I not sure to what field exactly this question belongs, but math/statistics seemed closest to me. So here we go:
It is a method of estimating a value that informally goes like this (bear with me). You pick two values. One that is clearly too low and another that is clearly too high. Then you try to bring values closer together by repeating the first step. When you found minimal too high and maximal too low values, that you can still define as too low/high, you stop and choose a value between and that is your estimated value.
I would like to know what is the official name of this method (if it has one) or if there is any similar or related mathematical/statistical estimation method?
If you take the midpoint between your high value and your low value, and then substitute that in for the new high or low (depending), that would be called a binary search. There may well be other names for it, but that's the one I'm used to.