Probability of skill at board games

[Gerenuk]

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?

 

[zli034]

Player x and y can have a specific amount of points for each of each round, after N rounds x has set of points and y has his own set of points too. You can use independent z test on average points per round between x set and y set. If the N is small say < 30, you can use independent t test. If distribution of x and y are not normal and have very different standard deviations. You should use nonparametric methods, like rank sum based tests.