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 Unfortunately, time outdated my computer and software had become unaffordable.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 most of the time, 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

How often does your number win? The all-time winning frequency of each number based on actual draw results beginning from the very first draw of PCSO's Ultra Lotto 6/58 started (2015 - current);
Identified sets of periods considered significant in establishing the probable potentials of lotto numbers.
Trending values based on periodic winning frequency; standardising the parameters that delimit probabilities.
Timeliness - the probability of an event to take place again such as when a number is likely to win again.
Trending Numbers
Recent winning frequency of each number
Common Forms and Patterns of Lottery Results
- Top vs bottom numbers
- Low vs high numbers
- Odd vs even numbers
Probable winning range of numbers: Not all combinations are probable
Distances: Predicting the next probable numbers

Data Sampled In The Study and Scope

For the study of this lottery system 6/58, results from PCSO's 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 6/58. 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 PCSO's Ultra Lotto 6/58 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

With over 40 million combinations, your chance, therefore, 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.

The MOE, therefore, is (+ -) 1.93%. 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; or would there be a group that would not produce a winning number?

Dividing the numbers or data into different groups reveal more information as to which numbers win most often. In Chapter 9, 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 winning frequency of a lotto number.
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. Usually labeled as Freq or Frq or simply Win.
Occurrence: Usually based on a given criteria, the number of times a number or a set of numbers with homogeneous attribute have recurred or exist either from the entire database or from a snapshot of the database, such as 30-day period. For example, how many times #33 had won based on a recurring 30-day periods. This may also be referred to as recurrence.
Instance: The number of times an occurrence can be found from a group of records based on a certain parameter or set of parameters. For example, if #33 had won 25 times from a thousand draws, how many times did it win twice consecutively?
Instance of instance (ioI): The existence of instances based on a narrower criteria. 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. As study progresses, the trending period may change.
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 or markers.
Rank: This is presented as an ordinal number such as 1st, 2nd, 3rd, 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 this 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.
All-time is the all-time frequency of winning of each lotto number, in other words, the numbers of times each lotto number has won so far since the first draw of PCSO's Ultra Lotto 6/58. 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). In July 2025, lotto number 6 remained on top with 163 wins at 11.93% probability. The number with the least wins went to #27 with 120 wins at 8.78% probability; while #37, the former lowest ranking number, rose to the 50th place with 130 wins at 9.52% probability.
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 PCSO's 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 (Standard 01)

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 mostly 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 to form 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.

Standard 02: Low To High Ratios

The following chart is based on more than 1100 results (PCSO's 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?

Low To High Numbers Ratios (Data 03)

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 2023; 80.7% in 2025) in probability, your numbers are best if they are a mix of (figures may change as records are updated):

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 2023 (1.46% in 2025). In 2018, it was 2.3%. Likewise, playing all high numbers (30 - 58) gives you a chance of only 0.95% in 2025 (1.5% in 2023); 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 occurred only 20 times in 2025 (16 times in 2023); while all high numbers occurred only 13 times (in 2025); 9 times (in 2023).

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 2023). 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 Numbers Ratio
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%

These probability ratios, most likely, would remain the same, no matter how much quantity of records (draw results) we add to the database. This is true based on the principle of the Law of Large Numbers.

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.

Which numbers are low or high?
	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.

Common Low-High Patterns
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.

Timing of Low:High Combinations

Yes, 3 low and 3 high numbers are the most probable combination; however, we cannot disregard that the 2:4 or 4:2 combinations are also possible. So, the next question is: when do you play 3:3, 2:4, 4:2 or even the 5:1 or 1:5 ratios?

The following data reveal when the probable ratios ideally win.

Occurrence of Low:High Number Combinations (Data 04)

Three low numbers, three high numbers combination (3:3). This ratio usually occurs immediately draw after draw. In other cases, it will occur after one draw of not occurring. Generally, this ratio can occur within 1 to 6 draws as shown by the Elapsed Time values. Rare instances would be within 7 to 11 draws. What this is saying is that, say, today the winning combination was 3 low numbers and 3 high numbers. In the next draw, it may occur again; or it may occur after 2 draws of non-occurrence. In rare cases, it may not occur for a longer period such as 7 - 11 draws of non-occurring. During those days of non-occurring, the other ratio probabilities occur.
Four high or low numbers, two low or high numbers combination (4:2, 2:4). Likewise, these ratios can possibly occur within 1 to 6 draws but at a slightly lower probability. Their non- occurrence can extend within 7 - 10 draws. There is a possibility that these ratio patterns may not occur within 11 - 16 draws but most probably not longer.
Five or six low numbers or five or six high numbers (5:1, 1:5, 6:0, 0:6). These are the low:high combinations that rarely occur. Though they can occur again within a shorter period but most likely their next occurrences may take even longer than 38 draws of not occurring. In other words, once any of these ratios occurred, it may take up to 38 draws of not occurring.

To apply this probability standard, combine your numbers following these ratio 3:3, 4:2 or 2:4. If you prefer to be adventurous, play the other ratios as well. Observe however, that if recently, the winning combinations contained 5 or 6 low numbers or 5 or 6 high numbers, stick to the most probable ratios instead.

Specific Low and High Number Patterns

The low to high number ratios discussed previously ignore the actual positions of both the low and high numbers in the order they were drawn. This may be difficult to observe when combining your numbers for the reason that this method is tedious. Anyway, let me present the data.

