Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?

Let us use an example to solve this question. The game is played on the complete graph Kₙ (n ≥ 2), which consists of n vertices, each pair of vertices joined by an edge.

Now, Initially all edges are unpainted. At each turn, A chooses an edge, which B paints blue or red. Now, B will win if, after the last edge is painted, there is a vertex which is joined to all other vertices by blue edges. If that doesn't happen, then A wins.

The winning strategy of B is described by 3 rules which are;

Rule 1; Paint the last edge blue.

Rule 2. Never paint an edge red if that would result in two red vertices being joined by an unpainted edge.

Rule 3. Use red paint whenever permitted by Rules 1 and 2.

Thus, if n >2, the first edge will always be painted red, the second will always be painted blue.

In conclusion, when we apply that same scenario to our question it is the same result and as such Player B has a winning strategy for all n ≥ 2.

Read more about probability at; https://brainly.com/question/24756209

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