The question of "effective range" seems to come up fairly regularly. The truth is only you, the person asking the question, can ever answer it. I can help explain how you can answer it for yourself.
#1 Define "effective" for your intended use. Do you need to deliver a certain amount of energy on target such as for hunting? What size target are you shooting and what percentage hit rate is acceptable?
You just keep walking the range back based on the limiting factors. First limiter, trans-sonic range causing bullet instability. Probably 800-ish yds. Next limiter, energy if hunting, just look up the distance where it drops below desired level. Final limiter, your actual accuracy at extended ranges vs. target size.
So, at one end of the spectrum you can have a .338 Lapua rifle capable of 1MOA out to 2000 yds...and a shooter who can't hit the broad size of a barn. Max effective range, 200 yds.
Or, you can have a master long range shooter using his 300 WM hunting rifle wanting at least 1500 ft/lbs of energy for elk. His max effective range would be ~700yds for elk even though he may be able to hit at 1000yds 10/10.
#2 Test the accuracy of your rifle/ammo/optic/shooting position/shooter skill combination at various ranges (ideally progressively further until the hit percentage drops below acceptable level).
You can extrapolate of course for extended ranges. Let's say your mini is grouping 2" at 100yds from your desired shooting position with your chosen ammo.
Let's say you want to hit an 8" target 80% of the time and energy is no factor. We'll have a max effective range of probably about 400yds. At first glance, you'd think it would be 100% at 400 as the rifle was shooting 2" at 100. However, at 400, wind will play a role as will atmospherics and range estimation issues likely bringing our hit rate on an 8" target to between 80-100%.
Easiest way, discarding energy, is to just take your group size @ 100yds and multiply until the number gets bigger than your intended target size. This is a true theoretical "max" though as it doesn't factor range estimation and wind, just raw mechanical accuracy potential extrapolated for distance.
Your group size used should be no less than 5 and ideally 10 to be giving a true representative sample of the rifle's mechanical accuracy. A random 1/2" 3 shot group doesn't mean the mini can reliably hold 1.5" at 300 or 5" at 1000yds!