The total number of unique 6 low-high sequences that can be formed with either low or high number or both is 64. In other words, we are looking for 6-character patterns that contain only L and H. The following chart gives you an idea which low-high pattern usually yield positive results. The chart does not show all the 64 patterns due to lack of space; but hovering on each bar reveals the details.

Frequency of Specific Low and High Number Sequence (Data 05)

For now, you can still see the variances between each pattern. In time, as the database grows, the variances will become minimal as they reach the average rate, which is 1.56% or 1/64 (Law of Larger Numbers).

How to apply the data

With the Law of Larger Numbers in mind, consider betting on the patterns with lower rates, that is lower than 1.56%. In time, these lower rate patterns will eventually reach its goal of 1.56%. It is for that reason that these lower rate low-high number patterns are more likely to occur compared to those higher rate patterns.

To illustrate.

Assuming the pattern LLHHLL has a frequency rate of 3.14%, it is most likely that its frequency will become dull. Meanwhile, the other patterns will try to catch up until every pattern goes closer to 1.56%, higher or lower. For that reason, you might consider instead HHLLHL, which has only 1.46% frequency rate.

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).

Note: Figures and rates may have changed as records are updated; that is, as new results are added to the database. On the other hand, with regard to the Law of Large Numbers, in time, the probability rates may just slightly change. The charts may present the most recent data based on the date stamped in Chapter 1 of Part II.

Algorithm for Programmers

Algo 04. For each decile group, identify the low and high numbers. When generating a combination, produce 3 combinations with either 3 or 2 low numbers.
Algo 05. As you input the winning lotto numbers,

(1) Identify which numbers are low (1 - 29) or high (30 - 58) to come up with a low-high sequence. For example, LHLHLH.
[2] Store this low-high sequence on a separate field on the results database.
[3] Run a process that will count similar sequences. For example, how many so far in the results database have the same LHLHLH pattern?
[4] Store the result (instances of the same pattern) on a separate field of the LowHigh table.
[5] As the LowHigh table is updated, update likewise, its probability percentage.

Guide for Spreadsheet Users

On the Results tab, determine the low-high sequence of each winning combination. Input this formula beside each winning combination. (For readability purpose, spaces were added in the formula; these spaces should be omitted on your spreadsheet):

IF (B3<30,"L","H") & IF (C3<30,"L","H") & IF (D3<30,"L","H") & IF (E3<30,"L","H") & IF (F3<30,"L","H") & IF (G3<30,"L","H")
Copy the formula up to the last row of winning combination.
B3 to G3 refers to the winning lotto numbers. L stands for low; H stands for high.
Result is concatenated string of Ls and Hs.

On the Tables tab, create a table that contains all the possible LH sequences. Beside each sequence, the count of all exact sequences are stored. On its side, calculate the probability rate of existence.

To count all the same sequences present in the Results database, input this formula:

=COUNTIF (Results!J$3:J,A3) where J$3:J contains the LH sequences; and A3 refers to form of sequence in the LowHigh table.

To calculate the probability rate, input this formula: =B3 / sum(B$3:B) where B3 is the value of count; and B$3:B is the column where all the values of count are stored. The function of the formula is to divide a specific value of count by the sum of all counts.

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 preceding and succeeding paragraphs inconsistent with the figures of the chart.

Probability of Odd : Even Ratios (Data 06)

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?

Standard 03. 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

Update.

As the database of results being tested grow larger, the odd-even patterns probability have become insignificant; or rather not showing significant changes at all. The Law of Large Numbers state that the larger the sample size is, the closer it gets to its average. There are 64 odd-even patterns. Assuming each pattern are occur equally, the average probability is 1/64 or 1.56%. If only a few results are being tested, we would see great deviation from the average. Some patterns may occur at 25% while others at 0%. However, as the number of results being tested grow larger, each pattern gets closer to 1.56%.

For the sake of presentation, below is a screenshot from my worksheet showing the top odd-even patterns. Notice that the highest probability is only 2.49%. The lowest (not shown) is only 0.73% for the pattern EEEEOO. In due time, all patterns will reach the average 1.56%.

Probability of Odd to Even Sequences (Data 07)

Following is the complete data presenting the frequency of occurrences of specific odd and even sequences. Hover on the bar to view the details.

Frequency of Occurrence of Odd:Even Sequences (Data 08)

Early Probability Results for Odd-Even Patterns (Prior to 2025)

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. [In 2025, these patterns were the most common at 2.49%%.]

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. [ In 2025, the probability were 1.3% and 1.1% respectively.]
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%. [ In 2025, the probability for this type of pattern were 7.5% and 8.7% respectively.]
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%. [ In 2025, the probability of 4 odd numbers occurring was 24.4%; of 4 even numbers is 2.5%.]
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. [ In 2025, the probability for this type of pattern was 34.6%.]
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

To this day 2025 and onwards, as the probability patterns reach their common average of 1.56%, any odd-even pattern is as good as any other.
Prior to 2022, the following were the results of the study when the sample size tested was still small. As of 2025, they are no longer relevant.

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.

Algorithm for Programmers

Algo 06. Have a separate table with two fields for odd-even sequences. The first field stores the odd-even sequence; the 2nd field stores the count of sequences present in the results database. Let's call this table tblOddEven. There are 64 odd-even combination sequences. Each time you enter a new result, determine the odd-even pattern; then add this occurrence to tblOddEven. To initially populate the table, run a process that reads the Results database; determine the odd-even sequence; than update the OddEven table.

