Calculate a pattern or guessing game

Question

Mathematics

In general, the question is rather vague, but I hope I can clarify:

There is a program that produces 4-6 characters. Let's call them xyzklm .
There is a player who reacts to these symbols and enters a number. Let 's call this number N.
The player acts according to a pattern that is known only to him. Based on this pattern, he chooses the number N, which he enters.

How can the program, after observing the player for some time, begin to predict what N he will bet? What methods should be used for this? Something like neural networks? Or something different?

Example of data that the program can have:
xyzklm = abcdef
N = 5

xyzklm = affae
N = -1

xyzklm = ffda
N = 2

xyzklm = edac
N = 0
and so on...

Answer 1

Maybe I'm wrong, but it's not necessary to use neural networks if the pattern is mathematical.
The value of the characters we will have is some X, and the value entered by the person is Y.
f(X)=Y
This f can be found based on the interpolation of statistical values.
If the value itself is 4-6 characters, then the number of such values ​​is finite and can be represented by numeric values. With the number of X, Y pairs, it is possible, by interpolation, to construct some function of 2-3 orders, which, with a certain degree of probability, will return the value that the person will enter. By increasing the number of experiments, we can get more accurate values. But, of course, it will be necessary to take into account the error.
All in all, I think it's worth seeing.this way

Answer 2

oeis.org/
But in the general case, the task of “finding out a pattern” is meaningless, since many different “patterns” can be fitted to any sequence, which give completely different continuations.

Answer 3

darn it

Answer 4

It's not very clear, are the characters random, or can the program generate them at its own discretion?
If the latter, then it can really be built according to the principles of self-learning neural networks.
And further. If a person can respond differently to the same set of characters,
then the program may not make an interpolation, but rather a probability distribution function.

Answer 5

It must be taken into account that no interpolation will cope with the task in which N is chosen not only on the basis of the current X (xyzklm), but also on the basis of its previous value. For example, if there are rules:

...
- If the current line contains A and the previous line contained A, then N = 1
- If the current line contains A, but the previous line did not contain A, then N = 2
...

Then this situation can no longer be described by functions of one argument. The number of arguments, of course, can be increased, but the depth of such dependence can always exceed this number. So, without certain restrictions on the algorithm by which the player obtains the values ​​of N, this is indispensable.