If it’s Blue’s turn, where should he play? What if it’s Red’s turn?
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.
In last week’s puzzle Blue tried invading at A and just managed to escape, while Red walked away with 225 points.
Can you find a better place for him to start?
In Puzzle #6, Blue has several ways to fail.
Blue can’t make territory with 3 on the right. Red shuts that down with 4, and then locks Blue in with 6.
Blue can’t escape with 3 on the left. Red shuts the door with 4, and then blocks Blue from making territory with 6.
So what will work? Blue 3, shown here. It prevents Red from playing there. Now if Red makes any move other than 4 or A, Blue plays at A and makes territory immediately.
Note that although Blue escapes with 5 and 1 is safe from becoming a prisoner, Red can follow up with 6 at B and take a total of 15^2 = 225 points, so this isn’t a very good outcome for Blue. He had better ways to invade — the next puzzle will look at that.
Red thought he had this area covered, but Blue decided to invade with 1. Red responded with 2, and now Blue is looking vulnerable. How can Blue save this post?
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
John’s Go Page describes Go in ten statements. It uses some pretty clever language to squeeze the description into so few rules, and it describes area scoring, where I would have preferred territory scoring, but I think that would have definitely required an extra statement or two.
Here is an attempt to unambiguously describe Senket in as many sentences:
- Senket is played on a 31 x 31 square grid of points, by two players called Black and White.
- Each point on the grid is either empty, or may be colored black or white.
- Two points on the grid of the same color may be connected by a fence if they are opposite corners of a 1×2 rectangle, and if the fence would not cross any existing fences.
- Starting with an empty grid, the players alternate turns, starting with Black.
- A turn is either a pass, or coloring an empty point one’s own color and adding as many valid fences of one’s own color as are desired.
- The game ends after two consecutive passes.
- Territory is any enclosed section of the board (including the edges) that does not contain opposing territory.
- Rule 7 applies recursively, working out from unambiguously valid territories.
- Each set of territories connected by fences scores points equal to the square of the sum of the area contained within the territories and the number of opponent’s posts contained with the territories.
- The player whose territories sum to the greater point total at the end of the game is the winner. Equal scores result in a tie.