And your method is unfamiliar to me! I have no idea where "Variance of 18 000 bets of 200BTC at 49.5%: 200 * sqrt(0.495*0.515*18000) = 13 500" comes from. My method is to simply apply the central limit theorem.
Its supposed to be standard deviation not variance, edited that mistake.
Using the formula for the standard deviation of a binomial distribution: √[np(1-p)]
n= 18000 bets, p = 0.495 and (1-p) = 0.505
Well, the binomial distribution does not really fit here, as it measures the number of successes without placing any weight on losses.