For Spreadsheet Users

In the Results database, add a new column to store the odd-even sequence. Use this formula: =MAP(B3:B,C3:C,D3:D,E3:E,F3:F,G3:G, LAMBDA(a,b,c,d,e,f, IF(ISODD(a),"O","E") & IF(ISODD(b),"O","E") & IF(ISODD(c),"O","E") & IF(ISODD(d),"O","E") & IF(ISODD(e),"O","E") & IF(isodd(F),"O","E")))
Input this formula beside the very first record of Results database and let it do the sequencing for the rest of the results. Each time a new result is added, the sequence is automatically written.
On a separate sheet, create a table that contains all the possible odd-even sequences.
- On the first row under Pattern, add this formula: =SORT ( UNIQUE ( FILTER ( Results!K3:K, Results!K3:K<>"")), 1, TRUE). This formula will extract the odd-even sequences on the Results database with duplicates eliminated.
- Beside each sequence, enter this formula to count the occurrences of same odd-even sequences: =COUNTIF ( Results!K$3:K, E3 ). Copy this formula up to the last record.
- In the 3rd column, enter this formula to calculate the probability rate: =F3 / SUM ( F$3:F ). Copy the formula up to the last record.
- Each time a new result is added, the odd-even table is automatically updated.
Note that spaces are added in the formula for readability purposes. In actual spreadsheet, the spaces are not necessary. Following is a sample of the table.

For related topics, search:

How to map in a spreadsheet a list that determines the odd-even sequence of an array of numbers.
How to filter in spreadsheet to show only unique records sorted in ascending order.

Probable Winning Range

All are possible but not all are probable

It is true that any 6-number combination is possible, but not all are probable, at least, not just yet. For example, 1 • 2 • 3 • 4 • 5 • 6 is a possible combination because such can definitely exist. However, statistically, with PCSO's Ultra Lotto 6/58, it's not just yet. In case, it has happened, most likely, it won't occur twice.

Setting The Bounds

Winning numbers usually come from within a probable range

The total possible 6-number combinations that you can form out of 58 numbers from 1 to 58 is 40,475,358. All these combinations are possible but not all are probable.

By arranging each result from lowest to highest number, statistics has revealed that certain numbers do not win at certain positions. For example, in the first position, common winning numbers are from 1 to 16 with a probability of 93%. If you want to consider 100% probability, then you have to consider all the numbers up to 45 even if such number has won only once.

Frequency of Winning Restrained To Positions

Data 09 presents the calculated frequency of winning of each lotto number in the ordered position to establish the probable range as to which number should be the smallest in a combination and which number should be the largest. For example, in the combination 06 • 07 • 10 • 21 • 34 • 51 in numerical order, the number six (06) is in the 1st position because it is the smallest number; while #51 is in the 6th position because it is the largest number. The rest of the numbers take their positions as 2nd, 3rd, 4th and 5th.

The next question is: Is there a rule as to which number should be the smallest and the largest in a combination?

On record, the smallest numbers that were formed in winning combinations were numbers 01 - 45; which means numbers 46 to 53 cannot (yet) your smallest number in your combination. If you want to achieve only 99% probability, your smallest numbers can only be within the range 01 - 30. On the other hand, your largest number in a combination can only be within the range 21 - 58. To limit your probability to 97.3%, your largest number can only be within 34 - 58. Note that #01 will always be the first number in any combination. It can never be the 2nd, 3rd, 4th, 5th or 6th because it is the smallest of all numbers 01 - 58. Likewise, #58 will always be on the 6th because no number is larger that 58 in a lottery system 6/58. Number 02 can only either 1st or 2nd; while 57 can only be 5th or 6th. Numbers 03, 04, 05 are also limited up to 3rd, 4th and 5th positions respectively. Numbers 54, 55, 56, 57 and 58 can never be the smallest number in a combination. All other numbers can either be at 1st, 2nd, 3rd, 4th, 5th or 6th position.

To illustrate:

If your combination is, 47 • 49 • 50 • 52 • 55 • 58, the probability of this to win is 0% for the reason that, on record, no combination has won yet where the smallest number is 47. On the other hand, if your combination is something like 02 • 06 • 12 • 17 • 18 • 20 where #20 is the largest, the probability for this to win is also 0%. These findings are based on 2025 study. If ever, in the next few years, that 0% probability may change to 0.1%.

There are also other numbers, at this time of study (2025), that have 0% probability if it is in the 2nd, 3rd, 4th or 5th position. For example, numbers 49 - 54 have not won yet as the 2nd smallest number in a combination. Also, numbers 05 - 12 have not won yet if they are the 2nd largest number.

Following is the result of the 2025 study that presents the probability of each number to win in the ordered positions. These figures may change as new results are added to the database.

Frequency of Winning In The Ordered Position (Data 09)

To understand the data just above, if a lotto number has a zero value on a particular position, it means that it is unlikely to win at 0% probability. If the value is 1, it has a 0.1% probability.

Probable Winning Range (Standard 04)

Data 09 is summarised in the table that follows. It presents the most probable winning numbers in the ordered positions, or what is referred hereto as the probable winning range. These ranges of lotto numbers excluded those that had only less than 2% probability. These data are based on 1373 ~~337~~ ~~386~~ results covering up to 2025. This standard may be constant long-term but may change eventually after a number of years as the volume of data increases.

