What is the most accurate way to predict a combination?

Question

Mathematics

Good afternoon!
There is a game with dropping 8 numbers (each from 0 to 99). Those. 8 different numbers drop out at a time, for example: 8, 91, 17, 25, 42, 31, 98, 65. I have an array with 500 such dropouts. What is the most accurate way to predict which numbers will come up?
The most logical and the first thing that comes to mind is to calculate what number fell out most often, respectively, there are more chances that it will continue to fall out. But how to predict exactly which numbers (8 pieces at a time) are most likely to fall out together? Thank you!

Answer 1

This is the task of finding patterns. That is, in fact, you need to find an algorithm, a formula, a function by which these numbers are generated. This is not an easy task.
Let's start with the fact that there can be two options: either there is a formula, or it is not. Random number refers to the option when there is no formula. Although a pseudo-random number can be described, this is a separate, borderline case (because if the number should be random, but there is a formula, then this is essentially a mistake by the author of the algorithm, and the answer will depend on what you need and what you do - fixing the error or its operation).
But even if there is a formula, it is not at all necessary that you can find it. For example, humanity has long been searching for patterns in the outside world with varying success. We proceed from the fact that everything is somehow arranged, but how exactly, we can guess. We look, we observe, and then bam - we notice a pattern, draw it up in the form of a scientific discovery and rejoice. The laws of physics, chemistry, the same mathematics - all this is the result of a search for patterns and good luck.
Thus, what can be a simple offer in your case? You can formulate a hypothesis and test it. Then one more - also check. Etc.
You can automate this in the following way. Make a list of mathematical functions and operations that you think could be applied. You make other assumptions. For example, about the fact that each group of 8 numbers does not depend on the previous one, that is, you need to guess the rest from the first numbers from the group. Or, on the contrary, that the next group depends on the previous one, then you need to guess the numbers based on what happened in the past. Well, in fact, you enumerate algorithms (formulas), no matter how wild it sounds.
That is, formulas can be, for example, like this: (N * 917 mod 512), or (N * N mod 100) and so on (mod is the remainder of the division, and N is the number number). That is, these are some functions based on some arguments. You need to figure out how to present them as data, and sort through them in turn.
But, as I said above, there may not be a formula, or you can’t guess it even with enumeration, or it may be so complex that a smart comprehensive enumeration will take years. Good luck! :)

Answer 2

If the order is not important, then this is a clustering task. The task is to find 8 centers of groups. One of the methods is kNN.

Answer 3

Read about Markov chains.