Introduction
The Tarken Glacier puzzle is a game of Dots and Boxes! Also known as Sticks or Dots-Squares or tons of other names.

The aim of the game is to makes boxes (squares) out of lines while not letting the other player (Computer in this case) gain boxes.

This game as a lot of strategy to it but when you know the different patterns and how to play against them, you will win 99.9% of the time. (I leave 0.1% here because we are still humans after all and we make mistakes)

This guide is in 2 parts.
The first part will show you the simple strategies that allows you to win the game easily.
The second part is meant for those who want to get the Thinking Out the Box achievement.

This achievement is required for the Game Master achievement and is the hardest achievement of all puzzles.
A lot of RNG is involved into that achievement but this guide will give you tips and strategies to reduce that RNG drastically. (It is not possible to remove the RNG entirely.)

And here a proof that the achievement is quite possible.
It took me between 100 and 150 tries (I lost count) before getting it.
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-won.jpg

Part 1 – The puzzle
First thing first, you can check the Wikipedia page for the game of Dots and Boxes for the basic strategy to win.

With the strategy written on Wikipedia, you can easily win against the computer.

For this guide, I will go a little more in depth and provide you with the perfect strategy to win nearly 100% of the time.

Please take note that the game has a timer and that the timer is VERY SHORT. Speed is required and you shouldn’t be taking too much time to think your next move.

Nomenclature
For the purpose of this guide, I will use different terms when talking about certain things.

Line(s) – They are the line that connect 2 dots on the field.
Box(es) – When 4 dots are connected into a square, it’s a box. A filled square.
Square(s) – Like a box except it doesn’t imply that the square is filled.
Pattern(s) – A pattern is a series of squares that, when adding a third line to the square of that series, the entire series can be taken by either the player or the computer AI in the same move.
Loop(s) – A kind of pattern that doesn’t have a beginning or an end. A loop pattern.
Opened pattern(s) – A kind of pattern that has a beginning and an end. Open on both ends.

The computer AI
The important thing to know is how the AI react to the game.

I believe there is 3 steps in which the AI go through.

Step 1. Is there a 3 lines square that can be filled to score a box?
Yes? Fill it and go back to 1.
No? Go to 2.

Step 2. Is there a line that can be filled without giving a score to the player?
Yes? Pick one line from all the lines found and fill it then end turn.
No? Go to 3.

Step 3. Which lines will give the least amount of boxes to the player?
When found, choose a line at random from the lines that reward the same amount of boxes as the lowest possible amount, fill it and end turn.

It is fairly easy to know which step the computer AI will be applying next.

The double-cross strategy
As mentioned on the Wikipedia page, the double-cross strategy is the strategy to use in order to control the flow of which patterns are given to the computer AI.

This strategy is quite simple and will allow you to force the computer into giving you the bigger patterns on the play field.

Here’s a simple example.
In this game, I am blue and the computer AI is red.
This computer act differently than the rift AI and actually tries to use the double-cross strategy against me, but as I take control of the fight earlier than him, I have total control on the choice he make and the computer can only pick what I want him to pick.

We first need to have a pattern of at least 2 squares in order to perform the double-cross strategy.
This strategy consist in giving away 2 boxes to the other player in order for him to give you the next pattern.
Here we have a 3 squares pattern we can fill.
A 4 squares pattern we cannot fill but we can close and give to the computer.
And a 10 squares pattern that we absolutely want that we can also close and give to the computer.
We want the computer to give us the 10 squares pattern.
Against the Rift AI, you could simply fill the 3 squares and give the 4 squares as the Rift AI doesn’t apply the double-cross strategy and would simply give you the 10 squares pattern.
But the AI used for this guide applies the double-cross strategy. So if I give him the 4 squares pattern, he will force me into giving him the 10 squares pattern.
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-doublecross1.png
This is what you need to do. You fill squares until you have 2 left skip a line and close the 2 boxes so the computer will have to take them and give you the next pattern.
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-doublecross2.png
After giving him 2 squares, I am the one who can now do what I want with the 4 squares pattern.
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-doublecross3.png
In this case, I apply the double-cross strategy a second time, forcing the computer in giving me the much wanted 10 squares pattern. Therefore I won the game.
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-doublecross4.png

You can easily win the puzzle in Rift by applying this strategy, but this will not net you 99.9% win rate if you don’t understand the double-cross strategy on a loop pattern.
Furthermore, against AI that applies the double-cross strategy, a 2 squares pattern must be cut in half when there is 3 lines needed to fill those 2 boxes (Like in this picture).
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-2squares.png
Or it must be closed when only 2 lines are needed to fill the 2 boxes. (I can’t manage to reproduce it against an AI that use the double-cross strategy, so no picture)

Double-cross for loop patterns
The Double-cross strategy works like a charm when you have an opened pattern, as you can simply take all but 2 boxes. When you are dealing with a closed loop pattern, you cannot give away only 2 boxes and must give 4 boxes.

