Take a look at the following paper about the Maximum Drawdown distribution:

[On the Maximum Drawdown of a Brownian Motion][1]


  [1]: http://alumnus.caltech.edu/~amir/drawdown-jrnl.pdf

The authors end up with an approximative series for the density. It is implemented in the function *maxdd* of the R-package *fBasics*. There are convenient functions *dmaxdd*, *pmaxdd* and *rmaxdd*. Calculating the Expected Drawdown should be easy.

Just compare your results with the output of this package (mean, quantiles, etc.) and you should be fine. 

Actually, there is no need to "simulate" drawdowns of a brownian motion then - just take random samples with *rmaxdd*.

When you say "match" or "close" you probably mean that the means converge if sample size increases?

By the law of large numbers, the means of the sampled maximum drawdowns will converge to the expected maximum drawdown (although convergence maybe slow - expecially if the distribution does not have finite variance). Actually, the empirical distributions "approach" the maximum drawdown distribution.