Position >>	1st	2nd	3rd	4th	5th	6th
Lowest	1	3	10	22	32	43
Highest	16	25	39	46	56	58
Prob%	88%	84%	87%	76%	86%	87%

The data above serve as bounds (lower and upper limits, or probable winning range) that can guide you when forming your combinations. For example, the lowest number in your combination should be between 1 and 16. For the second position, your next lowest number should be between 03 and 25, and so forth and so on. However, we cannot set this lower and upper delimiters as standard because the probability can still change as new results from the lottery are added.

Taking the Risk of Choosing Numbers Beyond The Limits

Of course, you can take a risk of including one number outside the bounds because it is still a possibility thought not yet positively probable as of this time.

Perfect and Extraordinary Combinations

A perfect combination would be when all the 6 numbers in a combination are within the probable winning range. However, not all results are perfect. Based on 389 results, 67.9% were perfect combinations; the rest, referred to as extraordinary combinations, had only 3 to 5 numbers winning that were within the probable winning range. An example of a perfect combination is the 26 Dec 2017 result which was 09 • 22 • 35 • 41 • 44 • 46. The 31 Dec 2017 result ⎯ 06 • 14 • 15 • 24 • 25 • 43 ⎯ showed 1 number, which is 25, outside the limits (outside the range of 32-56).

So, how likely that a winning result would be within the probable range?

The table that follows shows how much of the actual results were within the probable range. There's almost a 70% chance that all 6 winning numbers would be within the probable range; about 91% chance that 5 numbers would come from within the range; and 97% chance that 4 numbers would come from within the range. (Prior to 2025)

Numbers Within Bounds	Occurrences	Prob
6	168	67.9%
5	90	23.1%
4	24	6.2%
3	11	2.8%
2	0	0%
1	0	0%
0	0	0%

Which column usually plays within bounds?

Which column in the ordered positions usually give a winning number within the probable range?

The probable range of numbers in the 1st to 5th positions usually give a winning number at 81% - 88% probability. The probable range in the 6th position usually gives a winning number at 92.6% probability.

Significance of Setting These Limits

By eliminating what's not probable, setting the lower and upper limits have reduced the number of possible and probable combinations to just about to 1.6 million or 0.0000616% probability rate. That's already good news compared to 40.4 million combinations.

In A Nutshell

Picking your 6-number combination from the probable range gives you a ~

49.9% chance of winning the jackpot;
77.5% chance of winning 5 numbers; and
91.2% chance of winning 4 numbers.

Form your lotto combination in a numerical order from lowest to highest number. Statistically, winning numbers come from a select range of numbers. Presented below are the probable ranges at 99% probability; and 86%-91% probability, if you want to ignore those numbers that had less than 2% chance of winning.

Your	Probable Range
Combination	93%-97% Prob	76%-88% Prob
1st number (smallest)	01 - 20	01 - 16
2nd number	02 - 35	03 - 25
3rd number	09 - 43	10 - 39
4th number	13 - 52	22 - 46
5th number	23 - 56	32 - 56
6th number (largest)	38 - 58	43 - 58

Tip & Strategy

Play 9 combinations as follows:

5 combinations where all 6 numbers are within the probable range
3 combinations where all 5 numbers are within the probable range in which ~
- 1 combination contains your 2nd number that is outside the probable range;
- 1 combination contains your 5th number that is outside the probable range;
- 1 combination contains either your 3rd, 4th or 1st number that is outside the probable range;
1 combination where all 4 numbers are within the probable range except the 1st and 2nd numbers.

Algorithm for Programmers

Algo 07. Create a Bounds table with 6 fields: 1st, 2nd, 3rd, 4th, 5th, 6th.

Each time a new result is added, determine the smallest number in the combination, the 2nd smallest, 3rd, up to the largest number.
For each lotto number, search the Bounds table. If the lotto number already exists, no update is necessary. If it does not exist, add a new record.
Sort the Bounds table in ascending order each time it is updated.
Initially, you can populate the Bounds table by running a program that performs the same algorithm.

For Spreadsheet Users

Create a new tab sheet and call it Bounds as shown in the image below.
For each cell under the 1st column, add this formula: =COUNTIF ( BYROW( Results!$B$3:$G, LAMBDA(rowvalues, MIN(rowvalues))),$A3). This formula counts the frequency of the lotto number if it is the smallest number (MIN is minimum)
Under the 2nd column, add this formula: =COUNTIF ( BYROW( Results!$B$3:$G, LAMBDA(rowvalues, SMALL( rowvalues, 2))), $A3). This formula counts the frequency of the lotto number if it is the 2nd smallest number in the combination.
Under the 3rd up to 5th columns, add the same formula just preceded but change the value of SMALL( ROW VALUES, 2) to 3, 4, and 5 depending on the column you are working on.
Under the 6th column, add this formula to every cell: =COUNTIF( BYROW( Results!B$3:G, LAMBDA( rowvalues, MAX(rowvalues))), A3). This formula counts the frequency of a number if it is the largest number in the combination (MAX is maximum).

For related topics, search —

How to count by row the smallest values in an array in spreadsheet
How to count for every row in spreadsheet the largest value in an array of data

Predicting the Next Winning Numbers

Calculating Distances to Restrict Your Numbers

Is it possible to figure out which numbers can probably win based on restricting factors? You already learned, in the previous sections, that not all numbers are probable. Yet, there is still that challenge of picking the right numbers. By restricting further your method of combining or choosing the numbers that you want to play, you can narrow down your selection of numbers to the most probable ones. This time, you will learn about the distance factor, which is simply the difference between two consecutive numbers. Likewise with Bounds (Probable Range), we can establish these delimiters if we arrange each combination from smallest to largest number.

