50 yds
There are guns/loads that will throw deadly looking patterns at 50 yds. But there is more to it than that.
Remember that a shotshell/gun throws its payload in a cloud (3D) not a disk, (2D) and the entire cloud may well not arrive at your turkey. Unless one is shooting at their gobbler in a perfectly open setting (possible but not the norm) there is every liklihood that there will be limbs, branches, vines grass, that will strip pellets from the cloud and thin the resulting pattern at any range. I have "missed" two gobblers that were well within range because a branch of some size was just off the muzzle by a short distance, but out of my line of sight. I blew the branch to bits, but no gobbler. This is an exaggerated example, but the point is, one may start with 1-3/4 oz of shot, but that will not necessarily be what arrives on target.
Leveling and shooting at a gobbler is far different than the controlled situation at the pattern board. You may be in an awkward position,(from assorted reasons) the gun mount compromised by a headnet, the gobbler shows up unexpectedly from an odd angle, or you may be fighting your nerves, or a combination of all the above. This can result in poor sighting and poor shooting, and a target that is fringed and not centered.
All the above supports my stance to use enough gun/shell and not to make gobbler shooting a long range proposition.
I have killed a few gobblers at 50 yds+ or so, but every one at this distance shared these things in common:
-it was wide open, as on a ROW or pasture, and I underestimated the range. I would not shoot 50 yds + by choice, these shots were by error
-I was shooting 3" shells, with 1-3/4 oz of lead shot or more, from a rifle sighted gun I had sighted and tuned carefully, with a turkey choke
-the bird was down and mine, but not really a clean kill (stomp)
Finally, it was previously mentioned that #2 (lead) shot is a good turkey load. I cannot agree. Large coarse shot does not lend itself to spring gobbler hunting, where the object is to saturate the head and neck with pellets.
We're not pass shooting geese.