The 2008 crisis highlighted the linkages between the financial sector and the real economy, as well as between the corresponding stabilization policies: macroprudential and monetary (M&Ms). Our game-theoretic analysis focuses on the increasingly adopted separation setup, in which M&Ms are conducted by two different institutions (e.g. in Australia, Canada, Eurozone, Sweden, Switzerland and the United States). We show that separated policy M&Ms are not as sweet as their chocolate counterparts, in fact they may turn sour. The main reason is that a strategic conflict is likely to arise between the autonomous prudential authority and the central bank in addressing exuberant credit booms, such as those during 1998-2000, 2003-2006 and 2011-2016. In this conflict - that manifests as the Game of Chicken under some parameter values - each institution prefers a different policy regime. In particular, both the prudential authority and the central bank prefer to do nothing about the credit boom and induce the other institution to respond instead; arguably the case of Sweden, Norway and other countries post- 2010. To allow for richer strategic interactions, we postulate the concept of Stochastic leadership, which generalizes Stackelberg leadership and simultaneous move game by allowing for Calvo-type probabilistic revisions of policy actions. We show that the most likely outcomes are Policy Deadlock, Regime Switching and Macroprudential Dominance, but all three are socially undesirable. This is not only because of excessive financial and economic cycles, but also because monetary policy coerced into leaning against the wind loses full control over price inflation. The separation setup of M&Ms is thus subject to a macroprudential version of unpleasant monetarist arithmetic.