Lottery System 6/55: A Probability Study

Featuring PCSO's Grand Lotto 6/55

SCOPE

This report studies results from PCSO's Grand Lotto 6/55 drawings. It covers results from 19th April 2010 until the date shown here. The study is a work-in-progress; thus, some statistics may change as new results are added.

PART I

Lottery System 6/55: An Overview

What is Grand Lotto 6/55

Grand Lotto 6/55 is a system 6/55 lottery. It is a form of lottery wherein 6 winning numbers are drawn out of 55 numbers from 1 to 55. From the player's point of view, it is a lottery system wherein the player bets on 6 different numbers from number 1 to 55. In the Philippines, this type of lottery system is called Grand Lotto. In other countries, it may be called or labeled differently.  Whatever it is called, the system remains the same.

How Do You Play Grand Lotto 6/55?

To play the game, you pick 6 numbers from 1 to 55. Each number must be unique; you cannot pick a number twice. Your 6-number combination however does not require any order. Use the wage card specific for Grand Lotto.

To use the wage card, simply mark the numbers that you want to play. Pick only 6 numbers for each box. There are 4 boxes labeled A, B, C, D. If you made a mistake in marking numbers, mark the void tag. If you have no specific numbers to play, use LP, which stands for Lucky Pick. By marking LP, the system will generate the lotto numbers for you.

You can play your numbers up to 6 consecutive draws. Simply mark the number of draws found on the left side of the card.

What are System Plays?

There are 7 system plays: 5R or roll 5, system 7 up to system 12.
  • 5R. In 5R, you mark 5 numbers. The system will generate your 5 numbers and combine them with all the other numbers 1 to 55. For example, if your numbers are 12345, the system will generate 50 combinations such as 123456, 123457, 123458 up to 1,2,3,4,5,55. You may also mark LP if you do not have particular numbers in mind. If you marked LP, make sure that you also mark 5R. This will cost you ₱1200.
  • System 7. In S7, you mark 7 numbers. Based on your 7 numbers, the system will generate 7 6-number combinations. For example, if your numbers are 1234567, the system will generate 123456, 123457, 123467, 123567, 124567, 134567, 234567. If you do not have particular numbers in mind, mark LP instead and make sure that you mark S7 as well. This will cost you ₱168.
  • System 8. Mark 8 numbers or mark LP. The system will generate 28 combinations. This will cost you ₱672.
  • System 9. Mark 9 numbers or mark LP. The system will generate 84 combinations. This will cost you ₱2016.
  • System 10. Mark 10 numbers or mark LP. The system will generate 210 combinations. This will cost you ₱5040.
  • System 11. Mark 11 numbers or mark LP. The system will generate 462 combinations. This will cost you ₱11,088.
  • System 12. Mark 12 numbers or mark LP. The system will generate 924 combinations. This will cost you ₱22,176.

How Much Do You Wage To Play the Game?

For each number combination you play, you pay 24 PHP. ₱20 is the price of the ticket; ₱4 goes to documentary tax. Since the Philippine lottery started, a lotto ticket had not been taxed. Starting in January 2018, under the Train Law of President Duterte, each ticket has been taxed 20%.

How Do You Win and How Much if You Matched Your Numbers?

If your 6 numbers matched the 6 winning numbers that were drawn, you win the jackpot prize. You win a consolation prize if you matched only 3, 4 or 5 numbers. The winning numbers do not follow a particular order, which means, how the numbers were drawn is irrelevant.

Match Prize Tax
6 numbers ₱30 million* 20%
5 numbers ₱200,000** or less 20%
4 numbers ₱3,000** or less
3 numbers ₱20 fixed

* The minimum or starting jackpot prize is ₱30 million. This is divided equally among the winners should there be more than 1 winner. Deducted from the jackpot prize are:
  • 1% commission for the agent or lotto outlet that sold the ticket.
  • 20% tax on winnings
** For the second and third prizes, these are further lessened depending on the number of winners. For example, if only ₱10 million is allotted for the second prize, and there were 80 winners, the ₱10,000,000 will be divided by 80, reducing the second prize to only ₱125,000. 

All prizes above ₱10,000 are taxed 20%. This took effect also in January 2018 as part of the Train Law. TRAIN stands for Tax Reform for Acceleration and Inclusion.

How Many Combinations Can Be Formed with 55 Numbers?

You can form 28,989,675 combinations from numbers 1 to 55 wherein each combination comprises 6 unique non-repeating numbers in no particular order. 

What's The Odds of Winning Lotto 6/55?

