Game-playing Evolutionary Algorithms, specifically Rolling Horizon Evolutionary Algorithms, have recently managed to beat the state of the art in win rate across many video games. However, the best results in a game are highly dependent on the specific configuration of modifications and hybrids introduced over several papers, each adding additional parameters to the core algorithm. Further, the best previously published parameters have been found from only a few human-picked combinations, as the possibility space has grown beyond exhaustive search. This paper presents the state of the art in Rolling Horizon Evolutionary Algorithms, combining all modifications described in literature, as well as new ones, for a large resultant hybrid. We then use a parameter optimiser, the N-Tuple Bandit Evolutionary Algorithm, to find the best combination of parameters in 20 games from the General Video Game AI Framework. Further, we analyse the algorithm's parameters and some interesting combinations revealed through the optimisation process. Lastly, we find new state of the art solutions on several games by automatically exploring the large parameter space of RHEA.