Did you know that your numbers have more chances of winning if the difference between two numbers is less than 10? That's the general rule. However, in every rule, there are exceptions, which will be explained here further.

Distances Between Two Numbers

Establishing The Value Differences Between Any Two Consecutive Numbers

Highlights

In the ordered position (smallest to largest) of your lotto numbers, if you subtract a lotto number from the next one, the calculated difference should be any from 1 to 41.
The smaller the value of the difference, the greater the probability.
If you sum up all the distance values of a combination, common values are any from 10 to 57. Any value outside these delimiters are improbable for now.
If you are playing numbers in multiples such as in multiples of 3s or 2s, etc, most likely they are not going to win, because as of this writing, nothing of that sort has won yet.
All winning combinations on record (based on 1375 results) consist of at least one distance value of 1 to 9. The others are mostly combined with 10 -19 or 20 - 29.
More than 50% of the winning combinations on record consist of unique distance values; while almost 40% consist of one duplicate values.

Setting the Standards

To determine the distance factors, each draw result must be arranged numerically from the smallest to the largest number. For example, the order of the 8 May 2018 result 19 • 27 • 07 • 46 • 18 • 53 would be re-arranged as:

07 • 18 • 19 • 27 • 46 • 53

Then, the difference between every 2 consecutive numbers are calculated. The value of the difference is referred to as the distance between 2 consecutive numbers; or simply distance. Thus, in the preceding example, the distances between the numbers are:

Distance AB = 18 – 7 = 11
Distance BC = 19 – 18 = 1
Distance CD = 27 – 19 = 8
Distance DE = 46 – 27 = 19
Distance EF = 53 – 46 = 7

You now have the distances:

11 • 1 • 8 • 19 • 7

If you sum up all these numbers, you get the sum of all distances:

11 + 1 + 8 + 19 + 7 = 46

The sum of all distances 46 is the same as the distance between the largest and the smallest number, thus;

Distance FA = 53 – 7 = 46 = Sum of all distances in that particular combination

With the numbers in a combination arranged from smallest to largest, A refers to the 1st number, which is the smallest. B refers to the 2nd number, which is the 2nd smallest; C is 3rd; D is 4th; E is 5th; and F refers to the 6th number, which is the largest. Distance AB (or B minus A) therefore, means the difference between the first and second number. Distance BC is the difference between the 3rd and 2nd numbers (or C-B); and so forth and so on.

Significance of the Distances

Our planets in the solar system maintain their orbits because of gravity. If one planet changes its force of gravity, it affects the orbits of all the other planets. Imagine the lottery balls as a group of small planets which maintain their positions based on alternating fixed set of distances. By determining the distances between 2 numbers, you can figure out the probable numbers next to another number.

For example, if the common distance is 12, then you would know that the probable next winning number after 21 is 33 calculated as follows:

21 + 12 = 33

where 21 is the given lotto number, 12 is the probable distance, and 33 is the calculated next probable winning lotto number.

These values of distances, the sum of the distances included, form a set of delimiters. Delimiters act as constraints in such a way that they prohibit you from combining just any number of your choice. Delimiters ensure that your combination is within the probability zone.

So, how do you figure out the probable distances?

Probable Distances Between Two Numbers (Standard 05)

As mentioned earlier, the differences between two numbers of every result were calculated. As a result, the following table presents a summary of the findings in 2025 covering 1,375 results.

Distance		Prob
From	To	%
1	9	65.02%
10	19	26.78%
20	29	6.60%
30	41	1.60%

Proof of Data

To give you an idea what the data look like, following is a screenshot of the calculated data in Google Sheets.

The first data table that you see, Distances Between Consecutive Numbers, calculated the distances or differences between the numbers of all the winning combinations. Column BA or AB would be 2nd number minus the first number. Column CB or BC would be 3rd number minus the 2nd smallest number; and so forth and so on. Remember that the winning combinations were re-arranged numerically smallest to largest in order to establish these constraints or delimiters.

Column Sum adds up all the values of the distances.

How often does a particular distance occur?

The second set of data, Distances Frequency & Probability, counted the occurrences of each distance value calculated under columns BA, CB, DC, ED, FE. As a result, recorded distances ranges from 1 to 41. No distance occur that is greater than 41. The value of occurrences calculates how frequent a particular distance is resulted from the winning combination.

Each value of occurrence is then divided by the sum of all occurrences to get the probability rate or percentage ratio. Notice that the highest percentage is 10.05%; the lowest, which is not shown, is actually 0.01% corresponding with the distance value of 41. To make the data more meaningful, the data were divided into four and are summarised above where distances of 1 - 9 make 65% of all outcomes. This means that if the difference between two of your lotto numbers is from the range of 1 - 9, then, your numbers are good, probability wise. On the other hand, if the difference between two consecutive numbers of your combination is greater than 41, might as well change the larger number to a smaller one so that it fits the probability zone. Any distance value of greater than 41 has 0% probability (for now). You can find the complete data, as a column chart (Data 10), in the next sections.

The probability of duplicate distances and sum of distances are discussed separately in this chapter.

