The advantage of the initiative

Recently, the list of solved two-person zero-sum games with perfect informa tion 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 i s 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 ga me. In this paper, we distinguish two main concepts valid for many two-person g ames, namely initiative and zugzwang. The initiative is defined as an actio n of the first player. The notion of zugzwang is adopted from the game of c hess. To investigate the impact of the initiative we determine the game-the oretic values of a large number of Ic-in-a-row games and over 200 Domineeri ng 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. (C) 2000 Elsevier Science Inc. All rights reserved.