at 500 with about 711 ft-lbs. of energy left. Not enough energy(that's what's important. Not the velocity.)
Don't get hung up on energy. Bullet type is more important.
For example, if you have 700 ft lbs of energy with a full metal jacket, in the heart-lung area, you're not going to do much damage.
Where as if the same weight bullet, with 700 fl lbs energy, that disintegrates, comes apart is several small pieces its going to be devastating.
That is how the Berger and similar bullets are designed to work.
I contacted Berger about the min. velocity their bullets need to work as designed. I was informed, the remaining velocity needs to be 1800 fps.
Using my example (from the earlier post) I shoot 87 gr Bergers with a MV of 3000 fps. Using those numbers I have a remaining velocity of a hair over 1800 fps at 800 yards.
Now I haven't shot a deer at that distance, but my longest antelope shot was 637 yards, another at 580. In both cases the Berger bullet totally destroyed the vital area (heart-lung) area. The damage I detected at this range convinces me that Berger is right, at 1800 yards the same bullet hitting the vital are would definitely work on deer size animals.
Don't get hung up on Kinetic Energy. Many years ago, I attended the Northwestern Traffic Institute, "Accident Reconstruction" course. In the class we used math to shot that the KE of a bumble bee, if travelling fast enough, could exceed that of a train, and stop train. Math said it would, reality is a different matter, we know the bee would disintegrate, even if you could get it going fast enough, and would have no effect on the train.
On the other hand, during WWI, when tanks first hit the battle field, GIs discovered that if you inverted the 30 Cal '06 bullet you could penetrate the armor and stop the tank. ("Weeks" Man Against Tanks, 1975). These bullets didn't do this with KE, what would happen, the lead core was so hot it burned through the armor, setting ammo and fuel on fire.
Take an arrow, it doesn't have much in the energy department, but the head enters the body, cutting blood vanes, nerves, etc.
So really, it isn't energy, its how the bullet reacts inside the target.