No limit is good and bad. Thats why it sounds like WW3 with a lot of the hunters or should I say shooters since thats what it sounds like! Some can't help themselves with all those rounds in the mag.
There is no longer any limit on the number of rounds when hunting deer. Not sure which year they removed the limit. You don't have to plug your shotgun anymore.
Magazine Plugs
When hunting for migratory game birds and waterfowl (i.e., doves, ducks, geese, woodcock, etc.), it is illegal to use a shotgun capable of holding more than three shells, unless it is plugged with a one-piece filler that is incapable of being removed without disassembling the gun (See Waterfowl & Migratory Birds). There are no restrictions on magazine capacity for hunting of any other species.
There was a limit published in the free DNR hunting and trapping regulations book around 10 years ago and prior. I dont know when they lifted the limit of rounds carried but the last time I saw it in the regulation booklet it WAS 3 rounds just as in the migratory game bird and waterfowl regulations. Like I said it WAS at one time but as other have posted it does not look to be listed this way now. I have hunted the past few years with my prefered 870 rig with a 20" barrel and the extended mag tube but I have always inserted a dowel for a magazine plug to limit me to 3 rounds just in case. You can always call Atterbury or call your local SD and have them leave a message for your county conservation officer to call you back if you cannot reach them directly.
Been deer hunting since early 80's, no shell limits then.
This from around '95 (870 Wingmaster, 20" Remchoke, rifled choke- w ext tube- used just this one season). Saw him across field in the rain, 'bout 250 yards in CRP/short pine planting, snuck up and then belly crawled (was already drenched) to see how close I could get.
Shot him at 20 yards LOL. Blew the rain off his back with frontal hit, just saw the mist......so jumped up to see where he was running (since I had 7 more slugs to burn). He was down right there, slid back in his tracks even LOL.
First shotgun deer for me was in '87, Mossberg 500 Regal, held 6. No plug required then.