I've often heard/read over the years that a 3 shot group tests the rifle and a 5 shot group tests the shooter.
I do 3 shot groups with my centrefires and 5 (or sometimes 10) with 22LR because the ammo is cheap and its fun. All hunting rifles, I'm sure competition target shooting is a different story.
Most modern rifles I've used have been capable of pretty reliable sub-MOA 3 shot groups with ammunition they like.
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