In this picture, the computer AI placed a line on the pattern on the top. The pattern was the same as the one on the bottom before the computer played. In order for me to force him into giving me the next pattern I must give him 4 boxes.
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-doublecrossloop1.png
To do so, if you have a bigger pattern than 4 boxes, you take any extra boxes (in this case we take 2 boxes from the six boxes pattern) and you cut the 4 last boxes in half like in this picture.
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-doublecrossloop2.png
The computer will received 4 boxes but you will still have total control on the rest of the game so long as you keep applying the double-cross strategy.

The easy win strategy
This strategy is purely for the Rift computer AI.
It is meant to beat the Rift AI algorithm and not meant for use against human players or other algorithms.

The strategy is simple…
Try to make as many 4+ squares opened patterns as possible. Then apply the double cross strategy.
If you manage to get 3 such patterns, you have an assured win.
Here is an example of what it should look like:
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-easywin.png

This is all that can be said for this first part of the guide.

Good luck.

Part 2 – The achievement
This part of the guide is meant for those who absolutely want to gain the achievement “Thinking Out the Box”.
The achievement requires you to win with the computer only having 1 square.

The winning set of patterns
There is only 1 possible set of patterns that will allow you to win with the computer only having 1 square.

You need to have 2 patterns.
A pattern with only 1 square.
A pattern that cover the 24 other squares.

Getting such a set of pattern is actually easy.
For example, it took me about 10 tries against this other computer AI that also works with RNG to actually make one:
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-dotnbox1.png

The problem here is that… it is my turn to play and the only choice I have is to give the 24 squares pattern to the computer.
This is caused by being the first player to play. It means that every time you reach a 24 squares pattern with a lonely square, it will always be the computer turn to play…

Except!
If the 24 squares pattern is in a loop.
It require 35 lines to make an opened 24 squares pattern + 1 leftover square.
It require 36 lines to make a loop 24 squares pattern + 1 leftover square.

I won’t bother trying to get that pattern again against this computer AI as it take a lot of time, luck and patience to get.

How to reduce RNG and improve chance to win
It is no secret that this achievement is extremely highly RNG dependant. But there is several tricks to reduce the amount of RNG.

Leaving lines opened for the computer to take.
The most important trick to reduce RNG is to reduce the amount of unnecessary move you make and leave those moves to the computer to do.
Here is an example:
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-leavinglines.png
The red line here is what you SHOULDN’T take. Not taking this line means you have a move to use elsewhere and it add a line to the stacks of lines the computer can randomly pick from.
This drastically reduce the chances the computer cut you off when trying to create a 24 squares loop pattern.

Close the pattern ASAP
In order to make sure you get a loop pattern, it is of the utmost importance that you close the pattern.

Here is an example of what I mean:
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-lolwin.png
While this isn’t a loop as the start and the end do not meet, it is very close.
As you can see, the entire pattern is closed preventing any exit out of the box. Only thing that was missing here was for it to be in a loop.
Close enough

Start with the 3 corners
One of the most dangerous places are the corners.
You need to at least secure 3 corners or else you will not manage to make a 24 squares loop pattern. So start with securing 3 corners. The fourth corner isn’t as important as you still need 1 box out of the pattern.

Restart the game
If you are aiming for the achievement, don’t bother with finishing the game when you clearly can’t make it.
In order to restart the game, wait until it is your turn to play and run back to the dream console. The game will be reset and you will be able to pick up another ticket to play.

Patience
It is the only other trick I can give you. RNG is a … and one must be patient or extremely lucky in order to get this achievement.

Conclusion
I wish everyone who wants to get this achievement good luck and hope this guide could help people to complete this puzzle or improve their chance at the achievement.

First thing
The puzzle entrance is found here:
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-mappuzzle.jpg

And the lever to enter is located there:
Guide to Tarken Glacier puzzle and Thinking Out the Box achievement-thelever.jpg

Second thing
When trying to go for the achievement, you need to be VERY FAST. You have 24 boxes to get, so the number of clicks needed is quite high.

Additional Guide Tips Welcomed!