Don't run from snipers, you'll just die tired (idea)
This expression has gained greater popularity due to the advent of [multiplayer] games in which a "[sniper]" weapon is available to players. However, in the strictly military sense, there is an inherent [fallacy] in this advice.
First, a sniper type weapon generally has a slower [murder rate|reload rate] than many more modern (and less accurate) weapons. They are generally single shot weapons, specifically [bolt action] rifles, which require some time to reload and re-aim before being ready to fire again. Therefore, if you find yourself confronted with a [sniper], moving immediately after a shot allows you to take advantage of the reload window, during which the sniper will not be able to kill you.
Second, since a sniper generally won't reveal his or her presence until a target is lined up, if you're still able to move after the sniper has fired a shot, he's not aiming at you. Therefore, you should find [cover] quickly, before he CAN aim at you.
Finally, if everyone freezes whenever a sniper fires a shot, it is easy for the sniper to select their next target, as all of the targets that were previously considered are [standing beside my grave|in the same place]. If an entire group moves at once after a sniper fires, it is extremely unlikely that the sniper can track all of the targets simultaneously and at least a few of the would-be survivors will reach cover.
In conclusion, if you find yourself confronted with sniper fire, it's best to move immediately after the sniper has fired, and [duck and cover|find cover] before he can fire again. After that, [If you're not smart enough to figure this out on your own, you shouldn't be doing it|you're on your own].