Dots and Boxes Game

Dots and Boxes Game

When I was in high school, one of my favorite ways to waste time in class (not recommended) was to play a game called dots and boxes (although at the time we just called it dots). I was very surprised to find later that this game belongs to a class of games called “Impartial Combinatorial Games”. These are games where the moves available to the player depend only on the position of the game, and not the player.

In a game of Dots and Boxes, we start with an initial grid with dots at each row and column intersection. At each player’s turn, they have the option of drawing either a horizontal or vertical line between two neighboring dots (depending on if the dots are in the same row or column). If a player fills in the last line on a box (the 4th side), we say that player “owns” the box. The game ends when there are no neighboring dots without a line between them. At the conclusion of the game, the player who owns the most dots is declared the winner.

The game is impartial because there is no restriction on which move a player can make other than the fact that a player cannot re-do a move that has already been made (a partial version of this game would be if player one could only move horizontally and player two could only move vertically).

I have implemented a javascript version of this game. Check it out and let me know what you think.

I also spoke earlier about the discovery that this game in particular was an active area of research. I wanted to provide a link to a paper entitled “Solving Dots and Boxes” by Joseph K. Barker and Richard E Korf that speaks about winning strategies for each player in a game of dots and boxes.

K Means Clustering for 2013 NFL Stats

I just did some data mining on the stats from 2013. Nothing too exotic, just a bit of k-means clustering based on the 2013 defensive stats. http://www.pro-football-reference.com allows us to copy and paste the entire set of defensive stats at once for a whole year. So I just ran the stuff through my k means clustering program. My assumption is that the more clusters, the more the different defensive positions and defensive positions skill levels will distinguish themselves.

I realize though that simple clustering won’t necessarily know a LB from a DE or a S, but good stats are good stats so I just wanted to see who the program paired together. I’ll see if I can later find a better set of stats to play with.
Check it out