5 of these numbers had won 130 times (12.7%)
Any 4 of these numbers had won 262 times (25.6%)
Any 3 of these numbers had won 340 times (33.2%)
There were only 5 instances when none of these numbers had won. Therefore, 1019 out of 1024 draws, the chance of, at least, one of these numbers to win is 99.5%;
The chance of winning a price is 73%.
The chance of winning a jackpot is 2%.

Sounds good? Yes, but the drawback is that you need to play 475,020 combinations each time; and this will cost you ₱9.5 million pesos each time you play. Hmm! Perhaps, there's another way.

(Note that these figures were true only in 2022. For an updated list of the top 29 winning numbers, see the previous chart Data 01.)

Top vs Bottom Numbers

Let's look at the data just presented from a different perspective.

All bottom numbers made it to the jackpot only 5 times, a 0.5% probability. Choosing all bottom numbers, therefore, is not advisable.
A mix of 3 top numbers and 3 bottom numbers is the most probable with a 33% chance of winning.
Second to the 3:3 top:bottom ratio is either: 2 top numbers and 4 bottom numbers (20% probability); or 4 top numbers with 2 bottom numbers (25% probability).
Having 5 bottom numbers or 5 top numbers in your combination is possible to win but at very rare chances (at 6% and 12% probability respectively).
To increase your chances to 79%, play 3 combinations following these top:bottom combination ratio: 3:3, 2:4, 4:2.

Observation

It's not every time that the top winning numbers win. Most frequently, the winning numbers are spread through top to bottom. Moreover, though the same numbers remain on top, it does not mean that they remain active. There were periods when top winning numbers hibernate; not winning for a longer period. Thus, it may be necessary that we look at top winning numbers at current time and shorter periods. We will analyze that further in later chapters.

Try This Exercise

The objective of this exercise is for you to observe how numbers behave randomly. It is up to you whether you wish to actually play your numbers; or just observe. Using Data 01 under Winning Frequency of Each Number, combine 6 lotto numbers.

When picking the numbers you intend to play, pick through top to bottom numbers. Pick 1 number from each group. Do not pick uniformly. Think random.
Form a second combination. This time, pick 2 lotto numbers from one group and one each from any four of the remaining groups leaving one group with no chosen number.
Find out in the next draw how many of your numbers had won.

How To Do It Manually

Without the aid of a spreadsheet program, you can do your own analysis with just a pen and a paper.

List the actual lottery results from the most recent 21 consecutive draws.
For each lotto number, count how many times it has won.
Mark the top 29 numbers. It can be more than 29 or less depending on how many numbers would tie in one place.
Further divide the top 29 into 3; and the bottom numbers into 3 as well forming six groups.
For each group, select one number to make a combination. An option is to pick 2 numbers from one group and one each from any of the remaining groups.
To analyze further, for each succeeding draw, mark the winning numbers on your list, say with a stick or an asterisk, whatever you wish. In time, after 3 or more draws, you will find out which of the six groups are frequently producing the winning numbers.

In A Nutshell

The numbers that usually win are not all the time from the top numbers, ie the numbers that have won most. Bottom numbers also win from time to time; and mostly often, those in between. A good combination is usually a mix of top and bottom numbers. You have 3 options: 3 tops and 3 bottoms; 2 tops and 4 bottoms; 4 tops and 2 bottoms. This does not mean however that 5:1 ratio – 5 tops and 1 bottom; or 1 top and 5 bottoms – is not possible. It's just that it rarely happens.

Notice also, in Data 01, The Winning Frequency of the 58 Numbers, the probability rates are very close to each other. We can deduce, therefore, that the individual probability of each number to win is no longer substantial. An alternative is to use the frequency data by grouping them into quantiles such 6 or 10 groups. In later chapters, we will explore further the significance of quantiles and how each group of homogeneous data can help in determining the potential winning of each number.

Algorithm 01, 02, 03 for Programmers

If you have programming skills and wish to develop an application related to lotteries, your first algo (01) is to count the number of times each lotto number wins. To make your frequency data more significant, convert your frequency data into percentile ranking (algo 02) and then group them into deciles (algo 03).

Low vs High Numbers

Which numbers win most: 1-29 or 30-58?

Most people play numbers of important dates such as birthdays. For that reason, their combinations are mostly low numbers 1 - 31. If you’re playing only low numbers, what are your chances of winning?

At this point, you already know that winning numbers are usually a mix of top and bottom numbers. Though playing only the top 29 numbers may appear promising, it is not practical for the reason that you still have 29 numbers to choose from. So, what if, there is a way to narrow down your choices of numbers. This chapter looked at the winning probability of low versus high numbers.

Which Numbers Are Low or High

First, let us define which numbers are to be considered low or high.

The lottery system 6/58 uses 58 balls numbered 1 to 58. Divide 58 into 2, the result is 29. So, the first half ⎯ 1 to 29 ⎯ are the low numbers while the second half ⎯ 30 to 58 ⎯ are the high numbers.

Low To High Ratios

The following chart is based on more than 1100 results (Ultra Lotto drawings from 8 Feb 2015 - 2023 or beyond depending on updated records). It reveals whether most jackpot numbers are made of all low or all high numbers; or a mix of low and high numbers. If a mix, how many numbers should be low and how many numbers should be high?

Based on the chart you just saw, the ratio of low to high numbers is best at 3:3 followed by 4:2 and 2:4 ratios. This means, that at 79% in probability, your numbers are best if they are a mix of (the probability rate may change depending on updated records):

3 low numbers and 3 high numbers
4 low numbers and 2 high numbers
2 low numbers and 4 high numbers

Playing all low numbers (1 - 29) gives you a chance of only 0.8%. In 2018, it was 2.3%. Likewise, playing all high numbers (30 - 58) gives you a chance of only 1.5%; in 2018, the probability was 1.3%. It is possible to play all low or all high numbers but the chances are very rare. All low numbers occured only 16 times; while all high numbers occured only 9 times.

Playing 5 low numbers, on the other hand, or 5 high numbers gives your numbers a chance of winning by only 9.7% and 8.6% respectively. In 2018, the ratios were 8.6% and 8.9%. On record, 104 of the 1074 jackpot numbers contained 5 low numbers; while there were 92 jackpot numbers that contained all 5 high numbers.

