It depends on the kind of tired.
When I'm just tired from a days work, it's about 11pm and my eyes are falling all the time, I generally suck at everything I do.
But when I'm at a friends house, we spent the whole day drinking,smoking and playing games I tend to get extremly focused at about 3am when my whole body just exists for the purpose of beating that goddamn final boss in Super Ghouls n' Ghosts.In that state I'm awesome at most Games,though I'm better at old Games,cos newer Games tend to be way more exhausting for your eyes,specially FPS's.