How to apply this standard

If you are playing only one combination, applying this standard is easy with the use of a calculator; or mental subtraction would do just fine. However, if you plan to play 10 or more combinations, applying this standard may be tedious. Using a spreadsheet app may be handy.

If you do not want to keep a note of the summarised data above, just remember 1 - 41. The smaller the distance, the better; and do not exceed 41. As for the sum of distances, do not go beyond 10 - 57.

Visual View of Distance Frequency Probability

The following column chart presents all the probable distances and how often they occur in every draw. Note that the smaller the value of the distance, the greater its frequency of occurrence. The next question is: how small should the distance be: 1- 9? 10 - 19? 20 - 29? Let's start first from what it should not be.

Distances Frequency and Probability (Data 10)

The Risk Zone

The distances 24 to 41 can guarantee only 4.03% probability. This means that if the difference between two consecutive numbers is between 24 - 41 inclusive, there’s a little probability that your combination is likely to win. It is possible but it rarely happens.

For example, in this combination 01 • 42 • 50 • 53 • 57 • 58, the difference between 42 and 1 is 41, making this combination unlikely to win. To make it a probable combination, you can change 42 to any number between 22 and 37. This range ensures that your numbers are good both with #01 and #50.

If you want to take a risk, by all means consider any distance beyond 22 - 37.

The Safe Zone

If the differences between two consecutive numbers are between 1 and 23 inclusive, your combination has 95.97% chance of winning. Well, not exactly a better chance of winning; but rather, a better combination of numbers that aligns with the history of winning combinations.

Exploring More About the Distances

What if you limit your distances to a mix of 1 to 9 only? For example: On June 29, 2025, the winning combination was 14 • 36 • 17 • 22 • 34 • 29. Arranged smallest to largest, that is to be: 14 • 17 • 22 • 29 • 34 • 36. To subtract each from the next, the results are: 3 + 5 + 7 + 5 + 2; add them all up and the result is 22.

Distance values of 1 to 9 were present in all of the sampled results (1,375, as shown in the stats below); which means that every winning combination consisted of at least a distance value of 1 to 9. These distance values are the top 9 most common. But how many of the results actually consisted only values of 1 to 9?

Presenting the data. This is based on 1375 results studied. —

The figures under In Results refer to the number of winning combinations that consist of any distance value stated in the column Distance . The columns 5 to 1 breaks down the figure in In Results into number of instances falling within the same distance range. For example, of 1375 results, only 66 of those contain all 5 values within 1 - 9. One of these results won in 5/31/2015 with the numbers 35 • 37 • 45 • 51 • 52 • 54. Subtracting one from the next, you get the distances: 2-8-6-1-2, which are all within the range 1 - 9. The 0 column is the exact opposite or its non-existence in the results. Therefore, if 10 -19 were found in 1078 results, they were not found in 297 results.

Distance Value of 1 - 9

All winning combinations (1,375 all in all) consisted of at least one instance of a distance value that is less than 10; i.e. 1 - 9. So, it is safe to say, as a general rule, that your combination should consist of at least a distance of any value from 1 to 9.
At most, three instances of 1 - 9 is the most common; followed by four instances, then two.
Seldom that all five distance values are 1 - 9; it had occurred 66 times, though.
Very uncommon that only one instance of 1 - 9 is present in a combination. There were only 9 combinations that matched that criteria.

Distance Value of 10 - 19

The next most common distance values are 10 -19 which made 78.4% of all the results (1078 / 1375).
It is not probable that all distance values are any from 10 -19. (See row 10-19, column 5).
Having four of these distance values is possible but it rarely happens. Only 8 out of 1,375 results that such had occurred.
The most frequent scenario is to have one or two distance value of 10 - 19 be present in your combination. At other times, having three is okay.

Distance Value of 20 - 29

This is easy to remember. Your combination can only have an instance of any distance value of 20 - 29, making it 31.93% of all 1375 results. Having two is possible but not very probable.

Distance Value of 30 - 41

This is the rarest of all distances to occur. Its probability is only 7.56% for values 30 - 39; and 0.44% for values 40 or greater.

The next question is: Which of these values usually go with another? If the most common is to have three values of 1 - 9, what are the other two? Let's look at a different picture of the data.

Probable Combination of Distance Values

Following is a screenshot image of the data presenting how often a particular distance value go with another value.

You can see from the table below that the most common form of distance mix are: 32000, 31100, 41000; followed by 23000 and 40100 as runner ups. The 1st digit refers to distance value of 1 - 9. The 2nd digit refers to distance value of 10 -19; the 3rd, 20 - 29; and so forth and so on.

The distance mix of 32000 means: 3 values of 1 - 9; and 2 values of 10 -19. The triple zeroes means no distance value from 20 - 41. As an example is: 5 • 2 • 2 • 17 • 13 corresponding to lotto numbers 4 • 9 • 11 • 13 • 30 • 43 (Sep 20, 2015 result). [9 – 4 = 5; 11 – 9 = 2; 13 – 11 = 2; 30 – 13 = 17; 43 – 30 = 13]

At a different perspective, examine the data just above, Probable Mixes of Distances. This set of data presents which set of distances usually go with what set. You can see that the most common is a mix of 1 - 9 and 10 - 19 (1078 results). You may ask just how many 1 - 9 and how many 10 -19? Just look at the other table Instances of Distances for Every Combination. The possible mixes are: 32000, 41000, and 23000.

