The question should be, how far can you accurately shoot a .22
That's the $64 000 question.
As indicated... start by defining the size of the target and the hit ratio
Define what you mean by ACCURACY....
The current ELR standard is a 12"X12" plate... 3 shots in the row. for this, I think 500yds is pretty much the max for that lucky 'world record'.... at 300yds, you can pound it all day with the right set up.
Somewhere between the two... is the accuracy limit on that size of target.
Now make that target 36"X36"..... until a definition or standard is created, the question is not readily answered.
Jerry makes a very relevant point. You can shoot a .22LR at long distances and hit things, but until there's a meaningful standard defining accuracy it's apples and oranges. It's possible to hit a 12"X12" steel plate three times in a row at 500 yards, but how difficult is it to do regularly or on command? Perhaps there isn't yet an answer to that question. The problem remains -- how should long range .22LR accuracy be measured? What are some reasonable standards so shooters can be discussing the same thing?
The word "precision" gets used to describe all kinds of things. During World War II, the US Army Air Forces conducted what it euphemistically termed "daylight precision bombing." Among its most enthusiastic proponents was Theodore Barth, the president of Norden, the bomb-sight maker. He optimistically declared in 1940 that a 15 square foot target was not difficult to hit from 30 000 feet. Events were to prove, however, that such predictions were rose coloured. Bombing accuracy, measured as a percentage of bombs that land within 1000 feet of the target, was throughout the war never more than one-third of all bombs, even when averaging in radar-controlled bombing, which was developed late in the war. In other words, daylight precision bombing was never precise. It was by the sheer weight of numbers of bombers and bombs that made the difference in strategic bombing.
The point is that optimism should not be allowed to characterize what is meant by accuracy or precision. If hitting a 12x12 inch plate three times in a row at 500 yards with a .22LR is considered a top-level measure or standard of accuracy -- just as repeatedly shooting 12mm edge-to-edge or better ten-shot groups (about .25" center-to-center) is a measure of a high level of accuracy at 50 yards, and quite challenging to achieve -- then it would not be a regularly achievable objective. The comparison may not be apt, but the top standard must be something that is indeed very difficult to achieve, but possible with a combination of three things, the rifle, the ammo, and the shooter.
Since the upper-most levels of accuracy are by definition not easily achieved, and certainly out-of-reach for the average shooter, it is imperative that there be a standard of accuracy that most everyone can relate to and agree on. Perhaps there are reasonable limits in terms of distance. The further the distance, the greater the role of good fortune comes into play. Considering the impact of wind and the limitations of all .22LR ammo, that alone should give pause when considering standards for extreme long range standards of accuracy. Standards in accuracy at any distance should not depend on the happy circumstances that can sometimes arise by virtue of sending enough rounds downrange, or, as in the case of bombing in WWII, dropping enough bombs so as to be sure that the target is destroyed.
Until there is that standard, comparisons of accuracy will be like discussing apples and oranges. It may well be that like daylight precision bombing during WWII, it will take some time to more fully understand what accuracy standards at very long .22LR distances really ought to be. Unlike WWII and precision bombing, where there were great efforts and achievements in technology, such as the ability to launch bombing raids involving hundreds of bombers at a time over many days, as well as radar-controlled bombing, it is questionable whether there are any realistic expectation of technological developments developments in .22LR rifles or ammo that will significantly improve what's available today.