All rifles will shoot under 1/3 MOA once in a while with a couple of few-shot groups. How often is seldom mentioned.
All rifles shoot group sizes somewhere between zero MOA and some larger size as follows:
40% of the groups will be about average in size.
30% will be a little bigger, or smaller.
20% will be a lot smaller, or bigger.
10% will be the smallest, or largest.
A rifle whose smallest group is .3 MOA and largest is 1.5 MOA is more accurate than one whose smallest group is .2 MOA and largest is 2 MOA. Simply put,rifles whose largest groups are smaller is more accurate than rifles whose largest groups are bigger. Doesn't matter what the size of their smallest group is. Don't forget that the smallest groups can happen when all the variables tend to cancel each other out or everything is perfect; what do you think is more likely?
Smallest groups are seldom the first ones fired; nor are the largest ones.
The popular way to judge accuracy is whatever shoots the smallest few-shot group. If neither one of the first or second few-shot group is not tiny, the load's typically considered inaccurate.
So, beware of most claims for accuracy of a given rifle. The accuracy any will produce is what the rifle and two other contributing parts of the shooting system have for repeatability. Here's what each part of the hand-held shooting system contributes to how close together bullets land on target:
25% rifle. 25% ammo. 50% shooter.
Having watched several people shoot the same rifle and ammo but the targets have a 4 to 5 times spread of smallest groups to largest, 'tis obvious to me that us humans are the biggest variable.
Keep this in mind reading reviews of rifles for accuracy. Ammo, too.
I'd pick a commercial rifle make and model that has a good track record for accuracy in competition wherein the best accuracy is paramount. From what I've gleaned in results, Savage tends to be a good choice.
http://savagearms.com/news/article/?id=2K5nTzegQ