The following was the result of the same study done in 2018. Four years after, the probable ratios have remained the same ⎯ 3:3, 2:4, 4:2.

Low	High	Freq	Prob
0	6	5	1.3%
1	5	35	8.9%
2	4	89	22.6%
3	3	119	30.2%
4	2	103	26.1%
5	1	34	8.6%
6	0	9	2.3%
		394	100%

More About Low and High Numbers

Now that you know that the common lottery 6/58 winning result is a mix of 2 to 4 low and high numbers, your next question in mind, perhaps, which number should be a low or a high one. The following table determines which ones are your low and high numbers. (This assumes that your numbers in a combination are arranged lowest to highest.) These data, which were based on 2018 study, may have little significance, but just out of curiosity, you may take a look.

	1st	2nd	3rd	4th	5th	6th
Low	389	354	265	146	43	9
High	5	40	129	248	351	385
% Low	99%	90%	67%	37%	11%	2%
% High	01%	10%	33%	63%	89%	98%

The low-high probability rates in the above table are easy to remember. When forming your combinations, just follow these rules (assuming that your numbers were in lowest to highest order).

Your very first number and your second number should be a low number (1 - 29). The probability that it is a low number is 99% and 90% respectively.
Your 5th and 6th numbers should be a high number (30 - 58). The probability that it’s a high number is 89% and 98% respectively.
Your 3rd and 4th numbers can either be a low number or a high number. The 3rd number is more often a low number (at 67% probability) than a high number (at 33% probability); the 4th number is more often a high number (at 63% probability) than a low one (at 37% probability).

You can also observe these patterns. There are only 3 patterns that you have to remember. L means low; H means high.

Ratio	1st	2nd	3rd	4th	5th	6th
3:3	L	L	L	H	H	H
2:4	L	L	H	H	H	H
4:2	L	L	L	L	H	H

However, we do not exclude the possibility of 5 or 6 low or high numbers to win a jackpot. In 2023 study, based on 1,153 results, 20.38% of the results contain either 5 or 6 low or high numbers; which is equivalent to 235 results. This rare combination of low and high numbers may repeatedly happen within 28 draws of not occurring. To capture the possibility of jackpot numbers to produce 5 or 6 low or high numbers, playing 4 low or 4 high numbers in your combination would do the trick because in such case, you would have matched 4 of the low or high numbers.

Odds of Winning After Eliminating the Least Probable Low-High Combinations

The least probable low-high combinations are:

6 low numbers
6 high numbers
5 low numbers
5 high numbers

These types of combinations comprise 7,837,830 combinations. By eliminating these least probable combinations from the total possible combinations of 40,475,358, your odds of winning for playing one combination only increases from 0.00000247% to 0.000003064%. So, the number of probable combinations now after eliminating the least low-high probable ones is 32,637,528.

Try This Exercise

You've learned so far about the probability of top-bottom numbers and probability of low-high numbers. Now, try to make a combination using the data presented in Chapter 1.

Combination 1 (3:3 ratio)

Step 1. Following the 3:3 ratio, pick one low number and one high number from the top numbers. For example:

6 • 34

Step 2. Pick one low number and one high number from the bottom numbers.

18 • 39

Step 3. Pick another number from the top number and one from the bottom number. One must be a low number and the other must be a high number.

43 • 29

Your final numbers are:

06 • 18 • 29 • 34 • 39 • 43

Combination 2 (2:4 ratio)

Do Steps 1 and 2. In step 3, this time, pick two low numbers - one from the top and one from the bottom numbers. For example:

14 • 26

Your second combination:

06 • 14 • 18 • 26 • 34 • 39

Combination 3 (4:2 ratio)

Do Steps 1 and 2. In step 3, this time, pick two high numbers.

54 • 47

Your 3rd combination:

06 • 18 • 34 • 39 • 47 • 54

In A Nutshell

So far, the standards that we have established, when combining your lotto numbers, are:

Your numbers should be a mix of top winning and bottom winning numbers. Refer to the very first chart for the list of top and bottom numbers.
Your numbers should be a mix of low and high numbers using the the high probable ratios of 3:3, 4:2, or 2:4. If you prefer to be more adventurous, play the 5:1 or 1:5 ratio (probability of 9.68% and 8.57% respectively)
The all high numbers occurred only 9 times (0.84% probability); while the all low numbers occurred only 16 times (1.49% probability).

Odd vs Even Numbers

Which numbers win most: odd numbers or even numbers?

The superstitious may prefer odd numbers over even numbers, or vice versa. But actually, superstitions have nothing to do with odd numbers winning over even numbers, or the other way around. However, statistics may reveal which type of number wins mostly: odd numbers or even numbers.

Odd-Even Winning Probability

The following study both contains data from 2018 and earlier; and 2022 and earlier. In 2018, the study covered only 441 drawing results. The probability findings for odd-even patterns were significant then. After four years, 583 actual lottery results were added to the study increasing the subject of the study to 1024 drawing results.

Findings in 2022

After studying 1024 drawing results, the odd-even patterns are no longer significant. In other words, any odd-even combination pattern is as good as the other with probability rates ranging from 0.68% to 2.64%.

The probability for the number of instances, however, remain the same with 3:3, 4:2 and 2:4 as the common odd-even ratio. If you feel being adventurous, also try 1:5 or 5:1. This is also possible, but it rarely happens, with probability rates of 8.7% and 7.5% respectively

The following pie chart gives the rest of the data. Data here are updated from time to time; thus, you might find the figures mentioned in the succeeding paragraphs inconsistent with the figures of the chart.

The 2018 Study on Odd-Even Winning Probability

In order to come up with significant probability of odd-even patterns, each result studied was arranged numerically from smallest to the largest number.

Highlights

The odd-even probability is useful if your numbers are arranged numerically from lowest to highest.
If your goal is to make all 6 numbers right, playing all odd numbers or all even numbers do not give you better chances of winning.
The most probable ratio of odd to even are 3:3, 2:4 and 4:2.
If your numbers contain 5 odd numbers or 5 even numbers, consider shifting them to 2:4 or 4:2 pattern.
Doubles (2 odd or 2 even numbers next to each other) are as popular as odd and even next to each other.

