My guess is that Usogui has more MP, he opened more doors, reached the 50/50 decision and then back tracked since he couldn't be certain he'd get it right, went back to a certain area to wait on Amako to bait him into thinking he had less MP and before Amako could accumulate more MP and then choose a wrong door on purpose in the area or simply wait till his time is up wait on Amako so he could waste Amakos MP and prevent him from winning the game if Usogui got his 50/50 wrong.
Or something like that, my guess is that Usogui has more MP than Amako thinks he has because Usogui back tracked.