I don't think anybody here is advocating that we should all be shooting 10 shot groups. The value is pretty limited for most people and most guns, and there are also other ways to determine that information (like shooting multiple groups at various ranges, which you presumably HAVE done) I think what Form is trying to explain is the inherent limitations of a 3 shot group. And he is correct. Statistically, it's a very poor measure of precision if all you ever shoot is are those three shots and no others. He's also trying to explain the difference between precision and accuracy, which lots of people don't understand. A true 1/2 MOA gun would be very PRECISE but that doesn't mean is ACCURATE. Was that 1/2 MOA 1000 yd group you shot centered perfectly on the target, or was it a little off? On the flip side, an 2 MOA gun can be very very ACCURATE... but only if enough shots are taken to reasonably determine the center of the group.
Accuracy and Precision
You will need to shoot more with a low precision gun than a high precision gun to get to the same absolute level of "accuracy" i.e. centering the group on the bullseye within a fixed error range. If your gun can really shoot 1/2 MOA for 3 shots every single time, then you don't need 10 shots to have good accuracy.
You are really confusing precision and accuracy there. What if that 1/2 MOA group was 3 ft to the left? Still a dang good group, but you would miss the deer! Just because you can shoot a 1/2 MOA 3 shot group, does NOT mean you can hit a 1/2 MOA target on demand. Or even a 1 MOA target for that matter. I've proven this to myself many times. My main sporter rig will shoot sub MOA 3 shot groups from a bench the vast majority of the time and in fact has many "one hole" 100 yd groups to it's credit. However, it is very very difficult with that gun to go 5 for 5 on a 3" sticker at 300 yds (~1 MOA). 10 for 10 would be impossible, even with it's most favored load. For what I use that gun for, I simply don't care. The main thing is the all shots are within close proximity to point of aim and not consistently high/left or any other place.
Fundamentally, the more samples (shots) you have to measure, the more you know about the precision of the gun and the better you can adjust the accuracy via the scope. However, as has been noted... it's totally irrelevant for most people, including me. Our targets are big and close and the gun/ammo error is much smaller than our environmental or human induced errors in the field. However while 10 shots aren't required... and it's true that 3 shot groups probably cover what you need, I think you might find at least 5 shot groups during sight in will result in less fussing around trying to center groups at longer ranges or wondering why you had to add 2 clicks on the next trip to the range, etc. At least it has for me.
(Side note on the "law of averages"
Law of averages - Wikipedia)
