It is easier to choose a range than to pick a specific number

Choosing the exact numbers for the next lottery draw is difficult, but selecting numbers from a specific set is relatively easier. You don't know if a particular number, such as number 7, will appear in the next draw. However, if you group the numbers according to certain rules, such as 7, 14, 21, 28, 35, 42, 49, 56, 63, and 70, your chances of one or more numbers from this set appearing in the next draw are significantly higher. 

The lottery's partitioning algorithm is a method that uses sets(or partition) to replace selecting individual numbers. It doesn't require choosing specific numbers but rather arranges all numbers into different groups using various mathematical partitioning methods. Based on historical trends, certain sections are selected or excluded using the lottery generator to generate the next set of numbers.

Partitioning algorithm theory

Firstly, the partitioning algorithm arranges all numbers into a matrix, forming a rectangle. Different lotteries have different partitioning methods, and even for the same type of lottery, there can be various forms of rectangles. 

The partitioning algorithm involves two important basic conceptual parameters. The first parameter is how many numbers to partition. For example, the following image shows three types of partitions for Mega Millions. It represents dividing all the candidate numbers into groups of 5, 7, or 10 numbers per group.

The second parameter involves one of two partitioning methods: horizontal partitioning or vertical partitioning. In the image below, the partitioning is done horizontally with 7 numbers per partition. After partitioning, each partition is sequentially numbered starting from 1, and the partition numbers are displayed on the left side. The boxed area represents the first partition, which includes the lottery numbers 1, 2, 3, 4, 5, 6, and 7.

Let's take a look at another partitioning diagram, the vertical partitioning diagram for Mega Millions, with 10 numbers per partition. The third partition in this diagram includes the numbers 3, 13, 23, 33, 43, 53, and 63.

So far, we have learned about the partitioning methods used in lotteries. Now, let's discuss how many partitioning methods a particular lottery can have. The formula to calculate the number of methods is: n x 2, where n represents the number of numbers per partition, and 2 represents the options of horizontal or vertical partitioning. Therefore, for Mega Millions, there are 3 x 2 = 6 different partitioning methods. The theoretical introduction to partitioning is complete, and we can now proceed with data analysis.

Probability analysis of the partitioning algorithm

From the above, we can see that there are various forms of partitioning. Therefore, the partitioning algorithm also involves a significant amount of information. It requires a large amount of data analysis. In fact, when generating lottery numbers, we don't need to use all the partitioning methods. Each drawing will have only a few partitioning methods that exhibit favorable patterns to choose from. Your task is to spend time analyzing them. Once you grasp it, playing becomes easy, and the accuracy is relatively high.

Let's take a look at one particular grouping method based on vertical partitioning with 7 numbers. We need to select a total of 5 numbers, and the diagram below explains how many partitions they should occupy. Interestingly, the most common scenario is occupying 4 partitions, followed by 3 partitions, while the case of occupying 5 partitions only occurs 17.35% of the time. Occupying 2 partitions represents a situation where numbers appear very densely, with a lower probability. However, we can still track this pattern, and we will delve deeper into the analysis in the future.

Data analysis of the partitioning algorithm

Similarly, here is a trend chart based on vertical partitioning with 7 numbers. The X-axis represents the drawing sequence, with the most recent draw on the far right, and sliding left reveals more historical records. The Y-axis indicates which partitions the 5 numbers from the Mega Millions results fall into. If a draw has 5 points, it means the numbers are located in different partitions, while fewer than 5 points indicate that multiple numbers are in the same partition. We know that there are a total of 7 partitions, and in theory, they should be evenly distributed.

The reality often differs from the theory, as seen in this chart. We can observe that the first partition is relatively dense, while the seventh partition is noticeably sparse. This is because they are opposite to the pattern observed in the preceding period, where the seventh partition was dense and the first partition was sparse. From this chart, we have our first strategy with the partitioning algorithm, which is to select or exclude a specific partition. We will discuss the specific operations of the filter later on.

The partitioning algorithm also involves trend analysis by tracking the total number of partitions occupied. The probability analysis of how many partitions the lottery results should occupy has already been discussed. The following chart depicts the trend of the total number of partitions. Similarly, the X-axis represents the drawing sequence, while the Y-axis, unlike before, represents the total number of partitions occupied by the results of each draw. From the chart, we can observe that the trend aligns closely with the probabilities discussed earlier. Most draws occupy 4 partitions, and the occurrences of 5 partitions and 3 partitions are also significant. From this chart, we have our second strategy with the partitioning algorithm, which is to predict the total number of partitions.

Indeed, we know that the partition algorithm has two methods. You need to find a pattern that you prefer to determine whether the next draw will fall within a specific partition or exclude a certain partition. Alternatively, you can also make a prediction about the total number of partitions in the next draw.

How to use the partitioning algorithm

Each partition method has two filters. The first filter is straightforward, where you simply choose the total number of occupied partitions and add it to the lottery calculator for filtering. The second filter is a special one, and you can add this filter repeatedly, each time selecting only one specific partition. For example, in the provided image, the first partition is selected as a "must include" option, indicating that in the next draw, at least one number from the first partition will definitely appear, and it could be one or more numbers. Similarly, you can also use the "exclude" option by selecting the second radio button to exclude certain partitions.

Conclusion

The principle of the partition algorithm is to select a range instead of selecting a single number. It provides relatively high accuracy compared to choosing individual numbers. There are multiple ways to partition the numbers, and the number of partitions can vary greatly depending on the specific lottery. You can choose to include a specific partition or exclude it when using the lottery generator. Alternatively, there is a simpler method where you only need to determine the total number of partitions occupied by the lottery results. Due to its information richness and high accuracy, the partition algorithm is one of the essential algorithms for lottery generation.