Major Odd-Even Patterns

There are seven (7) major odd-even patterns.

Six odd numbers
Six even numbers
Five odd numbers, 1 even number
Five even numbers, 1 odd number
Four odd numbers, 2 even numbers
Four even numbers, 2 odd numbers
Three odd numbers, 3 even numbers

Which of the patterns just mentioned commonly win?

The Odd-Even Probability

3:3 Odd-Even Ratio

If your combination has 3 odd numbers and 3 even numbers, you have a better chance of winning compared to all-odd numbers or all-even numbers. The probability that a result would have 3 odd numbers and 3 even numbers is 33.7%(36.5 in 2018).

4:2 & 2:4 Odd-Even Ratios

If your combination has 4 odd numbers and 2 even numbers, most likely your numbers can win by 25.1% probability. If your combination has 2 odd numbers and 4 even numbers, your odds of winning is 22.3%.

1:5 & 5:1 Odd-Even Ratios

If your combination has 5 odd numbers or 5 even numbers, your chance of winning is a low 7.2% probability and 8.8% probability respectively. If you notice that your combination has this pattern ⎯ 5 odds or 5 evens ⎯ might as well change one of the odd numbers to even; or change one of the even numbers to an odd number to increase your chance of winning. The 5 odd numbers or 5 even numbers may rarely happen but they remain possible.

All Odd or All Even

Playing all odd numbers or all even numbers are the patterns that you can ignore because together they make only a probability of 2.8%.

Odd-Even Patterns or Sequence

Note. As of today, the odd-even patterns probability is no longer significant.

Perhaps, you’re wondering which of your numbers should be odd or even and in what order. Should your first number be odd or even? What about the 2nd, 3rd, 4th, 5th and 6th?

The answer is any of your numbers can be odd or even because the probability of any number to be odd or even, without regard to ratio, is almost the same; ranging from 48%-53%. Therefore, the chance of a winning number to be odd or even is almost 50:50.

However, by eliminating what’s not probable, we would be able to zero in the patterns that are most probable.

Alternating Odd and Even Numbers

Starting with the alternating odd-even patterns (eg OEOEOE or EOEOEO), results show that this type of pattern does not frequently happen. Its probability is only 6.1%. So, might as well avoid this type of pattern. [As of today, these patterns are the most common at 2.54% / 2.64%.]

This probability also means that at least 2 consecutive numbers are either both odd or both even.

Straight Odd vs Straight Even

OOOOOO or EEEEEE

Six (6) odd numbers straight or 6 even numbers straight. This pattern has occurred only 2.5% of all the results. You can avoid these patterns. [ As of today, the probability is 1.37% for both patterns.]

OOOOO or EEEEE

Five (5) odd numbers straight or 5 even numbers straight. This type of pattern has occurred only 2.8% of all the results. If we add the 6 straight patterns, the probability of having straight 5 odd or even numbers becomes 5.3%. [ As of today, the probability for this type of pattern ranges from 0.68% - 1.27%.]

OOOO or EEEE

Four (4) odd numbers straight or 4 even numbers straight. This type of pattern has occurred only 13.5% of all the results. If we consider the 6 and 5 straight patterns, the probability of having 4 straight odd or 4 straight even numbers is 18.8%. [ As of today, the probability for this type of pattern ranges from 0.68% - 1.95%.]

OOO or EEE

Three (3) odd numbers straight or 3 even numbers straight. This pattern has occurred 35% of all the results. The probability however, of having 3 straight odd or even numbers is 53.8%. On the other hand, there is also a probability that such pattern cannot exist at 46.2% probability. This means that your combination may or may not have this type of pattern. [ As of today, the probability for this type of pattern ranges from 1.07% - 2.25%.]

OOOEEE or EEEOOO

This type of pattern (double straight 3 odds and evens) has occurred only 3% of all the results. You can avoid this type of pattern. [As of today, the probability for these patterns are 1.56% and 1.17% respectively.]

Doubles or 2 Odds or 2 Evens Straight

The probability that 2 straight odds (OO) or 2 straight evens (EE) to exist is 93.9%. This means that, at least, one double can exist in most every result. The chance that such pattern does not exist is only 6.1%. [As of today, having the most common type of pattern, its probability ranges from 0.88% - 2.44%. ]

1 Double. OO or EE. A single double can exist at 47.5% probability. Related patterns are OOEOEO, EOOEOE, OEOOEO, EOEOOE, OEOEOO, EEOEOE, OEEOEO, EOEEOE, OEOEEO, EOEOEE.
2 Doubles. OO OO or EE EE or OO EE or EE OO. Two doubles can exist at 44.4% probability. These doubles can exist in any order. Related patterns are EOOEOO, OEEOEE, OOEEOE, EEOOEO, OOEOOE, EEOEEO.
3 Doubles. This type of pattern is rare. It has occurred only at 2% of all the results. Related patterns are OOEEOO, EEOOEE, OOOOEE, EEEEOO, OOEEEE, EEOOOO.

You don’t have to memorize all these patterns. Just remember that there can only be one or two doubles in your combination. The rest of the numbers should be alternating odd-even or even-odd. [As of 2022, any odd-even pattern is as good as the other.]

In A Nutshell

There are 64 possible odd-even combinations or patterns. These patterns are applicable only if the numbers in your combination are arranged in ascending order (lowest to highest number).
The 3:3, 4:2, and 2:4 ratios are the most significant ones among the seven (7) odd-even ratios. Together, they comprise 81.1% in 2022 (82.7% in 2018) of all the results studied. So, when forming your combinations, limit your numbers to these odd-even ratios.
Though the ratios 5:1 or 1:5 is rare, it is possible.
The all odd or all even numbers combination is also possible but with very low chances (both at 1.3% probability). Both have occurred only 14 times out of 1074 draws.
Two consecutive numbers may either be both odd or both even or one odd and the other even. The patterns OO, EE, OE, and EO share almost equal probability.
Your combination should have one or two doubles (2 straight odds or evens). The remaining numbers should be alternating odd and even. [This is no longer true as of 2022.]
3 odd numbers straight or 3 even numbers straight are also common at 50:50 chance.
If you wish to play only the most probable 88% patterns, you can avoid these patterns: OEOEEE, OEEEEO, EOOOOE, OEEEOO, EEEEEO, OOOOOE, EEOOOO, EEEOEO, OEEOOE, EEOOEE, EEEEOO, EOOOOO.

