A tough variance problem (at least for me)

[TNixon]

If, given a specific winrate and std.dev, I wanted to know the odds of having an upswing or downswing of size X, over Y hands, how would I go about figuring this out?

For example, what are the chances of having a $500 downswing at some point over 1k hands, with a winrate of $.16/hand, and a std dev of $1.02/hand?

The complicated part of this is that a drop doesn't have to be a continuous loss in every hand, just a drop from point A to point B. So a sequence that went WLLWLWLLW would be considerered to have a downswing of 3, even though the longest consecutive downswing is 2.