Building further on work of Marin and Wagner, we give a braid-type skein theory of the Links-Gould polynomial invariant of oriented links, prove that it can be used to evaluate any oriented link and prove that it is also shared by the V_1-polynomial defined by two of the authors, deducing the equality of the two link polynomials. This implies specialization properties of the V_1-polynomial to the Alexander polynomial and to the \mathrm{ADO}_3-invariant, the fact that it is a Vassiliev power series invariant, as well as a Seifert genus bound for knots.
