The key of solution is taking the data-generating process into account. In Let’s Make a Deal game (Fig. 6.1), the host must open a door without a car behind it. Both your choice and the real location of car will affect the host’s choice. The opened door here is the collider. Conditioning on the collider create a non-causal association between your door and location. (or opens the path between your door and location). Therefore, you’d better switch. Suppose there is an alternative game called Let’s Fake A Deal (Fig. 6.2). In this game, the host open a door randomly. Thus, only your choice will affect the host’s choice. Then switching has the same chances as not switching.