15
I would suggest an alternate (simpler) strategy:
10
Going first, you should be able to force a win.
Using @kaine's terminology:
box - an area on the board that can be made into a square
square - a box of 4 lines
three - a box of three lines which can be made into a square on the next turn
safe - a move that doesn't result in a three
Moves are enumerated as follows:
* 1 * 2 *
3 4 5
* 6 * 7 *
8 9 ...
10
The player who can win is
by this strategy:
9
First player wins
Example:
5
Since there were exactly 32 empty spaces, I tried to push the ability of my computer and enumerate the best possible move starting from all $2^{32}$ states. For each state, the code finds the maximum number of squares you can get more than your opponent.
In a few minutes, the code found that the best result is -9. That is, whatever you do, you cannot win ...
4
Let's name the lines.
+---+---+
| K |
+---+ L + J +
| H I |
+ G +---+---+
| |
+---+---+ F +
| D E |
+ C + A +---+
| B |
+---+---+
The winner can be found by analyzing the game regardless of the position.
Now that we know the winner, who is which color?
And Bob's last move would ...
4
This is my first experience with Dots and Boxes, so please be kind if I am making some terrible mistakes. Per the wikipedia link:
An expert player tries to force their opponent to be the one to open the first long chain, because the player who first opens a long chain usually loses.
That is what we will try to do. Initial analysis shows four "safe" (...
4
Most likely you wish to avoid connecting any dots that would allow your opponent (computer) to place a box. As such, you're left with individually choosing one of the following possibilities (marked with red):
All other possibilities will render a box for the opponent.
Possible play sequences are between the player P and computer C are:
P draws 1:
C ...
4
The game Boxes is another form of the game "Dots and Lines" or "Dots and Boxes", where the strategy is understood as a game of early control. The idea is to force the opponent into a condition to draw the third line into a long chain of near-complete boxes, where the ability to complete boxes with the fourth side yourself in a repetitive, connective manner ...
3
Not as interesting as a manual analysis, but here is a brute-force solver, written in Python. (Warning, CPU intensive for about two minutes)
from collections import defaultdict
VERTICAL, HORIZONTAL = 0, 1
#represents a single line segment that can be drawn on the board.
class Line:
def __init__(self, x, y, orientation):
self.x = x
self....
3
The goal of dots and boxes is to be the person that makes the last (and biggest) group of boxes. To that end, you need to figure out how many regions there are and which one is smallest.
Here are your potential boundaries of regions.
And here is one example of how it could play out:
Here you have 6 regions, so you want to let the computer take the first (...
3
The player can't win. Analysis to follow.
Here I've marked the "safe" moves in blue. We will call them 1, 2, and 3 counter-clockwise starting from the left. The sacrifices I have marked in green. Let us call them A above and B below. Finally I have marked a move inside the lower right square in red.
First to address the red move.
Any move inside the ...
2
This is an unwinnable position if the computer plays perfectly.
I need an even number of chains
I am player one, as an even number of moves has been made, and there are an even number of dots.
(This is known as the chain rule, and anyone who is unfamiliar with it should learn it as it is a key to winning dots and boxes. The number of squares already in ...
2
The key to perfect play in this game seems to be the number of lines in the center cross at the end of turn 6! Warnig I"ve not taken the time to put my 39 drawings into the computer so this is a map of the complex (largely brute force) proof. This was all done by hand but I figured out which of the 3 out of 4 possible 7 line patterns with no squares or ...
1
Second player wins.
After that,
Then,
On first player's second turn,
In the end,
Alternately,
1
The best you can win is 10 boxes. The computer always wins by getting at least 15 boxes.
In this image, playing any of the red edges gives you 10 boxes if the computer plays optimally. If you play the green edge, you get only 9 boxes. Playing any of the blue edges gives you even less, only 8.
The computation was done using the same code I used for the ...
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