Gerrymandering is the process of drawing electoral district maps in order to manipulate the outcomes of elections. Partisan gerrymandering occurs when political parties use this practice to gain an advantage. Increasingly, computers are involved in both drawing biased, partisan districts and in attempts to measure and regulate this practice. Several of the most high-profile proposals to measure partisan gerrymandering involve the use of past voting data. Prior work primarily studies the ability of these metrics to detect gerrymandering. However, it does not account for how legislation based on the metrics could affect voter behavior or be circumvented via strategic voting. We show that even in a two-party election, using past voting data can affect strategyproofness. We further focus on the proposal to ban "outlier maps," which appear biased toward a particular party when compared to a random sampling of legal maps. We introduce a game which models the iterative sequence of voting and redrawing districts under the restriction that outlier maps are forbidden. Using this game, we illustrate strategies for a majority party to increase its seat count by voting strategically. This leads to a heuristic for gaming the system when outliers are banned, which we explore experimentally. Applying a version of our heuristic to past North Carolina voting data shows that these strategies can be found for real states under some stricter assumptions. Finally, we address some questions from the recent US Supreme Court case, Rucho v. Common Cause, that relate to our model.