In this paper we investigate the game of Konane, using Combinatorial Game Theory and game-specific solving strategies. We focus on narrow rectangular boards (m×n boards with m⩽4). These are dubbed as Linear Konane, Double Konane, Triple Konane, and Quadruple Konane, respectively. The initial boardcontains black and white stones in a checkered pattern, with a gap of two adjacent empty squares to enable moving. Only capture moves are possible. Depending on the exact location of the initial gap (the setup) we have four classes of initial Konane boards (two for Linear Konane), namely all combinations of a horizontal or vertical setup in the middle of the board or at a corner. For solving narrow Konane boards two notions proved very useful. First, we define moves that cannot be prevented by the opponent as safe moves of a player. Second, two fragments are independent if there is no way they can ever interact. Using these two notions Linear and Double Konane have been completely solved. Triple Konane was solved except for the horizontal corner setup. For Quadruple Konane only the vertical setup in the middle of the board was solved.

中文翻译：

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解决窄 Konane 板

在本文中，我们使用组合博弈论和特定博弈的解决策略来研究 Konane 博弈。我们专注于窄矩形板（m×n 板，m⩽4）。它们分别被称为线性Konane、Double Konane、Triple Konane 和Quadruple Konane。最初的棋盘包含方格图案的黑色和白色石头，两个相邻的空方格之间有一个间隙，可以移动。只有捕获动作是可能的。根据初始间隙（设置）的确切位置，我们有四类初始 Konane 板（Linear Konane 有两种），即在板中间或角落的水平或垂直设置的所有组合。对于解决窄 Konane 板，有两个概念被证明非常有用。首先，我们将对手无法阻止的动作定义为玩家的安全动作。第二，如果两个片段无法交互，则它们是独立的。使用这两个概念 Linear 和 Double Konane 已经完全解决了。除了水平角设置外，Triple Konane 已解决。对于 Quadruple Konane，仅解决了板中间的垂直设置。