Pen Raised Pheasant and Wild Pheasant require 2 different types of hunting and shooting.
Example
Pen raised birds on a preserve will be pointed and flushed. They are slow and fly straight up then level off.
You can kill these with a 410 and #9 shot
Wild Birds normally don't hold well for a dog and run off. Flushers reallyhelp.
You need all you can bring to kill wild ones. 12ga 3 3/4 drams 1 1/4 #6
Growing up hunting in SD we never used dogs just walked the ditches and
hedge rows. when you got close to the end they would fly.
Hunting without dogs taught us to kill birds close enough to you so you could find them so we always shot IC