Three shots are the current "Golden Standard" for accuracy because inprint Gunwriters use three shot groups. But, except for marketing, three shots are basically meaningless as a standard for accuracy.
There is an excellent article at the end of the Oct 2014 Shooting Sports USA on group size and accuracy:
http://www.nxtbook.com/nxtbooks/nra/ssusa_201410/ This foundational article was written by small bore prone competitors who wanted to shoot perfect scores. In small bore prone a Match is a 40 shot event of two twenty shot targets. The typical 1600 round Smallbore bore prone tournament is 160 rounds fired for record, divided up into four 40 round Matches. Therefore the referenced article assumes that a 40 round group is the baseline.
This is a 20 shot group. Half of the 40 rounds for a "match".
As anyone can see in table six, at least at 100 yards, a five shot group is 59% of the size of a 40 shot group, a 10 shot 74%, and a twenty shot 88%. A three shot group is below contempt, but three shot groups are the current standard for the shooting community because the leaders of the shooting community, that is in print Gunwriters, have convinced the shooting community that three shot groups are an exact measure of accuracy and consistency.
What we should recognize is that Gunwriters are shills for the industry. They don't exhaustively test the weapons they are given for several reasons. The first is time and materials. Gunwriters are given a flat fee for their articles, the less they shoot, the less they spend, the more money they get to keep. The less time and material they have to spend on the current article, the more time and less money they have to spend on the next. That is one reason, and another is because even though these guys get weapons that are "worked over", they are not interested in proving the inherent accuracy of the thing, because the inherent accuracy of the thing may not be so great.
Originally I shot ten shot groups for everything. That took a lot of time and at the end of a shooting day I would be sort of punch drunk. I have gotten lazy and have been shooting five shot groups to see if there is a pattern. Then, if I think I have found a real winner load, I will come back and shoot more down range. What I have learned, is small groups based on small shot counts can be very misleading. You have to get the round count up to really be sure of your load.
This is an example:
This seemed promising
but a twenty shot group, and not as wonderful as the five shot group
but it would mostly hold the ten ring at 300 yards
I think the real problem is the barrel. I have a custom 270 Win barrel on another rifle and that rifle shoots like a house a fire.
When I can keep ten shots inside the ten ring at 300 yards, I feel the load is accurate, at least to 300 yards. Whether or not it is accurate further out takes testing to verify.
I remember asking the third place guy at the NRA Smallbore Championships about the number of rounds he needs to shoot downrange to have confidence in his ammunition, and for him, it was about a brick of 500 rounds.
A bud who shot on Larry Moore's Long Range Team asked Larry about the number of rounds needed to have confidence in a load, and Larry said "about 20,000"! Larry was an Engineer and his first Job out of College was working at Springfield Armory with John Garand. Larry did win the 1000 yard Wimbleton, with a 30-06, and as a test engineer at Aberdeen Proving Ground he tested every rifle through the M16, during the period when the US Army was selecting a service rifle replacement to the Garand. Larry had incredible access to ammunition and firearms as a test engineer, so 20,000 rounds is understandable from the aspect of someone who has unlimited resources.
I will go with ten rounds at 300 or 600 yards, and then I will get the round count up on subsequent visits to the range. Some of my 308 Win loads I shot thousands of them in competition and you get a real good idea of the quality of a load when you burn a couple of barrels out with them.
A shooting bud said that the real test of a bullet and barrel is a 600 yard group, but, if you can't dope the wind, you might as well be throwing rocks. There is a big pile of rocks in front of my firing point!