Pure Strategy occurs when the best strategy for each player is to choose the same option for all plays of the game. If there is a pure strategy, A plays i and B plays j (say), then the ijth element (the payoff to A per play) is called a saddle point.
Player A would prefer to have the largest value possible from those highlighted.
In the diagram this can be seen to occur when the line V = 2 + 7X intersects with V= 6 - 3X which occurs at the point as determined below.
The minimax criteria is to maximise the minimum values. To find the solution for B's strategy we need to identify and solve the 2 by 2 pay-off matrix associated with A's optimal strategy. In this case that will be the columns associated with the lines V= 2 + 7X and V= 6 - 3X. Hence
The value decides the type of the show to be put out in order to maximise the ratings over the coming TV season. The value against Detective has more gain (approximately 3.33) and hence it has to be put out in order to maximise the ratings.