The Advantage of the Initiative

Abstract Recently, the list of solved two-person zero-sum games with perfect information has increased. The state of current knowledge is that many games are a win for the first player, some games are draws, and only a few games are a win for the second player. For games with three outcomes (won, drawn, lost) a game is commonly defined as fair if the theoretical value of the game is drawn. For these games as well as for games with two outcomes (won, lost) we were tempted to examine which concepts characterize the outcome of a game. In this paper, we distinguish two main concepts valid for many two-person games, namely initiative and zugzwang . The initiative is defined as an action of the first player. The notion of zugzwang is adopted from the game of chess. To investigate the impact of the initiative we determine the game-theoretic values of a large number of k -in-a-row games and over 200 Domineering games as a function of the board size. The results indicate that having the initiative is a clear advantage under the condition that the board size is sufficiently large.

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