Here's a paper that wccanard and I wrote about simple loony endgames in dots and boxes:

Playing Simple Loony Dots and Boxes endgames Optimally

The first part of the paper consists of results about loony endgames that wccanard found way back, and which are familiar to those of you who read his articles. The second part presents and proves an efficient algorithm that tells you whether to open the smallest loop or the smallest chain in a simple loony endgame, and how you can compute its value. I found this algorithm about 5 years ago, and now wccanard and I finally managed to write everything up in a paper, submit it to a journal (called Integers), and get it accepted.

It probably has little practical value to a dots-and-boxes player, but those who enjoy mathematics may find it interesting.

Very impressive :) contratulations. Are you mathematicians?

Wccanard is a mathematician (in a completely different field though), I'm not. Five years ago I was still in high school and I did a project on dots and boxes. Wccanard helped me (a lot) through email and after my project was finished he suggested we could write a paper together.

All the math in this paper is basically high-school level mathematics – mostly a combination of many simple deductions and some modulo stuff. You definitely don't need to be a mathematician to understand this paper :)