Minigame: Dots - Solution

Puzzle Location: Angel Island

Next Puzzle: Stars

There's a very nice website explaining general strategies for this game here. For the version of the game we presented in Genome, the opponent (Genodix employee) played a simple strategy based on a "spokes" pattern--when possible, the opponent's turn was used to put lines in squares where another side is already drawn, in one of two patters:

or

Using this strategy ensures that a chain of boxes will be created where there is only one "long chain." (In dots-and-boxes speak, a long chain constitutes a chain of lenght greater than 2.) A sample game that describes this concept is given below. The challenger (in blue) moves first, and alternates with the opponent (black) putting lines in between boxes, eventually ending up in the following situation:

At this point it is blue's turn and no matter what move blue makes, a box will be given to black. Blue will therefore give the smallest number of boxes away and will put a line in for the box in the bottom right hand corner. Black will draw the final line and take the box (labeling it "k" ... we'll use "b" for Blue) and will then take the next turn and put a line in for the box in the upper right hand corner. Blue will go next and take that box and then put in a spoke for the middle box on the right hand side. Black will take that box and puts a line to give up the two boxes available on the left hand side (bottom two boxes). It is now Blue's turn. Recall that blue is the challenging game team. Black has set things up perfectly. By using the spoke strategy, black has set up the game so that there is only one "long chain," the one that goes through the middle. If Blue makes the expected move, blue will take the two boxes in the left column and give up the long chain to black. This will give a final score of Black: 6, Blue: 3. Since the goal is for Blue to get at least 4 boxes, blue will have lost the game. The only way for Blue to win is to "double-cross." Note that the double-crossing described here is not quite the same as what is used in official "dots and boxes" parlance since it is being applied to a chain of length less than three. In order to win, blue must draw a vertical line in the lower left corner. Black only has two options: it can take the bottom two boxes in the first column and give up the "long chain," or give up both the bottom two boxes AND the long chain by adding a line between any two dots in the "long chain." Either way, blue gets more than four boxes and meets our criterea of a win. Taking the first scenario (which makes much more sense), we end up with blue a winner.

The key to winning here is what's called the "double-cross" strategy. You can read more about it here.