I upgraded my pad to a HORI Fighting Commander 4 recently. Upon booting up SG, I found that inputs on the controller would affect both characters in Training Mode (i.e., pressing right would cause both characters to go to the right; c.lp would have both characters throw out the move, etc.). Controls are also mirrored in the control configuration screen. That said, going to the choose controller screen shows only one controller, and plugging in a second controller fixes the issue (although starting the game up with only the FC4 after doing this unbinds all the buttons for some reason). Anyone else having similar issues?
