The question can be answered a couple of ways.
"What is the most accurate 1000 yard deer caliber"
Could be answered with "30-30 Win" as it can reach a 1000 yards, but has set a number of accuracy records in the Shutzen discipline that lasted for decades.
Could be answered with 338 Lapua because it still has enough energy and momentum to kill a deer at 1000 yards. Sure as heck though it is overkill for normal hunting ranges. Same with the 7mm WSM or any of the magnums.
Of course, after a few hundred yards wind conditions determine group size more than caliber.
So I'll have to say the "30-30 Win" is the most accurate 1000 yard deer caliber.
Jimro
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Machine guns are awesome until you have to carry one.
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