I might just add that by far most hunters go to SD from between opening day and Thanksgiving. To add to what BK said, 1) the public and walk-in areas get a lot of pressure, while 2) crops on private ground are often not harvested yet, making many birds inaccessible to public-landers. 3) Weather, if there is moisture, it is almost always rain, the bain of all pheasants, and making for a muddy, slogging mess for the hunters and the dogs. If it is mild and fair, with plenty of cover, hunting can be very,very challenging. Wind can come early, or late.
My point is from Thx’g on, hunter pressure and competition are greatly reduced. Crops are usually mostly harvested, reducing hiding cover. Weather, ah-ha — the wild card, if precipitating, is usually snow, almost always an advantage to hunters within reason. 6 fresh inches — great! 1 1/2 feet with a 25 mph wind and -20* wind chill— very bad! But that’s weather roulette in the upper Midwest during late season.
Point being, there are reasons for going to SD later rather than early.
