Maker and Breaker on a Grid

Maker and Breaker alternately claim an unclaimed cell of a 4×4 grid, Maker moving first. Maker wins if at some point Maker owns all four cells of some row or some column. Breaker wins if the grid fills up without that happening. (Diagonals do not count.) Who wins with optimal play? Answer 'Maker' or 'Breaker'.

• game theory

Source: Maker-Breaker positional games (Erdos and Selfridge); the pairing strategy is standard. Statement written for AxiomIQ.