Designing a (video) game such that it is balanced-i.e. fair for all players-is a prevailing challenge in game design. Perhaps counter-intuitively, games that are symmetric with respect to (board) design, starting conditions, and the employed action set, are not necessarily fair games. Indeed, perfect play from all players does not automatically lead to a draw, but may probabilistically favour e.g., the first player to move. Even more so, asymmetric games-in which the action set of one player is typically highly distinct from that of another player-are generally unbalanced unless meticulous care has been taken to ensure that the asymmetry in the design does not skew win probabilities. In this context, the present paper contributes a method for automatically balancing the design of asymmetric games. It employs Monte Carlo simulation to analyse the relative impact of game actions, and iteratively adjusts attributes of the game actions till the game design is balanced by approximation. To assess the effectiveness of the proposed method, experiments were performed with automatically balancing a set of tower-defence games. Preliminary experimental results revealed that the proposed method (1) is able to identify the principal component of a game's imbalance, and (2) can automatically adjust the game design till it is balanced by approximation.