The Doctor can scarcely believe this is happening. It’s impossible, but he can’t deny the truth. After all this time, the Master is back; it’s a terrifying prospect, and yet it means that he’s not the last of his kind anymore. Two Time Lords have to be better than one, even if one of them is a mentally unstable, scheming monster.
Pleading with the Master has never worked, but the Doctor tries anyway, because he doesn’t have any other options. It doesn’t stop the Master from absconding with the Doctor’s TARDIS though.
Now they’re stranded at the end of time.