The AlphaZero algorithm has been successfully applied in a range of discretedomains, most notably board games. It utilizes a neural network, that learns avalue and policy function to guide the exploration in a Monte-Carlo TreeSearch. Although many search improvements have been proposed for Monte-CarloTree Search in the past, most of them refer to an older variant of the UpperConfidence bounds for Trees algorithm that does not use a policy for planning.We introduce a new, improved search algorithm for AlphaZero which generalizesthe search tree to a directed acyclic graph. This enables information flowacross different subtrees and greatly reduces memory consumption. Along withMonte-Carlo Graph Search, we propose a number of further extensions, such asthe inclusion of Epsilon-greedy exploration, a revised terminal solver and theintegration of domain knowledge as constraints. In our evaluations, we use theCrazyAra engine on chess and crazyhouse as examples to show that these changesbring significant improvements to AlphaZero.