I tested my 12 gauge Remington 870 Express with 3" 1 7/8 oz, 5 shot and my patterning was great at 10 paces and more then adequate at 20 but was starting to lack at 30 but I still had over 10 bb's in the vitals on the head/neck but only had 3 at 40. Should I call this good and just not take anything over 30yds or should I look for a different choke or different shell?

What brand choke and load are you using. At 40yds, I was getting 10 in the head and neck with Fed 3in #5 1 7/8 oz. That was with a Rem. factory X-Full choke.

If you keep your shots to 30 yd.s or less you're OK. But, frankly a turkey gun should do much better than that. My first bird was shot with an old Rem. Model 11 with a factory 30" full choke barrel and a 2 3/4" Federal duck load. I got about the same patterns with that gun as you describe with yours. If you have time before the season, I'd recommend you look for a better choke/load combination.

You should be able to beat that quiet abit, Try a Remington Ventilator choke .655 and Winchester #5 Turkey loads, I shot one for years and on #5 lead shot it was awesome out of my 870. At 25 yards it would punch a hole about the size of a soft ball.

You can keep it like it is but you'll be passing up alot of birds at 35 and 40 yards.
Find you a choke with at least a .670 constriction and experiment a little more.

try hevishot, you'll probably be surprised

I had an 870, as does a close hunting buddy... patterned them together, (his was the 3 1/2" chamber, but was shooting 3" shells at the time), and we both found that the factory .665 choke worked well.

I tried a couple other chokes constrictions, a 650 showed promise with #6 lead, but I wasn't a fan of the lighter 6's.

12 pointer is right... I tried Remington Hevi-shot, (3" 1 5/8 load of #6) from the same gun and it was unreal. Add about 4x the pellet count at 40 yards, easily putting 30+ pellets in the turkey outline, with an average of 10 in the spine / brain areas.

The good thing is that Hevi-shot hits like the next larger lead counterpart, ie: Hevi #6 will hit as hard as Lead #5, with the added plus of getting more pellets when compared to the #5 counterpart.

Try a .665 choke with that Hevi-shot load out of your 870. The shells cost a bit more but I think you'll be very pleased. A tidbit more info... my gun preferred a non ported choke over the ported offering. Don't shy away due to the price, you'll only shoot a few shots a year to fill your tags and it's well worth the confidence when pulling the trigger.

A couple of questions for you? How spread was the pattern at 40 yds? Does your gun shoot point of aim at 40 yds? If your pattern was off at at 40 it might be the pattern is still good but it wasn't on the bird. There is a big difference between patterning difference between 30 and 40 yards. Any turkey gun should be able to kill out to forty yards just to be fair and ethical. If you misjudge a 30 yard shot and he was at forty than you probably have a wounded tom running around. Make sure your gun is dead nuts by shooting a target big enough to hold all the shot pattern. Place a dot on a car window sized piece of paper and shot that dot and 20 , 30 and 40 yards. If your point of aim is off adjust your sights or learn to compensate.

If you go to a 3" #6 with 2oz of shot you should most likely increase your pattern density. What choke tube do you have as well? Try the $20 Undertaker from H.S. if you are not Xfull choked. These tips should help get your gun on target. Let us know how it goes!

I have similar results with my 870 and a Rem. Super Full Turkey choke. Best load I've tried is the 2 oz. #5's from Winchester Supreme XX. I tried the Hevi Shot and about every other load last year and came back to this load. The 5's even patterned better than the same load in #6's.

I'm looking to try the new Federal Flight Control loads and see how they do. Might get a new choke too just to see.

it flies,
What choke are you using? Your patterns look like a screw-in I/C choke.
Check the marking on your choke. Try to buy an Undertaker or Rhino choke.