Blood Seeker, first seen in Zendikar and then reprinted in Magic 2012, has an ability that triggers when a player other than the controller of the Blood Seeker has a creature enter play under his or her control. When the ability resolves the controller of the Blood Seeker can have the controller of this creature that just entered lose one life.

Loss of life is not the same thing as taking damage. When a player takes damage it counts as loss of life, however the reverse is not true. This means that things that cause loss of life will not work with Bloodthirst. While most creatures will come into play during their controller’s turn, if one does enter play during another turn it will trigger the ability of a Blood Seeker controlled by another player. If the Blood Seeker controller were to then play a creature with Bloodthirst, this creature would not get the additional counters.