JMHO:
3-shot groups are fine to see if your hunting rifle/load is good enough for hunting.
For seeing just how accurate your rifle is, which necessarily includes comparing your rifle to other rifles of know accuracy, 5-shots is the universally accepted number of shots for a group. Of course, regardless of number of shots in a group, the more groups you shoot, the better.
Because there is some "bell-curve randomness" in the printing of groups, a 3-shot group size is not as repeatable as a 5-shot group size. Thus, a single 3-shot group is less likely to show a rifle's true accuracy potential than a 5-shot group. A good rule of thumb is that for a particular rifle and load, the 5-shot group will be *about* twice as big as the corresponding 3-shot group. In other words, a 3-shot one-inch group is *about* equivalent to a 5-shot two inch group. (Notice the word "about" is emphasized)
7- or 10-shot groups are even more reliable, but it is a case of diminishing returns, and the accuracy-minded shooting community has gravitated to the 5-shot group as the acceptable accuracy standard without going overboard on the number of shots required.
Regardless, if you are happy with your rifle's 3-shot groups, and you don't care about its 5-shots groups, then continue to be happy and go hunting, since the whole point of all this is to have fun (unless your a professional sniper where accuracy is serious business and you'll get laughed at if you start bragging about your gun's single 3-shot group).
Again, JMHO.