Trend Values

Frequency of Winning Within A Significant Period

Trend values are the number of times each lotto number has won within a certain number of consecutive draws beginning from the most recent one through prior. In the case of a system 6/58 lottery, a trend period comprises 21 draws.

In Chapter 1, you saw in Data 01 that the frequency probability of each lotto number ranges from 8% - 12%. The rates are very close you can deduce that each lotto number is as lucky as any other. This happens when you are dealing with a large number of data (termed population in Statistics). If you are going to picture a linear chart as a result of large volume data, you will see the line that seems to flatten out; or column bars that are almost of the same height. This is not true if your data population is just about a hundred or a little more. Statistically, however, a smaller population, depending on the type of your subjects, data can become insignificant or not closer to the truth.

Good thing, in a lottery, a smaller volume of data can be significant as well because we are not only after what is standard, but also what is trending.

The Trend Period

The trend period refers to the most recent 21 consecutive draws. Why 21? In a later chapter, you will learn how this 21-draw period was established as the significant period. This period is significant because this is where the action takes place. This is where you see which numbers are trending and not trending; which numbers are winning again and again, or about to win, and which are turning cold.

For the purpose of this report, we shall term Trend Value as the frequency of winning of each lotto number within a trend period only.

How The Trend Values Were Calculated

The trend period is variable. The 21 draws that it covers changes every time a new draw occurs. So, if there were a total of 1,008 draws, the study covered 987 trend periods; and for each of this 21-draw period, the frequency of winning of each lotto number were calculated. These calculated winning frequency is termed in this report as trend values.

Furthermore, the presence of common trend value for each winning jackpot numbers were counted and collected to determine how many similar trend values can usually exist in a winning combination.

The trend values were tallied and the result is summarized in the following chart as trend values of all jackpot numbers at the time of their winning.

Data 03. Probable trend values of winning numbers

Probable Trend Values as Delimiters

Let's examine the chart (Data 03) one by one.

The highest column on the chart has a trend value of 2. It means that lotto numbers that mostly win (28.3% probability) are those with a trend value of 2. In other words, if a lotto number has won twice, so far, most likely, it is going to win the third time.
The next highest column is that with a trend value of 1 followed by that with a trend value of 3. This reveals that lottery numbers that have won once (24.8% probability) are also likely to win again. Likewise, those lotto numbers that have won thrice (20.5% probability).
If a lotto number has already won 4 times (trend value 4) during the last 21 draws, there's only a 10.7% chance that it may win again.
If a number has won 5 times or more, its chance of winning again becomes very slim (3.5% if 5 times; 1.4% if 6 times; 0.4% if more than 6 times).
If a lottery number has not been winning for the last 21 draws (trend value zero or outside zone numbers), there's only a 10.1% chance that it could win. Outside zone numbers are considered cold numbers.

Below is the complete trend value data calculated from 1,008 draw results.

Data 04. Probable trend values of winning numbers

Instance of Trend Values

Now that you know that if a lotto number has a trend value of 1, 2 or 3, it is more likely to win compared to others. The next question is: if you would form your combination, would you pick all numbers with only a trend value of 2, or 3 or 1 or a mix? If it is a mix, how many 2's, 3's or 1's should there be in one combination?

The statistics below gives you an idea on how you can form your lotto combination based on trend values.

Data 05. Instance of trend values per jackpot set

Lotto 6/58 Instance of trend values per combination

Understanding the table

Instance 0-6. The number or existence of the same trend value in a combination. For example, 2 means that there are 2 lotto numbers in the combination that have the same trend value.

Trend values 1 to >4. TV stands for trend value.

The figures under each trend value column refer to the number of jackpot results that contain homogeneous trend values. For example, there were 380 results that contain a lotto number with a trend value of 1; and there were 301 results that contained 2 lotto numbers that had a trend value of 1.

The corresponding next 6 columns are the probability rates calculated as the figures in the first 6 columns divided by 1009 (the total draws).

Setting the trend value parameters

Based on the above data, we can now set the parameters to delimit our choices of combinations. For example, it is almost improbable that your combination to consist lotto numbers with 6 exactly the same trend values, such as something like this: 111111, 222222, 888888 etc.

What is more probable is that your combination to contain a mix of one or two numbers with a trend value of 1 or 2 or 3. If you would imagine the pattern, your trend value combination would look like this: 112233 in any order or position. In some cases, it may look something like this: 112223 or 122233 in any order or position.

There are other possibilities. Take a look at the summary below.

When forming a lotto combination —

Trend value 1. One or two numbers should have a trend value of 1 (37.7% + 29.8% probability). Think 1 or 11; or in rare cases 111 (11.7% probability). If trend values are 1111 (3.4%), might as well limit it to 111. It is better for at least one trend value 1 to exist rather than none (16.8%).
Trend value 2. One or two numbers should have a trend value of 2 (31.8% + 31.4%). Think 2 or 22; in some cases, 222 (18.1%). If there are 2222 trend values (4.3%), might as well remove one. It is more probable to have 2s rather than none (13.6%).
Trend value 3. One or two numbers should have a trend value of 3 (37.2% + 27.7%). Think 3 or 33 but rarely 333 (8%). More than 3 is almost improbable. It is OK if 3 does not exist.
Trend value 4. In some cases, one number can have a trend value of 4 (34.3%). Rarely that 2 numbers can exist with a trend value of 4 (12.3%). It is more often that trend value 4 does not exist (51.5%). It is almost improbable for the trend value of 4 to exist 3 times or more. Think 4 but never 444 or more; 44 is possible but rarely.
Trend value 5 to 8. In very rare cases, one can have a value of 5 or higher (collectively at 37%); however individually, the probability is 3.59% (for trend value 5) and 1.41% and lower for values higher than 5. So, you can disregard numbers with trend values 6, 7, 8 or higher. It is more often that they do not exist in every draw (71.6%).
In some cases (37%), you can include one cold or hibernating number (trending value zero). Though rarely, it is possible to have two (9.3%) but not more than that.

