Finalist: Elias Lundheim

Elias Lundheim, 18 år, Trondheim
Skole: Trondheim Katedralskole

The random pawn game problem

Chess is a board game where pieces on a board follow simple rules, and two players use these pieces to capture the opponent’s king. In addition to this traditional game, there have also been countless problems like the Knight’s Tour or the Eight Queens Puzzle. While many of these have been solved, some remain unsolved, where the answers are hidden behind a vast number of calculations. One of these problems is to find the number of unique chess games. One of the first to provide an estimate of this number was Claude Shannon who claimed in his 1950 paper "Programming a computer for playing chess" that the number would be about 1043, but many have come closer today.

I have had an interest for chess for a long time, and the idea of making a system of rules and values interacting with one another has always been intriguing. In my paper, I discuss one such system, and try to solve one problem within this system. I start with traditional chess as my frame, and add or remove move elements I want or do not want to be a part of my system. What I end up with is my own game which moves and behaves quite differently from traditional chess. It might be a bit of a stretch to even call it a game, since it does not have an end goal. None the less, the idea of making simple rules that create complicated scenarios is a passion for me. (Langton’s Ant is a great example of this.)

My initial thought for a problem was a quite practical one; If you throw some pieces onto a chess board, would two players be able to reach that position, starting from a standard board? What would be the likelihood of such a random board occurring? Calculating this for a full board would be nearly impossible with our current methods and computing power since you end up having to find all possible chess games, but I still wanted to explore the problem. To do this, I started at a much simpler level, with only pawns and a smaller board. My essay explores different ways of calculating this probability, and discusses various problems concerning the task.



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