You can also mix 3 sets of values such as: 31100 means 3 of 1 - 9, 1 from 10 - 19, and 1 from 20 - 29. For example: 5-2-12-2-23 derived from the winning combination on Jan3, 2016 — 26 • 10 • 5 • 24 • 49 • 12 or arrange numerically, 5 • 10 • 12 • 24 • 26 • 49. Just go ahead, make the subtraction.

Note that the other mixes such as solely 20s and 30s do not really mix.

The Unique vs Duplicate Factors

Based on the history of winning results of Ultra Lotto 6/58, the distances of most winning combinations are unique, making up 55.64% of all results. If two distances are equal, they make 38.31% of all the results. The rest have either 3 or 4; but 4 make only 0.44% of all the results, equivalent to only 6 actual winning combinations. (See the data, Frequency of Duplicate Distances, under the section Proof of Data.)

Is it possible to have equal distances?

What if your numbers are multiples of 3, such as: 03 • 06 • 09 • 12 • 15 • 18? To calculate their distances, they are all 3; the sum of which are: 3 + 3 + 3 + 3 + 3 = 15.

Though the distance value of 3 is good, which is the 3rd most common (with 614 occurrences), does it make your combination more probable? May be not. In fact, there's only 1 combination, out of 1,375 results, the sum of distances is 15. Moreover, no combination that has this form have won yet. To be in the safe zone, limit the duplicates to 1.

Therefore, it is not advisable to play numbers in which all the distances are the same or equal.

So, What Is Ideal?

What is ideal is to form a combination with unique distances. The 8 May 2018 result is an example: 7 • 18 • 19 • 27 • 46 • 53 with distances of 11 • 1 • 8 • 19 • 7.

The probability that a result has unique distances is 55.64%. Therefore, 44.36% would have 2 or more distances of equal value. The result of 1 May 2018 is an example of a result with 2 distances of equal value: 15 • 28 • 39 • 42 • 48 • 51 with distances of 13 • 11 • 3 • 6 • 3.

Three (3) distances of equal value is already very rare. There were only 6 instances when this study was initially made in 2018. In 2025, it has not changed. Having 4 or 5 equal distances is not probable.

How do we decide which distances should we mix?

The answer is above Instance of Distances for Every Combination.

The Sum of All Distances

Determining the difference or distance between two consecutive numbers is just part of a complete delimiting factor. The sum of all distances also play an important role in combining probable numbers.

Take a look at the following data.

Sums of Distances (Data 11)

The preceding column chart presents interesting facts about how winning numbers are combined. Let's take a look at where it peaks.

The Peak 42 - 50. Most winning combinations have a distance sum of 42 - 50. This make 42.53% of all winning combinations. If you're seeing lower columns between 42 and 50, these columns will eventually rise to catch up with the frequency of 42 and 50.
2nd Runner Ups 31 - 41 & 51 - 55. On the left side of the peak are the sums of 31 - 41 which make 29.13% of all results; on its right are the sums of 51 - 55 which make 15.37% of all results. Together they make 44.50% of all the results. If the sum of distances of your combination is any between 31 and 41 or 51 and 55 inclusive, your combination is still considered good because it's not all the time that the sum can be between 42 and 50, which are at the peak.
The Lows: 27 - 30 & 56. Each of these values make only less than 2% of all results. Together, they total 7.14%.
The Rares: 10 - 26 & 57. Each of these values make only less than 1% of all results. Together, they total 5.83%.

To illustrate the significance of the sum of distances:

Let's say, the lotto numbers in your combination are 01 • 03 • 06 • 10 • 16 • 17, which are the birthdays of your parents and siblings. If you are going to validate this combination, you calculate the distances such as:

3 minus 1 = 2
6 minus 3 = 3
10 minus 6 = 4
16 minus 10 = 6
17 minus 16 = 1
To add all the distances: 2 + 3 + 4 + 6 + 1 = 16.

Are your numbers good? Based on statistics, the distances are good because probability says that the lower the value of distances, the better. However, the sum of all the distances is only 16. Statistics also says that your numbers are good if the sum of all distances ranges from 27 - 55 to capture 92.43% probability. If you want to take a risk, you can proceed with your chosen numbers. Note, however, based on data, the sum of 16 has a risk factor of 0.22% probability. In fact, out of 1,375 results, there were only 3 winning combinations, the sums of which were 16.

In A Nutshell

So, how do you apply the probability of distances? Observe these rules.

If a distance is over 41, the probability is zero percent (0%).
The smaller the value of a distance, the greater the probability.
Remember that the difference between the smallest and largest number of your combination should be between 10 and 57 inclusive. This is the same as the sum of all distances.
Using a distance of 1 - 9 has 100% probability. It means that every result that was tested had at least 1 distance whose value is between 1 and 9. The threshold is actually 1 - 8. If you go lower than 8, it will cover only 1369 results instead of 1375; or 99.5% instead of 100%.
The most common instances of having distances between 1 and 9 is 2 to 4. This means that 2, 3 or 4 distances in your combination should rather be between 1 and 9 inclusive.
If 3 - 4 distances are between 1 and 19, the others would definitely be greater than 9 such as between 10 and 30.
You can mix sets of distances such as: 1 - 9 with 10s or 20s or both; but rarely with 30s and 40s.