To give you an idea, take a look at the snapshot of an actual database. Notice that most trending values are 1s, 2s and 3s. Let's sample number 18, which had a trend value of 2. This means that 18 had won twice during the last 21 draws prior to its third win, which was on Nov 9. It won on Sep 30 and Oct 11.

Sum of Trend Values

To further delimit your choice of combination, thus increase its probability, is to set the sum of trend values. To add each trend value per combination, you get the sum of trend values. Based on statistics, 91.4% of all winning results recorded sum of trend values ranging from 8 to 18.

A Simple Application

Suppose both lotto numbers 21 and 25 are top numbers. The former has a trend value of 3 while the latter has a trend value of 5. Which of the two is likely to win over the other? Based on our parameters, 21 is more likely to win again because 25 has already won 5 times.

Hot Zone Indicators

Almost half of the winning numbers come from the hot zone, which comprises the most recent 6 consecutive draws. If that is the case, what would indicate that a particular lotto number from the hot zone has a potential to win? To find out, we calculate the trend values.

Just so not to confuse you, the trending period is divided into two: the active zone and the passive zone. The active zone, comprising the first 9 draws, is where the action takes place. The remaining 12 draws is referred to as the passive zone where the numbers start to turn cold or become inactive.

So, in this section, we single out the numbers in the active section, particularly in the hot zone, to find out what makes them win over and over again. For the reason that the hot zone covers only 6 draws, a lotto number cannot have a hot zone indicator that is greater than six.

What follows are the calculated hot zone indicator for every 6-draw period that had passed.

Half of the winning numbers usually come from the last 6 draws at 48% rate. The rest of the winning numbers, at 51.8%, come from draws outside the hot zone as indicated by the zero trend value.

Lotto numbers with a hot zone indicator of 1 usually win most at 35.69% probability rate, followed by numbers with an indicator of 2 at 10.65%. It is very rare, at 1.6% only, that a lotto number with an indicator value of 3 might win again. Lotto numbers with an indicator value of 4 or higher is almost improbable to win again (0.12%). In other words, if a number in the hot zone has already won 3 times or more, it is unlikely to win one more time — possible but least probable. Following is the complete stats.

The next question is: what should your combination comprise with? Should you pick all 6 numbers with a trend value of 1? Find out next in that follows.

Based on the above data —

A winning combination usually comprises lotto numbers that have won once. In a combination, usually it contains 1 to 3 numbers with an indicator value of 1 (23.6% + 33.2% + 23.6% probability). In rare cases (11.1%), a combination may contain four numbers that have an indicator value 1. More than 4 is almost improbable. Think 1, 11, or 111.
If a lotto number has already won twice, a combination may contain one number with an indicator value of 2. More than 2 is improbable. Think 2, and in rare cases, 22.
It is very rare that a lotto number that has already won 3 times might win again. The chance of making it is only 9.6%.
If a lotto number has already won more than 3 times, it is almost improbable for it to win again.
Very often that 3 winning numbers come from the hot zone (or the last 6 draws). At very rare times, 4 numbers may come from the hot zone. This also means that 2 to 4 of the winning numbers could come from beyond the hot zone.

In A Nutshell

At this point, based on frequency studies, we have standardized some probabilities or set some parameters that will aid us in choosing the numbers that are likely to win compared to the other numbers.

Your numbers, preferably be a mix of top and bottom numbers based on these ratios: 3:3, 2:4, 4:2.
Lottery numbers with trending values of 1, 2 or 3 are likely to win again. These are numbers that have won once, twice or thrice from the last 21 draws.
Numbers that have won 5 times or more during the last 21 draws have lower chances of winning.
If a trending number has won more than 4 times, it starts to cease trending.
Counting only from the last 6 consecutive draws, if a lotto number has already won more than 3 time, it is unlikely to win again.

Doing your analysis manually

If you have no access to a spreadsheet program, you can do this analysis with just a pen and a paper.

Determine the trend values

On a sheet of paper, copy the most recent consecutive 21 drawing results.
Count how many times each lotto number has won.
In a tally sheet with 6 columns, write the numbers top to bottom based on their number of wins. That's your trend values.
Cross out the numbers that had won 5 times or more.

Determine the hot zone indicators

Considering only the last 6 draws (the hot zone), count how many times each lotto number has won in that period.
Mark the lotto numbers that have won only once and those that have won twice.
Cross out the numbers that had won more than 3 times, if any.

Pick and combine your numbers

Encircle the numbers that you will find first in the hot zone.
Pick one number from each column alternating the one you encircled and one you did not.
Make sure that no 3 numbers have the same trend value. Observe the parameters discussed previously. Also, preferably, pick encircled numbers with a value indicator of 1.
As an option, pick 2 numbers from one column of your choice and one each from any 4 of the remaining columns.
If you wish, you can form a few extraordinary combinations. These are combinations that contain one number with lesser probability.

There are other possibilities but these are the common ones.

Probability Based on Time

Would you be excited to find out when a lotto number could win again? Statistics can calculate that. All is needed is to count the days or draws between each number's time of winning.

Presenting the data.

Lottery 6/58 time of winning probability

For each lotto number, the number of draws was calculated between each time of winning. It answers the question: how long does it take for the same number to win again? The number varied but there were common figures.

The Table Explained

Age

There are three ways to understand age.

Age is simply the draws counting backwards starting from the most recent one, where the most recent one is Age 1. Age 2 would be referring to the draw that just preceded; age 3 is two draws prior, etc. So, age 30 would be the 30th draw counting from the most recent draw.
Age is also the number of draws from the last time a lotto number had won up to the time it had won again. For example, assuming draws are held everyday and that your number won on Monday, then again on Friday, counting from Monday, the calculated age is 4. In other words, it took 4 days (or draws) before your number wins again.
Age is also the number of draws since the last time it had won prior to the current day; or another way to look at it is: how long, in terms of draws, that your number has not been winning. For example, assuming draws are held everyday and that the last time your number had won was on Nov 11 and today is Nov 23, counting from Nov 11, the age of your lotto number is 12. In other words, your number is already 12 draws old.
Age is also the period when a lotto number is at rest or is not currently winning.

