before JD shut down the first time, Doog did some stats on longest losing and winning streak at 49.5%.

I believe loses was as big as 32 in a row, and wins was 19 or 20..  i'm not 100% sure of the stats. its in the old JD thread somewhere.

Remember that this isnt simple 50/50.  at 49.5/50.5, the max loss streaks will be longer than the max win streaks.  (thus you can see the house edge in action, sortof)