"Game Theory - F question"

[ArihantGarg]

I observed that that the sequence of players repeats after every 6 moves . Hence we can convert this into a Grundy game with 6*n states ( 6 states for each vertex in the graph) .

Then I set all vertices with no outgoing edges as Losing States for the team of the player who has to move on that turn.

Now using these as the base states , I built the other states based on 4 cases : -

1. Current player on this node has an edge to a vertex with his team winning and he is not a joker. In this case this node is also winning for his team.

2. Current player on this node has an edge to a vertex with opposite team winning and he is a joker. In this case this node is losing for his team.

3. Current player on this node has all adjacent vertices with opposite team winning . In this case this node is losing for his team.

4. Current player on this node has all adjacent vertices with his team winning . In this case this node is winning for his team.

After evaluating this, we will have some nodes winning , some nodes losing , and the remaining nodes will be draws.

[sg60692]

The code seems well implemented. However, as this is the first game theory question it would be a good exercise to add a proof as well of why the algorithm works in the first place.

[ArihantGarg]

Should I add the proof to the repository , or just in the pull request?

[sg60692]

In the pr description itself