It's a deceptively simple subject. If you've ever been in the service of Uncle Sugar, he says 25 meters and you're done--or at least he used to, back in the dark ages of the 1980s. God know what he says now. My research says it's a lot more complicated these days, since we now have a number of different types of ammo (M885, MK262 (I think that's it; it's a 77 grain round), M193 and so on) that have to be taken into account. The first video gives you a lot of background on the subject, including the ballistics, so you can understand what is going on with the round and not just doing "Monkey see, monkey do".
The second video gets into the interesting question of "Well gee, I've zeroed for 25/50/100 yards, and suddenly I need to shoot a target at 5 yards."
As you can see on the second video, if you're playing one of the 3 gun games, it really doesn't matter much what your zero is. You're going to get good enough accuracy that if you're aiming at the center of the A Zone on your target, you're going to hit it if you're doing your part no matter what your distance is.
Your issue is going to be that pin point accuracy you need if Marty the Meth Head has come barging into your home looking for money and has taken your wife/son/daughter hostage and is using them as a shield. Depending on how close you are, the difference between point of aim and point of impact could be 3+ inches. Depending on how much of Marty you can see, that may be the difference between hitting Marty and hitting Mom, or not hitting Marty and letting him have Mom. Neither seem to be good options.
So what can you do? There is the option of "maximum point blank range", an idea that's making the rounds. It isn't a new idea and it's a good, functional idea, but you may find it a little lacking in the accuracy department in the scenario described above. I certainly do. We can, as Aaron Cowan does (or in one case, fails to do) in the second video, use hold over to make the shot. If you've practiced enough, that can work, usually. Of course, if it doesn't, putting a target paster on Mom won't help much. You may be zero at a shorter distance, like 5 yards, but many AR sights don't have the ability to deal with that much parallax.
I'll grant that we're looking at a pretty far-fetched scenario for most of us. The odds that we'll have to pull off this shot are probably right up there with winning the lottery.
It will be some time yet, but I'm going to have to experiment with this. I've gotten my Form 1s back from ATF, and I'm going to be building a couple of specialized ARs for home defense. While these guns may well go shoot some sort of gun games, their primary purpose in life is the defense of the castle. The longest shots I anticipate with them is 100 yards, and the shortest is across the room.
It's a hell of a thing that we have to consider taking such measures.