Occurrence

Occurrence refers to the number of instances when a lotto number wins again after a certain number of draws. For example, age 1 has 637 occurrences. This means that there were 637 instances when some lotto numbers win twice in a row; or what some people call repeaters. Age 3 has 553 occurrences which means that there were 553 instances when some lotto numbers that after not winning for 2 consecutive draws, they won again on the 3rd draw.

The percentage (%)

The percentage (%) column is the rate of occurrences over all occurrences. The Accumulated % simply adds the percentage one after the other. It has the purpose to establish the colour zones.

The Colour Zones

The purpose of the colour zones is to establish the period, based on age range, as to where the winning numbers usually come from. Based on the just preceded probability data, the following findings reveal that:

Trend zone. The trend zone, also called trending period, is statistically established as the significant period for the reason that 90.25% of all winning numbers studied come from this 21-draw period. It covers ages 1 to 21 or simply the 21 consecutive most recent draws.
The trend zone is divided into two: the active and the passive zones. The active zone comprises the upper 11 draws (purple and green zones); while the passive zone comprises the lower 10 draws (yellow and blue zones). The active zone is the period where numbers tend to win again and again or remain trending (70.24% probability); while the passive zone is where the numbers turn cold or cease to trend (20% probability of winning).
Purple zone. The purple zone is also called the hot zone for the reason that almost 50% (exactly 48.49%) of all winning numbers come from the hot zone. This also tells us that the other half of the winning numbers come from the earlier zones. The purple zone covers the 6 most recent draws; or ages 1 - 6.
Green zone. The green zone is the area where the other winning numbers (21.7%) come from. So, if you are going to pick 5 numbers from the purple zone, pick 2 from the green zone. The green zone covers ages 7-11.
Yellow zone. 10.3% of the winning numbers come from the yellow zone. You can pick 1 number from this area. The purple, green and yellow zones together make up the 80% of the winning numbers. The yellow zone covers ages 12-15.
Blue and aqua zones. The blue and aqua zones make up the cold zone. Once a number reaches the blue zone, that number likely ceases to trend. The blue zone makes up 9.7% of the winning numbers; the aqua zone, 6.4%. Together, they make up 16.1% of the winning numbers. At rare times, one winning number can possibly come from the cold zone. The blue zone covers ages 16-21; the aqua zone, ages 22-30. Once a cold number has left the blue zone and has entered the aqua zone, there's a big chance for this cold number to hibernate.
Grey zone. The grey zone is referred to as the hibernation period. This covers the age period 31 to 60. Numbers in hibernation have only 3.3% chance of winning.

Following is the rest of the data showing the probability of less than 0.5% (collectively at 3.3%) of lotto numbers to win again while hibernating. So, if your favourite number is in hibernation, it is a good advice to set it aside for the meantime.

Combining Numbers Based On Colour Zones

Now that you know that almost 50% of the winning numbers usually come from the last 6 draws (purple zone) and the rest come from the other zones, how many numbers from the purple zone should you combine with those from the outside zones?

Presenting the data.

The Table Explained

Instance: Instances are 1 - 6 which is the existence of the age value in a winning combination. The absence of which is zero. It answers the question: how many of the jackpot numbers came from the purple zone and how many came from outside the purple zone.
Column labels 1-6 through 31+: These labels refer to the colour zones discussed previously. The numbers 1-6 up to 31 are referred to as ages aka prior draws; 31+ means ages older than 30. The figures under these columns are the number of cases such instance has occurred. For example, there were 320 cases when 3 of the jackpot numbers came from the purple zone; or 31% probability.
Percentages: The lower portion contains the calculated percentages of the figures above it.

Analysis of Colour Zone Data

Most probable. Two to four numbers from the purple zone can possible win the jackpot. One or two numbers may come from the green zone; and one number from either the yellow, blue or aqua zone. In a few cases, one winning number can also come from the grey zone.

So, when making your 6-number combination, observe these rules.

Purple zone. Pick 2 to 4 numbers from the purple zone. There's only a 10% chance that only one winning number can come from the purple zone. It is very rare that 5 winning numbers can exclusively come from the purple zone (6.9%). Further, it is almost improbable that all 6 winning numbers to come from the purple zone; possible but only 1.1% chance. Likewise, if you didn't pick any number from the purple zone, there's only a 1.3% possibility that it can bring you luck because, on the other side of the coin, there's a greater chance of 98.7% that at least, one number from the purple zone can make it to the jackpot.

Green zone. There's a 77.7% chance that, at least, one number from the green zone can hit the jackpot. One or two numbers can make it; three is also possible but less than 10% probability. Picking more than 3 numbers from the green zone is almost improbable. This means that if the numbers in your combination all come from the green zone, only 1, 2 or 3 can make it to the jackpot.

Yellow zone. There's a 47.7% chance that, at least, one number from the yellow zone can make it to the jackpot. Two or three is possible but the chance is only 9.4% or 2.2% respectively. There's a half-half chance (52.7%) that none can make it to the jackpot.

Cold zone. There's a 45.8% chance that at least one number from the blue zone can make it to the jackpot; 32.6% chance from the aqua zone. But there's also a 54.2% and 67.4% chance respectively that none can make it to the jackpot. At very rare cases, two numbers from the cold zone can make it to the jackpot. More than that is already improbable.

Grey zone. At 80.6% probability, no winning number in hibernation could make it to the jackpot. If you wish to risk, pick only one number from the grey zone.

Let's summarize.

Zone	Numbers to Play	Rare Case	Improbable
Purple	2 - 4	1 or 5	6 or none
Green	1 or 2 or none	3	4, 5 or 6
Yellow	1 or none	2	3, 4, 5 or 6
Blue	1 or none	2	3, 4, 5 or 6
Aqua	1 or none	2	3, 4, 5 or 6
Grey	1 or none	—	2, 3, 4, 5 or 6

Sum of Ages Delimiters

By calculating the sum of the ages for every winning result, you will be able to delimit the numbers you wish to play. The sums of the ages range from 10 - 150. The most probable sums are 29 - 81. The rest would just occur once or twice.

