This is the solution to the Senket puzzle of the week #5.
First, here is how the score breaks down before making any moves.
Blue in the upper left is worth 20^2 = 400 points (apologies for showing posts but counting area).
Blue in the lower left is worth 1^2 = 1 point, as is Red in the upper right.
Red’s main territory is worth 30^2 = 900 points. Red is substantially ahead at the moment.
Blue has two main options: make territory in the upper right at 9-9, or extend the territory in the lower left at 7-1.
Looking at 9-9 first, the results are dramatic as shown here. Previously the red and blue fences in the upper right enjoyed what might be called mutual life: the small red territory in the upper right invalidated the blue fence, and the blue territory in the upper left invalidated the red fence, leaving much of the upper right as unclaimed territory.
By making territory at 9-9, Blue now has Red’s fence trapped with no way to make territory or connect to any. Thus Red is now prisoners, and much of the previously neutral territory is now Blue’s.
Blue’s largest territory now contains 17 more squares and 4 prisoners, so it is worth 20 + 17 + 4 = 41^2 = 1681 points. Red 2 adds just 3 squares to his main territory, increasing it to 30 + 3 = 33^2 = 1089 points.
Blue wins handily.
If Blue plays at 7-1 instead, as shown here, he takes an extra 10 squares and 3 prisoners, but Red 2 at 9-9 then blocks Blue from making territory there. Blue can salvage an extra 3 squares, but the results isn’t enough:
Blue: 23^2 = 529 & (11 + 3)^2 = 196 for a total of 725.
Red: 30^2 = 900 & 1^2 = 1 for a total of 901