Optimal strategy in games with chance nodes

In this paper, games with chance nodes are analysed. The evaluation of these game trees uses the expectiminimax algorithm. We present pruning techniques involving random effects. The gamma-pruning aims at increasing the efficiency of expectiminimax (analogously to alpha-beta pruning and the classical minimax). Some interesting properties of these games are shown: for instance, a game without draw can be fair. A fair game may not be fair any more if it is played iteratively. To handle these phenomena, the use of additional indicators, such as the minimal guaranteed outcome value, is suggested.