The N-Tuple Bandit Evolutionary Algorithm (NTBEA) has proven very effective in optimising algorithm parameters in Game AI. A potential weakness is the use of a simple average of all component Tuples in the model. This study investigates a refinement to the N-Tuple model used in NTBEA by weighting these component Tuples by their level of information and specificity of match. We introduce weighting functions to the model to obtain Weighted- NTBEA and test this on four benchmark functions and two game environments. These tests show that vanilla NTBEA is the most reliable and performant of the algorithms tested. Furthermore we show that given an iteration budget it is better to execute several independent NTBEA runs, and use part of the budget to find the best recommendation from these runs.