Most turkey shoot guns are sleeved and back bored.There was an old man near me who used to make them for people.My best turkey shoot gun is a Winchester model 37 red letter .where it locks up is model 37 it has a Winchester model 12 chamber.Then 36" of barrel(looks like water pipe).This one is .639 .Shoots 9s awesome does not like 8s very much.As far as improving your odds you can run a swab through your barrel coated with vasoline it is good for one shot ,But thats cheating.You can lightly bite all of the way around your shell to get it almost open then spit in it .This is not cheating.One of the best factory guns is a Reminton 1100 ,2 3/4 with a 30" full chokebarrel most of these I have ever seen worked well at the shoots.I sometimes go to super shoots in Richmond Va. They shoot 60" barrels and scopes these shoots are for $10,000.Some of our local shoots vary in the rules a stock class gun must be able to stick a 20 gauge shell in the end of the barrel.Die hard shooters have some pretty strange rituals in this sport.
It's pretty much fun to watch .Luck sometimes has a lot to do with it.I went one time with a 870 special purpose 3" ,28" barrel with a double xtra full turkey ckoke and won 12 out of 13 rounds that night against modified guns.Brought home a truck load of meat .Enough pork to blow a gasket.