Algorithm for Programmers

Algo 08. Each time you input a new winning result, arranged the numbers numerically, smallest to largest; then calculate the differences (labeled as distances) between each two consecutive numbers. Update a separate table [tbl_distances] where distances are stored.
Algo 09. When generating a combination of lotto numbers, ensure that the numbers conforms with the rules of distances. The rules of distances are produced based on the data in [tbl_distances].
Algo 10.To populate initially the [tbl_distances], run a program that calculates the distances of every winning combination in the results database updating[tbl_distances] each time a record is processed. Set the rules of distances.

For Spreadsheet Users

Table of Distances

Create a separate sheet labeled Distance.
Create a table with 5 columns —AB, BC, CD, DE, EF—which will contain the values of distances. Populate the table with data by using the MAP function. Input this formula on the very first cell under AB.

=MAP( Results!$B3:$B, Results!$C3:$C, Results!$D3:$D, Results!$E3:$E, Results!$F3:$F, Results!$G3:$G, LAMBDA( a,b,c,d,e,f, SMALL( {a,b,c,d,e,f}, 2)-SMALL( {a,b,c,d,e,f}, 1)))

Copy the same formula to the very first cell in the next column, which is BC. Then change the parameters (in red) in SMALL to 3 and 2 respectively. Do the same thing with the other columns.
Add 5 more columns to count the instances of values. Name them as: 0, 1, 2, 3, 4 to count values that are 1 - 9, the 10s, 20s, 30s and 40s. The formula is as simple as: COUNTIF( A3:E3, "<10") to count the 1s-9s. For the 10s, 20s and 30s, use COUNTIFS.
Add another column to join the values you calculated in #3. Use this formula: JOIN( "", H3:L3) assuming your values are in H3:L3. Label this column Mix of Distances.

Table of Combined Distances

Create another table similar to Instance of Distances for Every Combination. You will find an image of this in this chapter. This is where you will summarize the Mix of Distances using the FILTER function.
Filter the results in Mix of Distances with this formula: =SORT( UNIQUE( FILTER( M3:M, M3:M <> "")), 1, TRUE) assuming your data are in M3:M.
Add another column to calculate the frequency of each distance mix by using a simple COUNTIF function.

These are all you need to monitor the probability of distances.

Manual Method

To calculate the distances of your combination, the manual method simply follows simple subtraction, which you can do it mentally or with an aid of a calculator. Then just be guided with the data you have seen here.

Comments

UnknownOct 6, 2019, 1:17:00 PM
pls give me nw the possible number to win 6/58
UnknownOct 23, 2021, 9:01:00 AM
Very informative. 😇
Endo maribelMar 8, 2022, 10:48:00 PM
Thank you so much very informative in japan how to cumpute? Please help me 🙏
Endo maribelMar 8, 2022, 11:14:00 PM
Please give me a possible number to win lotto 7 here in japan I need money because I don’t have work because of the pandemic🥲 this is my Facebook account maui dela Cruz endo

Ultra Lotto 6/58 Results Statistics and Probability of Winning

Why this came to be

A Few Words

just about what this is

No foreword :-)

What to expect in this report

What Covers The Study

Outline

General info

The Standards

Data Sampled In The Study and Scope

Brief general and mathematical facts

What Is A Lottery System 6/58?

How To Play PCSO's Ultra Lotto 6/58 and How To Win It

How You Win The Game

Probability of Winning A Lottery System 6/58

Permutations vs Combinations

Number of All Possible Combinations

Odds Of Winning

Margin of Error

Margin of Error Formula

Quantiles

Grouping the lotto numbers with related attributes

Method: Simple Basic Math

Frequently Used Terms

All-Time Statistics

Setting the Standards

General probability based on all results

Winning Frequency of Each Number

How often does your number win?

Winning Frequency of the 58 Numbers (Data 01)

The figures explained

Top Winning Numbers

Top 29 Lotto Numbers (Data 02)

Top vs Bottom Numbers (Standard 01)

Observation

Try This Exercise

How To Do It Manually

In A Nutshell

Algorithm 01, 02, 03 for Programmers

Low vs High Numbers

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

Which Numbers Are Low or High

Standard 02: Low To High Ratios

Low To High Numbers Ratios (Data 03)

More About Low and High Numbers

Timing of Low:High Combinations

Occurrence of Low:High Number Combinations (Data 04)

Specific Low and High Number Patterns

Frequency of Specific Low and High Number Sequence (Data 05)

How to apply the data

To illustrate.

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

Try This Exercise

Combination 1 (3:3 ratio)

Combination 2 (2:4 ratio)

Combination 3 (4:2 ratio)

In A Nutshell

Algorithm for Programmers

Guide for Spreadsheet Users

Odd vs Even Numbers

Which numbers win most: odd numbers or even numbers?

Odd-Even Winning Probability

Findings in 2022

Probability of Odd : Even Ratios (Data 06)

The 2018 Study on Odd-Even Winning Probability

Highlights

Major Odd-Even Patterns

Standard 03. The Odd-Even Probability

3:3 Odd-Even Ratio

4:2 & 2:4 Odd-Even Ratios

1:5 & 5:1 Odd-Even Ratios

All Odd or All Even

Odd-Even Patterns or Sequence

Probability of Odd to Even Sequences (Data 07)

Frequency of Occurrence of Odd:Even Sequences (Data 08)

Early Probability Results for Odd-Even Patterns (Prior to 2025)

Alternating Odd and Even Numbers

Straight Odd vs Straight Even

In A Nutshell