In many board games points are counted. Does some know the result to the following question? Assume that in each round points are given according to some normal distribution and points over the rounds are added up. Now say after N rounds the score of two players is X and Y. What is the chance that the higher score really belongs to a more skilled player (higher average in one round) and is not just a random result? Can I say something about the difference in average scores per round? For example how many standard deviations are between them? (or which other assumptions do I need to include to pose this question?) I'm not familiar with all concepts of statistics, but maybe someone can tell me where to plug in X, Y and N to get my result?