I find a drill bit about the same diameter as the hole in my adjustable measure. Set the measure and put the bit in it, wrap painter's tape around the bit to mark depth.
I drill a small pilot hole ever so slightly deeper than the hole I want. When I drill my full diameter hole I do two other things. If the antler is a lot thicker than the diameter of the hole, I drill it short of depth and use a larger rat tail file to make it bigger and to shape a "channel" on the pouring side. I also lube the drill bit with patch lube. As the antler and bit get hot the antler packs into and sticks in the grooves of the bit.
I wrap sandpaper around the file to finish, up to about 800 grit, polishing the inside so powder doesn't stick. Dress and polish the top edges the same.
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Careful with the curved ones.