Based on 28,989,675 combinations, your odds of winning a lottery 6/55 is 0.0000034% or 1:28,989,675. You have to play 289,896 combinations to increase you odds of winning to 1%.

If you are going to play all the 28 million plus combinations, it will cost you  ₱695,752,200.  You will have to wait for the jackpot prize to reach ₱878,475,000 just to breakeven (that is after deducting the 1% agent's commission and the 20% tax on winnings).

On the other hand, playing 289,896 combinations will cost you ₱6,957,504.

When are the Scheduled Draws of Grand Lotto 6/55?

The draws for Grand Lotto are held every Monday, Wednesday and Saturday at 9:00 PM televised live on PTV 4 and via live streaming on YouTube channel PCSO Gov.

How Can Probability Help Me Win Lotto 6/55?

It cannot but it can help you narrow down your choices of numbers. Not all the 28 million plus combinations are probable. By eliminating the non-probable combinations, you limit your choices to a few; thus increasing your odds but to just a bit.

Read more about Grand Lotto 6/55 probability studies.
Part II

All-Time Statistics

Setting the Standards

This section presents all data based on all results of Grand Lotto 6/55 from 19 April 2010 up to 2025. From time to time, the data are updated, therefore, you might see the values of statistics slightly changing.

Chapter 1

All-Time Winning Frequency

Which Numbers Win Most

The chart just below presents the winning frequency of each number. However, do not be excited yet. Numbers that have been winning most do not mean that they win all the time. There are times when they do not win. Call it the winning times of a number seasonal.

The second chart that follows presents a more significant information. Notice that the probability percentage of each number ranges from 1.41% – 2.18%. Not much of a difference between any number. This means that any number is as good as the other. However, it does not mean that the statistics does not serve a purpose.

Top vs Bottom Numbers

Do top winning numbers win all the time? To answer this question, the winning frequency of each number were ranked 1% – 99% where 99% being the highest. After every draw, the ranks of the winning numbers were determined, collected and tallied. The result is the data presented following this.

As mentioned previously, not at all times that top winning numbers win all the time. To prove that, examine the next set of data—the top winning numbers are those that usually rank 60% – 69%. In fact, statistically speaking, lottery numbers that ranked 90% – 99% had the lowest probability (8.14%) compared to other ranks. The following data sampled 1364 results from the Grand Lotto.


Top Ranking of Grand Lotto 6/55 Numbers

Notice, however, the percentage of occurrences of each rank group in the total results sampled ranges from 41% – 53%; which means that each rank group shares a fairly 50%, more or less, chance of winning. This statistics will probably be consistent even if the volume of sampled results increases (Law of Large Numbers). Therefore, whether you are playing a top winning number or otherwise, your number has a fair chance of winning. The story changes, however, when ranking is calculated based on a shorter period.

In Part III, Trend Probabilities, the same technique will be applied for shorter periods.

Combining Top and Bottom Numbers Based on Ranking

The next question is: Which rank do you combine with which rank? For example, would you combine 6 numbers that all rank 90% – 99%; or 60% – 69%; or a mix? These data answers the questions.


INSTANCES OF RANK GROUP IN A COMBINATION

The top labels refer to the rank groups where 0 is 1% – 9%, 1 is 10% – to 19%, and so forth and so on. The vertical labels refer to the number of instances of a particular rank group for every combination sampled. For example, compared to other rank groups, numbers that rank 80% – 89% are most common, with 40% probability percentage,. This means that 40% of the results sampled contain one number that ranked 80% – 89%. 

Notice, however, that the probability percentages of each rank group range from 34% to 40%, which is relatively at almost the same level of chances (see the first row of percentages). In cases where there exist two numbers from the same rank group, ranks 7 and 9 appear less probable compared to other ranks (see second row in percentages).

Significance of the Data

What is mostly significant from the data is that it is improbable for a combination to contain 5 or 6 numbers that belong to the same rank. To contain 4 numbers from the same rank is likewise almost improbable with 0% – 0.1% probability. There were only 6 results that fell into that category. Therefore, when combining numbers, make sure that no 4, 5 or 6 numbers belong to the same rank.

Specific Cases of Combined Rankings

Previously mentioned that top winning numbers do not win all the time. Winning numbers are usually a mix of top and bottom winning numbers and anything in between. Thus, playing the 6 top winning numbers is actually not a good choice. But how do you know which one is topping or not. In that regard, you really need a spreadsheet tool to assist you in determining the top and bottom numbers.

To help you with that, this report presents the winning ranks of each Grand Lotto 6/55 numbers which you can find at the beginning of this chapter.

Now, to answer: which rank do you combine with which? The following data reveals how winning numbers are usually combined based on their present ranking prior to its time of winning.


