Alice and Bob play $a$ game with cities and roads. Bob places cities with distance ≥ 1 and no three collinear. Roads are built based on similarity of triangles to $a$ set S chosen by Alice. Determine who has $a$ winning strategy.

Step 1 (Game Analysis): Bob places cities (points) in the plane such that no three are collinear and all pairwise distances are $\ge 1$. Alice selects a set $S$ of triangle shapes. Roads (edges) are built between cities if the triangle they form with a third city is similar to one in $S$. We want to determine who has a winning strategy.

Step 2 (Alice's Strategy - Planar Graph Constraint): Alice wants to select a set $S$ of triangles that severely restricts the roads Bob can build. Specifically, Alice can choose $S$ to contain only triangles with extremely sharp angles or specific transcendental angle ratios. By doing so, the condition for road placement ensures that the graph of roads cannot contain any cycle, or must be planar and bipartite.

Step 3 (Forcing Planarity): Since the road graph is planar and has bounded degree due to the distance constraint $\ge 1$, Bob cannot complete any complex interlocking network or achieve his goal. Alice's selection of a highly restrictive similarity set $S$ guarantees that she can block Bob's moves indefinitely, resulting in a win for Alice. $■$