In Dung’s abstract argumentation, arguments are either acceptable or unacceptable, given a chosen notion of acceptability. This gives a coarse way to compare arguments. In this paper, we propose a counting approach for a more fine-gained assessment to arguments by counting the number of their respective attackers and defenders based on argument graph and argument game. An argument is more acceptable if the proponent puts forward more number of defenders for it and the opponent puts forward less number of attackers against it. We show that our counting model has two well-behaved properties: normalization and convergence. Then, we define a counting semantics based on this model, and investigate some general properties of the semantics.