Thanatos has 9 Centaur Hearts which will boost the HP/vitality/whatever you want to call it of a character who uses it. He will give one to those entering the fights with the purpose of completing the mission. If you just want to F I T E without being concerned with the mission, then you don't get one.

(Wait, didn't Thanatos buy 10? Shut it. You know he's saving one for his not!boyfriend.)