Players in serious games may often need multiple trials for correctly completing a game task. Therefore, the number of attempts should be reflected in the score. This article presents three computational score models that take into account the number of attempts that a player makes to be successful. The models, which are extensions of test theory, quantify the random contributions to the scores that need to be removed. They also describe the influence of prior knowledge used for elimination of incorrect options, and take into account that the decision options in a node may not be equally plausible. In a series of simulation studies the score outcomes of the models are compared under various conditions. Results show that the number of trials cannot be ignored as they have a strong impact on the performance scores to be assigned. Neglecting the number of trials leads to inaccurate scores that significantly overrate the observed performances, occasionally up to 100% or even more. The effects depend on the number of decision options, the presence of obvious, correct or incorrect options given the player´s knowledge level and, to a lesser extent, different plausibility levels of the options to decide upon. The practical feasibility is high, because a simple score formula largely solves the problem.