Problem - Coin Game on DAG (Part 6)

Variations: What if there are multiple coins?

Then you need to track the entire game state (all coin positions) and build a product graph. What if players alternate between different graphs?

Model this as a larger game with state (current graph, coin position). The core technique remains backward induction, but the state space becomes more complex. With $k$ coins each on a DAG of $n$ vertices, the state space grows to $O(n^k)$, which is only feasible for small $k$.