Game-playing Evolutionary Algorithms, specifically Rolling Horizon Evolutionary Algorithms, have recently managed to beat the state of the art in performance across many games. However, the best results per game are highly dependent on the specific configuration of modifications and hybrids introduced over several works, each described as parameters in the algorithm. However, the search for the best parameters has been reduced to several 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 and some additional ones for a large resultant hybrid. It then uses a parameter optimiser, the N-Tuple Bandit Evolutionary Algorithm, to find the best combination of parameters in 20 games with various properties from the General Video Game AI Framework. We highlight the noisy optimisation problem resultant, as both the games and the algorithm being optimised are stochastic. We then analyse the algorithm's parameters and interesting combinations revealed through the parameter optimisation process. Lastly, we show that it is possible to automatically explore a large parameter space and find configurations which outperform the state of the art on several games.