We study the half-dependent problem for the king graph K_n. We give proofs to establish the values h(K_n) for n ∈ {1,2,3,4,5,6} and an upper bound for h(K_n) in general. These proofs are independent of computer assisted results. Also, we introduce a two-player game whose winning strategy is tightly related with the values h(K_n). This strategy is analyzed here for n = 3 and some facts are given for the case n = 4. Although the rules of the game are very simple, the winning strategy is highly complex even for n = 4.