Forming a combination based on colour zone parameters

You can analyze your combination using the colour zone parameters even without the help of a spreadsheet program. Here's how:

Form your 6-number combination based on parameters set with colour zones.
For each number, count the number of draws the last time such number had won. That will be the ages of the number.
Total the ages.
Observe the following rules:

Most probable. Sum must be between 29 and 81 inclusive.
Probable. Sum is between 20 and 28; or between 82 and 100 inclusive.
Least probable. Sum is between 10 and 19; or between 101 and 150 inclusive.
Improbable. Sum is less than 10; or greater than 150.

To give you an idea what lotto number ageing looks like, below is a snapshot of the actual database done in Google Sheets.

Let's examine the Nov 18 result. The age of #53 is 4 which means it was 4-draw old prior to its current winning. If you count 4 beginning from the results just above it, you will find #53 that won on Nov 9. If you will count all age 4's in the database (i.e. all results), you will have an idea if a number that is 4-draw old is likely to win again or not. Go back now to the previous data of ages and look for age 4. How often did numbers that were 4-draw old had won the jackpot?

Part II

TREND PROBABILITIES

What's Trending

Probability based on the most recent results

With a large data population, such as covering all drawing results that was covered in Chapter 2, the result of any probability calculation appears to be unchanging or non-varying. This means, that it becomes irrelevant to add more years of data to the study because you will achieve the same calculated results. The probability rates remain the same and tend to even out or flatten. For this reason, it becomes necessary to cover only a small population of data, such as only the most recent drawing results, in order to find out what is only relevant and really trending.

Trending Numbers

When we talk about the current trending numbers, we cover only the last 21 draws for the reason that the winning numbers tend to dissipate once they reach the cold zones (not winning after 15 draws). We cover the last 21 draws so that we would know which numbers, not only those that are trending, but also those that are ceasing to trend.

What follows are the current trending numbers together with the numbers that have ceased to trend. In other words, the top and bottom numbers.

<---------------- insert data here ------------------->

Trend Values

Trend Values are the winning frequency of each lotto number in a given shorter period called the trending zone or period. In the case of a system 6/58 lottery, a trending period covers 21 consecutive draws starting from the most recent one.

Winning Ranges

Hextiles - Disecting the top and bottom numbers based on ranking

RANKING

Let's look closer to the top and bottom numbers by identifying a third group called the middle numbers. We will be dividing the lotto numbers into three as follows based on frequency of winning: Top 1/3, middle thirds, and the bottom thirds.

The Hex Groups

For the lotto 6/58 study, the data were divided into 6 groups. Each hextile comprises one-sixth (1/6) or 16.67% of the data. If divided equally, each group comprises 9 or 10 lotto numbers. However, in this study, the lotto numbers were grouped, then ranked, based on the number of times each number had won. For that reason, a hextile or one-sixth group may include a variable number of lotto numbers ranging from 6 to 15 lotto numbers depending on each number's performance.

Group 1 (H1) comprises the top 1/6 (16.67%)
Group 2 (H2) comprises the 2nd top 1/6. Together with group 1, they make the top ⅓.
Group 3 (H3) comprises the middle 1/6 above the median. Together with groups 1 and 2, they make the top 50%.
Group 4 (H4) comprises the middle 1/6 below the median. Together with groups 5 and 6, they make the bottom 50%.
Group 5 (H5) comprises the upper bottom 1/6. Together with group 6, they make the bottom ⅓.
Group 6 (H6) comprises the bottom 1/6.

Top One-Sixth (H1)

Based on 323 results, the following are the top 16.67% winning numbers of Ultra Lotto system 6/58. Find here the latest standing of each number based on its winning frequency.

06 • 13 • 54 • 08 • 38 • 58 • 34

These numbers have won 289 times out of 1938 balls – a probability of 15.72%. Collectively and individually, they had won from 217 results out of 323 drawings - a probability of 67.2%. However, only 11 draws resulted to three winning numbers; and only 1 draw gave four winning numbers. This means that the other 206 results were no-prize winning results giving only 1 or 2 winning numbers.

Perhaps, you’re wondering why the top winning numbers are not exactly sure winners?

The answer is randomness. The balls have no fixed positions. The moment you touch one ball, the rest of the balls move. That’s the concept of randomness. For that reason, we can quickly come up with a conclusion ~

The winning balls are unpredictable.

If such is the case, is there a way to be, at least, closer? There’s only one way to find out and that’s with the use of probability.

The Top Thirds (1/3) Winning Numbers (H1 + H2)

The following are the next top winning numbers, making them, together with the top 16.67%, the Top One-Third (33.33%). These numbers belong to Group H2.

22 • 02 • 25 • 33 • 39 • 10 • 41 • 46 • 14

The Top 1/3 winning numbers make the 33.33% of all winning balls - a total of 635 balls equivalent to 303 draws out of 323 drawings, or 93.8%; 91 of those are prized winners having 3 to 5 winning numbers. Four draws produced five winning numbers; 19 draws produced 4 winning numbers.

Therefore, playing the Top 1/3 numbers gives you 28.17% probability of winning 3 to 4 numbers; but not 5 or 6 numbers. However, if the Top 1/3 consists of 16 lotto numbers, you need to play 8008 combinations in order to ensure your winning ⎯ not practical to play them all. Perhaps, there is a better way to play 16 numbers with a few combinations.

Moreover, if only 1 to 4 of the Top 16 numbers can possibly win from 93.8% of the draws, which other numbers are winning?

The Top 50% (H1 + H2 + H3)

So how many numbers should you play to raise your chances of winning to greater than 50%? Let’s add the remaining top numbers to complete the Top 50%. These numbers belong to the H3 group or the middle top 16.67% above the median.

23 • 27 • 29 • 11 • 40 • 56 • 15

Playing the Top 50% gives you 99.07% probability of your numbers making it to the results. Of this rate, 77.4% probability is attributed to winning prized money; ie winning 3 to 6 numbers. Here's the complete stats.

36.53% chance of winning 3 numbers
26.93% chance of winning 4 numbers
12.38% chance of winning 5 numbers
1.55% chance of winning 6 numbers (or jackpot)
18.89% chance of winning 2 numbers
2.79% chance of winning 1 number
0.93% chance of winning 0 number

Though there is a great probability that the Top 50% can give you the winning numbers, the chance of winning the jackpot is only 1.55%. If such is the case, it only means that the other winning numbers would be coming from the bottom 50% numbers.