COMBINING NUMBERS BASED ON PROBABLE RANKING

Examine the first set of data presented just above.

  • 89% of all results contain at least 1 unique rank. In most cases, two of the numbers have unique ranking (46%). For example: 11-22-34-35-40-45 (these are in percentages) where 11 belongs to ranks 10% – 19%; while 22 belongs to ranks 20% – 29%; while the rest are called doubles. In other common cases are when four numbers belong to different rank groups, or even 6; but rarely 3.
  • 70% of all results usually contain doubles; i.e. two numbers belong to the same rank group. In the previous example, 34 and 35 both belong to rank group 30% – 39%.
  • It is very rare, though possible, that three numbers can belong to the same rank group (13% probability). For example: 11-22-34-35-39-45 where ranks 34, 35 and 39 all belong to the same group, 30% – 39%.
  • All other cases are improbable or almost improbable.

Setting the Standards

The second set of data presented previously—Specific Combination Cases—reveals how winning numbers are actually combined based on their current rankings. Starting with the most common, combine your numbers as follows ~

  • D— 45% of all results sampled contain a double from any rank while the rest of the numbers (4 of them) are all unique. For example: the Sep 20, 2025 winning numbers 35 • 55 • 09 • 44 • 33 • 07 ranked as follows respectively: 19% 33% 23% 96% 87% 28% where 23% and 28% are considered doubles (coming from the same group); while the rest belonged to different groups.
  • 2D— 20% of all results contained two doubles: An example is: in percentages 17-73-71-83-33-12 (Sep 8, 2025 result) where 73 and 71 belonged to the 70%–79% group; while 17&12 belonged to the 10%–19% group.
  • U— 19% of all results contained unique rankings. This means that the ranking of all the 6 winning numbers belong to different groups. An example is the Sep 13, 2025 result: 33-62-83-01-12-23 (these are in %) where each rank come from different rank groups.
  • T— 9% of all results contained rankings of what is called triple, which means that 3 of the winning numbers belong to the same group.
  • The rest are very unlikely, if not, improbable such as H6 where all the 6 numbers could belong to only 1 rank group; which has not happened yet.
To apply these standards to your numbers, there are only 3 things that you have to remember: Double, 2 Doubles, and Unique. The rest of the cases are very rare, if not, improbable. If you want to be adventurous, you can try Triple (T) or Triple Double (TD).

Chapter 2

Probable Winning Patterns

Discovering Patterns and Sequences

Do winning numbers follow a certain pattern? For example, can winning numbers be all odd or all even or a mix? Do low numbers win more often than high numbers? Find out what statistics reveal.


RATIO OF ODD TO EVEN NUMBERS & LOW TO HIGH NUMBERS

Ratio of Low to High Numbers

The statistics define 1 – 27 as low numbers; while 28 – 55 as high numbers. Based on the above data, most common low and high number combinations are three low numbers and three high numbers (33% probability percentage). Other better chances are either 4 low numbers or 4 high numbers with a probability of 22% and 25% respectively. Together, they make a total of 80% probability percentage. In very rare cases, 5 low numbers or 5 high numbers are also possible with 7% and 8% probability respectively. At a very low probability of 1%, there were 23 cases when all winning numbers were all low numbers; and another 23 cases of all high numbers. The above data are based on 1646 results.

Ratio of Odd to Even Numbers

Examine the odd-even data. The statistics are not far from the low:high data results. Most common are 3 odd numbers together with 3 high numbers. In some cases, winning numbers contain 4 odd numbers or 4 low numbers. The less probable cases are 5 or 6 low numbers; and 5 or 6 high numbers.

These statistics may probably not change for a lifetime no matter how much you add to the results. Meaning, if the sampled data soon covers 2000 results or even more, statistics will reveal the same findings (Law of Large Numbers).

Setting The Standards

When combining lottery numbers you wish to play, observe the following:

  • A mix of low and high numbers has better chances of winning.
    • Combine 3 low numbers with 3 high numbers (3:3)
    • Combine 2 low numbers with 4 high numbers (2:4)
    • Combine 4 low numbers with 2 high numbers (4:2)
  • A mix of odd and even numbers has better chances of winning.
    • Combine 3 odd numbers with 3 even numbers (3:3)
    • Combine 2 odd numbers with 4 even numbers (2:4)
    • Combine 4 odd numbers with 2 even numbers (4:2)
  • If you want to be more adventurous, try the 5:1 or 1:5 ratios.
The same standards were established with the probability studies made for Ultra Lotto 6/58.

