Highly accurate measurements of the g factor of boronlike Ar are currently implemented within the ARTEMIS experiment at GSI (Darmstadt, Germany) and within the ALPHATRAP experiment at the MPIK (Heidelberg, Germany). A comparison with the corresponding theoretical predictions will allow one to test the modern methods of bound-state QED. However, at least three different theoretical values of the g factor have been published up to date. The systematic study of the g-factor value of Ar-40(13)+ in the ground [(1s)(2)(2s)(2)2p(1)]P-2(1/2) and the first excited [(1s)(2)(2s)(2)2P(1)]P-2(3)/2 states is performed within the high-order coupled cluster and configuration interaction theories up to the full configuration interaction treatment. Correlation contributions are discussed and results are compared with previous studies.