As one of the most widely used parsimony methods for ancestral reconstruction, the Fitch method minimizes the total number of hypothetical substitutions along all branches of a tree to explain the evolution of a character. Due to the extensive usage of this method, it has become a scientific endeavor in recent years to study the reconstruction accuracies of the Fitch method. However, most studies are restricted to 2-state evolutionary models and a study for higher-state models is needed since DNA sequences take the format of 4-state series and protein sequences even have 20 states.