A New Family of k-in-a-Row Games

First, this paper introduces a new family of k-in-a-row games, Connect(m, n, k, p, q). In Connect(m, n, k, p, q), two players alternately place p stones on an m × n board in each turn except for that the first player places q stones for the first move. The player who gets k consecutive stones of her own first wins. The traditional game five-in-a-row, also called Go-Moku, in the free style is Connect(15,15,5,1,1). For simplicity, Connect(k, p, q) denotes the game Connect(∞, ∞, k, p, q), played on infinite boards. Second, this paper analyzes the characteristics of these games, especially for the fairness. In the analysis of fairness, we first exclude the ones which are apparently unfair or solved. Then, for the rest of games, we argue that p = 2q is a necessary condition for fairness in the sense that one player always has q more stones than the other after making each move. Among these games, Connect(6,2,1) is most interesting to this paper and is named Connect6. Finally, thi...

• Type: Conference
• Year: 2006
• Where: ACG
• Authors: I-Chen Wu, Dei-Yen Huang
• Keywords: ACG 2006, Computer Graphics, Paper, first Player, first Player Places