Weekly Puzzle 7 is particularly challenging, hence the use of “discussion” rather than “solution.” Someday someone may be skilled enough at Senket to do a definitive analysis of a puzzle like this, but that person isn’t likely to be me 😉
Starting at 7-3 doesn’t work out very well for Blue. Red 2 closes him in immediately, and by Blue 7 the matter is settled. Red has given up 13 squares of territory (and Blue has take 2), but Red has a strong position to the left to gain 15 or more.
There are a number of ways for Blue at 6-2 to play out. Here are a few:
If Red 2 and 4 cut off the inside of the territory, Blue 3 and 5 run to the outside, and Red can only barely keep Blue inside. When Red 10 seals off the top, Blue 11 is necessary to protect the corner. Red 12 takes the sure 3 squares and takes 3 away from Blue, then Blue 13 takes 3 squares.
In the end, Blue has 17 units of territory and Red has only 15, but Red has tremendous outside influence. So from a points standpoint Blue is better, but Red is likely well ahead in the long run.
Blue at 6-2 could also end up as shown below, if Red chooses to block off the outside immediately. Toward the end, Blue 9 is intended to stop Red from easily taking another 8 or more squares of territory along the left wall. Instead, Red 10 takes 8 squares inside. Blue could have played 9 at 8-3, preventing Red’s inside aspirations, but then Red 10 at 3-6 would take 8 or more squares of territory, and again Blue has to deal with Red’s enormous outside influence.
Blue at 4-3 ends up much the way 6-2 did:
If Red blocks the outside immediately:
If Blue attempts to make reaching the outside a possibility with 1-5, Red is still able to contain him, leaving Red strong to the outside and Blue with very little.
As far as I’ve analyzed it, there is no spot that simultaneously allows Blue to mess up Red’s territory and escape to the outside himself. The basic decision comes down to inside vs. outside. I’d tend to take outside influence over minimal inside territory.