The All-Time Bottom Numbers

The other 50% of the numbers belong to the bottom group, comprising the 3 bottom hextiles.

The middle 16.67% bottom below the median (H4)
The upper 16.67% bottom (H5). Together with H6, H5 + H6 comprise the bottom thirds (1/3).
The lowest 16.67% bottom (H6)

The Middle Bottom (H4)

This is the first set of the bottom numbers below the median.

23 • 27 • 29 • 11 • 40 • 56 • 15

What is significant in this group is that it is very unlikely that 3 to 6 winning numbers could come from this group. So, if you find 3 to 6 numbers of yours in this group, most likely they are not going to win because the probability of 3 to 6 winning numbers to come from this group is only 2.2%. However, there is an almost 50%:50% chance that no or 1 winning number can come from this group.

The Bottom Third (H5 & H6)

Below are the numbers that belong to the bottom ⅓.

Bottom H5

44 • 19 • 17 • 52 • 57 • 20 • 07 • 21 • 30 • 32 • 48 • 26 • 31

Bottom H6

35 • 49 • 05 • 18 • 45 • 42 • 24 • 55 • 28 • 37

Comparative Stats of the Bottom Numbers

Winning Numbers	H4%	H5%	H6%
0	46.1	24.5	45.8
1	36.8	38.7	37.5
2	14.9	27.9	14.2
3	1.9	6.8	2.2
4	0.3	1.9	0.3
5	0	0.3	0
6	0	0	0

Observations

It is more probable that no winning number could come from group H4 or H6
There is almost a 50%:50% chance that one or no winning number could come from group H4 or H6
It is more probable that 2 winning numbers could come from group H5 rather than from groups H4 or H6
It is almost definite that no 3 to 6 numbers can come from groups H4, H5 or H6.
38% of the results comprised 3 top winning numbers and 3 bottom numbers.
There’s only 0.6% when a result comprised all bottom numbers. So, forget playing all bottom numbers.
Likewise, there’s only a 1% chance that a result contains all top numbers.
Therefore, your combination should comprise, at most, 3 top numbers and 3 bottom numbers. In some cases, you can play around the ratio 2:4, which means 2 top numbers and 4 bottom numbers or vice-versa.
Top winning numbers do not win all together. They share the spot with bottom numbers.
You have a slimmer chance if you pick your numbers only from the top 27. The top 27 lotto numbers comprise the top winning 50%.
The odds of winning increases if you include a few bottom numbers, starting with the middle 9.
Without the middle 9, there are greater chances to win 3 numbers.
With the middle 9 considered, the chance to win 4 numbers increases. Draw results usually comprise 4 top winning numbers and 2 bottom numbers.
Pick 4 numbers from the top 27. The middle 9 numbers are enough to be the source of the 2 bottom numbers.

Quantiles and Groups

Common winning number groups

Which numbers usually win? Are the tens winning more than the twenties or thirties? The forties over the fifties? Let's find out.

Highlights

A hextile or group of related numbers, say numbers 1-9, 10-19 or 20-29, would at most produce 1 winning number or none at all. If one hextile produced no winning number, another hextile would produce 2 winning numbers.

Groups By First Digit

In this study, I grouped the lotto numbers by 1s, 10s, 20s, 30s, 40s, and 50s to find out if there is a certain group that win most often. Thus,

Group 1 (G1) comprises the lotto numbers 01-09
Group 2 (G2), lotto numbers 10-19
Group 3 (G3), lotto numbers 20-29
Group 4 (G4), lotto numbers 30-39
Group 5 (G5), lotto numbers 40-49
Group 6 (G6), lotto numbers 50-58

Summary of Observations

No 6 numbers can win from one group alone. The probability is 0%. In other words, you cannot win the jackpot if your 6 numbers are any from 01 to 09 only; or 10 to 19; or 20 to 29, etc. For example, this is possible but not highly probable: 1 • 2 • 3 • 4 • 5 • 6 or 50 • 51 • 52 • 54 • 55 • 58.
Winning 5 numbers from one group alone is not also probable. It also has 0% probability.
Winning 4 numbers from one group alone is almost not probable. The probability is a very low 0.03% to 0.09%. There were only 8 instances reported out of 324 draws. This is an extraordinary case which occurs once for every 41 draws (1:41 ratio).
The probability of winning 3 numbers from one group alone is between 3.4% to 6.5% per group. Together, such case on average occurs once for every 4 draws (1:4 ratio) or 28.4% probability (92 cases over 324 draws).
The probability that 2 numbers would win from a single group ranges from 17.9% to 25% per group. All in all, such case has occurred 264 times out of 324 draws; or 81.48% probability. That is almost a 1:1 ratio (1:1.23 exactly). In other words, for every 27 draws, there are 22 instances when 2 numbers win from a particular group.
There is a strong probability that 1 winning number could come from each group. The probability ranges from 42.3% to 44.1% per group. All in all, such case has occurred 312 times out of 324 draws; or 96.3% probability. That is almost a 1:1 ratio. Exactly, that’s 26 cases for every 27 draws.
It is also possible that a group would not bring out any winning number. Such case happens when one group delivered 2 or more winning numbers. The probability of one group not producing a winner ranges from 26.9% to 33% per group. Collectively, such case has occurred 318 times, or a 98% probability; very close to 1 number winning from a single group.
In a Nutshell. There is a stronger possibility that a particular group would produce at 1 or 2 winning numbers. In such case when one group would produce 2 winning numbers, one group would produce none.
The table that follows summarizes the probability of each group to produce 1 or 2 winning numbers. Based on this table, you can already see the most probable placement of your numbers. For example, 1s are good as 1st number; or combined 1st and 2nd numbers. Your first number can mostly be 1s or 10s; while your 6th number can mostly be the 40s or 50s.

Probability Per Group in the Numerical Order
Group	1st	2nd	3rd	4th	5th	6th
1s	70.5	24.3	4.5	0.2	0.0	0.0
10s	22.3	42.1	30.4	11.5	2.3	0.0
20s	6.1	23.6	33.1	24.8	8.8	2.0
30s	0.9	9.7	24.1	34.9	25.9	4.5
40s	0.2	0.2	7.7	24.1	40.3	26.1
50s	0.0	0.0	0.2	4.5	22.7	67.3

Number Groups Probability