Rifle guys are always looking for that magic load that puts all the shots into the same hole and some of us have fixated on three-shot groups. Three-shot groups are fine for some things, like basic, very basic load development. If you can't get three shots to shoot into pretty much the same area on the target, the probability is that ten shots won't group there either. The problem comes in when we start to depend on three-shot groups as a valid indicator of good accuracy. It just ain't so.
Let's take my Savage 110 for example. A standard hunting rifle in .30-06, it's got the sporter barrel and a wooden stock. It's a solid dependable hunting rifle and it generally turns in groups that hover between one and 1.5 inches with good ammo. It's not a benchrest gun, but it turns in some amazingly small three-shot groups. Like this target I fired this morning.
That's a one-inch dot, by the way, and it shows five shots on paper. Three of them fell into 0.379 which is magnificent shooting for a bone-stock .30-06. The other two opened the group to almost 1.5 inches, which is about what I expect from this rifle and my indifferent bench technique. Let's look at another target that I fired last week from the same rifle, with a different load.
Do I use three-shot groups? Sure I do. If ammo won't group well with three shots, it won't group well with ten shots, so I use a three-shot group early in load development to show me what won't work. As I start to fine tune a load, I'll go to five shot, and ten shot groups. Those groups show me something about the rifle, my technique, and the ammunition.
Don't get hung up on three shot groups.