On a Maker-Breaker game there are two players, Maker and Breaker, where Maker wins if they create a specified structure and Breaker wins if they prevent Maker from winning indefinitely. A 3-AP is a sequence of three distinct integers a,b,c such that b−a=c−b. The (1,q) 3-AP game is a Maker-Breaker game played on integers 1 through n where every round Breaker selects q unclaimed integers for every Maker's one integer. Maker is trying to select points such that they have a 3-AP and Breaker is trying to prevent this. The main question of interest is the minimum value of q=q(n) for which Breaker has a winning strategy.

We found strategies for both Maker and Breaker that improve upon existing upper and lower bounds on the threshold value q in terms of n. Breaker can win games where q>√(2.99n) by essentially filling in the middle third first. Maker can win games in which q<√(n5.33) roughly by playing some amount of points in the middle and then creating more than q threats with an outside point.