Love the Martingale (juice makes it not as fun in sports betting though), and I especially love that most people think you are crazy when you first try to explain it.
You said it was a losing system...theoretically, if every bet placed has a chance of winning (which of course they all do) it is actually a 100% winning system. Even if you were rolling a 100 sided die and betting on one number every time, you would eventually win because the probability of winning is greater than 0.
No real way to determine probability of winning in handicapping, but in a perfect-lines world and blind choices it would be 50%, which puts the probability of a streak of 5 losses at 1/32, or 3.1%. Add one more level, and obviously it cuts in half, to 1.55%.
The problem of course comes from bankroll, and specifically from table maximums or book maximums in this case. If the limitations from yourself and from the book weren't in place you could never lose.