Intelligent strategies for several zero-, one- and two-player games

In this paper we present efficient and intelligent strategies for several zero-, one- and two-player games. Most of the games have been studied before or are related to other well-known games, but we present improved algorithmic techniques for playing them optimally. The main techniques we employed are dynamic programming, the Sprague-Grundy game theory and pattern extraction. We also make use of elements from computational geometry, like orthogonal range searching data structures.