A mathematical theorem that states, for any set of independent random variates with finite variance, that the cumulative distribution function of a normalized (scaled) sum of such variates approaches the cumulative distribution function for a normal distribution, as the number of variates increases. Under certain circumstance, the theorem states that the width of the central region of the associated probability distribution function narrows, and approaches zero, as the number of random trials (variants) increases and that the shape (of the central region) of the PDF approaches a normal PDF as the number of trials increases. If all variates are from a single uncorrelated random process, the theorem states that variance decreases as 1/sqrt(n) where n is the number of trials. Since each video poker hand is independent of all other hands, and since video poker's variance is finite, The Central Limit Theorem holds for all video poker, and the variance scales as 1/sqrt(n), where n is the number of hands. However, at the same time, the total bet or coin-in has been increasing proportional to n. Thus the variance in real units (dollars) increases without limit as the player continues to gamble.
See also: PDF, Coin-in, Variance, Central Limit.