Chapter 3

Probable Combination of Numbers

Setting Constraints and Limits

There are 28,989,675 possible combinations that can be formed for a lottery 6/55. However, not all of these combinations are probable. Establishing certain constraints limit your choices as to which numbers you can combine. For example, how probable is this combination to win: 50 • 51 • 52 • 53 • 54 • 55? Maybe very low for the reason that the smallest winning number on record in a combination is less than 40. With 50 being the smallest number make this combination unlikely to win a jackpot.

What about this combination: 1 • 2 • 3 • 4 • 5 • 6, the sum of which is 21? How probable is for this combination to win? On record, it is improbable for the reason that the smallest sum of a combination is 35.

Calculate the differences between these numbers: 1 • 11 • 22 • 33 • 44 • 55. The differences between all two consecutive numbers in this combination are: 10, 11, 11, 11, 11. Does this combination have a potential to win? On record, it has zero probability for the reason than no 5 distance values can be solely between 10 and 19.

In this chapter, we explore the probable combination of numbers by establishing the limits and constraints based on statistics in combining lottery numbers. We dig deeper into:

  • The bounds (lower and upper limits) of a combination.
  • The probable sum of winning numbers.
  • The probable spaces between two consecutive numbers.

The Prerequisite

In order to establish the constraints and limits in forming a lottery combination, the winning numbers of every draw should be re-arranged numerically—that is by arranging the numbers from smallest to largest. For example, these 1 Oct 2025 result of ~

463413200117
 would be sorted as 
011317203443

The Probable Lower and Upper Bounds

The following data can give you an idea the probable range of lotto numbers that usually make it to the jackpot.


WINNING FREQUENCY IN THE ORDERED POSITIONS

The above data is a snapshot of a complete set of data. The first table calculates the winning frequency of each number assuming a numerical order of lowest to highest. Take for example, lotto #2. If #2 is the smallest number in your combination, there's a 9.8% chance that it can win. However, if #2 is your second smallest, the chance is only 1.2%. Therefore, it is better to have a combination such as this: 02 •  09 • 18 • 24 • 42 • 48 where #2 is your smallest number rather than 01 • 02 • 18 • 24 • 42 • 48 where #2 is in the second position rather than the first.

In another perspective, examine lotto #22. If #22 is your favourite number, it is more likely to win if it is your 2nd, 3rd or 4th number because making it 1st, 4th or 5th has lesser probability. Perhaps 15 • 22 • 24 • 30 • 33 • 40 is much better than 22 • 24 • 30 • 33 • 40 • 55.

Following is a complete list of all the 55 lotto numbers and their corresponding frequency of winning.

Probable Winning Range for Lottery 6/55

To summarise the statistics just presented, the following data sets the standards of how low or small your first number should be; and how high or large your 6th number is. These parameters assume that the numbers of your combination are arranged lowest to highest.

There are 3 sets of probable range presented.

  • The first set excludes all 0% probability but includes all those with lower probabilities.
  • The 2nd set excludes all probabilities that are less than 2%; thus the number ranges are narrower compared to the first set.
  • The 3rd set excludes all probabilities that are less than 1%.


PROBABLE WINNING RANGE

To illustrate how to apply the data ~

  1. Your 1st number should be any between 1 and 39.
  2. Your 2nd number must be higher than your first number but not higher than 45.
  3. Your 3rd number must be higher than your 2nd number but not higher than 49.
  4. And so on....

If you want to exclude the number of lower probability, apply the number ranges in the 2nd set.

Following is the same set of data that excludes only the 0% probability. These data are updated from time to time.

Probable Sum of Winning Numbers

To make the probable range of lotto numbers stronger, we add another layer of restriction—the probable sum of winning numbers. It simply adds together the numbers in a winning combination. Done with every winning result, we establish what the common sums are. Following is the result.

Basic Statistical Measures About the Sum of Winning Numbers
Central TendencySum
Minimum35
Maximum287
Median168
Mean168
Mode16030 occurrences

Based on the basic statistical measures just presented, we establish the following range of sums.

Probable Sum of Winning Numbers
Sum FromSum ToOccurrencesProb %
>= 35<= 85261.5%
> 85<=13530217.3%
> 135<= 18584948.5%
> 185<= 23551229.3%
> 235<= 287603.4%

It is clear that the typical sums of winning numbers range from 85 to 235 making it at 95% probability. The least common sums are from 35 to 85 and 235 to 287. Any sum lower than 35 or higher than 287 is yet not probable.

Probable Spacing of Numbers

When combining numbers, how far should the second number from the first number; the third from the second; and so on? Is combining 50 and 51 better than 50 and 52?

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