Can you use the central limit theorem to prove that different people have different amount of luck over time in poker? Was a couple of years ago i studied probabilties and statistics so dont really remember how to use it. The theorem most often called the central limit theorem is the following. Let X1, X2, X3, ... be a sequence of random variables which are defined on the same probability space, share the same probability distribution D and are independent. Assume that both the expected value μ and the standard deviation σ of D exist and are finite. Consider the sum S_j_n = X1 + ... + Xn. Then the expected value of Sn is nμ and its standard error is σ n1/2. Furthermore, informally speaking, the distribution of Sn approaches the normal distribution N(nμ,σ2n) as n approaches ∞. If X_i i=1,...,n is the outcome of all possible pokerhands. S_j j=1,.. is for different players. Could you then say that average S_j / n tends to the normal distribution? If its not possible i guess its because the distribution, they are not the same, or are they?