Analysis of the one-dimensional Yut-Nori game: Winning strategy and avalanche-size distribution

Abstract

In the Korean traditional board game Yut-Nori, teams compete by moving their pieces on a two-dimensional game board, and the team whose all pieces complete a round trip on the board wins. In every round, teams throw four wooden sticks of the shape of half-cut cylinders and the number of sticks that show belly sides, i.e., the flat sides, determines the number of steps the team’s piece can advance on the board. It is possible to pile up one team’s pieces if their sites are identical so that pieces as a group can move together afterwards (piling). If a team’s piece(s) arrives at a site occupied by an opponent’s piece(s), it is caught and removed from the board, and the team is given one more chance to throw the sticks and proceed (catching). For simplicity, we simulate this game on a one-dimensional board with the same number of sites as the original game and show that catching is a more advantageous strategy than piling to win. We also study the avalanche-size distribution in the thermodynamic limit and find that it follows an exponential form.