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I put an aftermarket front iron sight on my Mini-14, As far as left and right are concerned, (not accounting for wind variation), will my zero be the same at 25, 50, 100 and even 300 yards? Can someone please help me and explain why?
Yes it will remain zeroed regardless of distance. The reason your rear site is all the way to the left is because the front site you installed is NOT centered, it too is off to left. If the front post on a rifle is “dead-nuts-centered” the rear site will be centered. But since it doesn’t always happen that way folks may need to adjust to the right or left. When people make the right or left move they are aligning the rear site to the front site.

Now if you have a rifle with perfect site alignment and adjust the rear site to impact 1” to the right at 100yds it will be 2” at 200yds, 3” at 300yds and so on.
 

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Therefore, the rifle will shoot straight at 100, 200, and 300 yards... but it will always be off "1/8" from true bore alignment??
A better question would be “as long as they all fall in the same spot, who cares?”

To answer your question I’m gonna say yes, but in really small numbers.
 
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