Overall, the key to defeating martingale (if you are the house) is to place a bet limit. Once there's a highest bet possible, the martingale player has to lose as soon as their local loss streak takes them to the point of butting up against the bet limit.
Note that if you consider a player with a non-finite amount of fundage and no bet limit the martingale is going to clean out the house eventually. However, these conditions aren't met in real life
That's not why there are betting limits. It's because of Kelly and in person, because of status.
This.
At 1% house edge, the Kelly criterion is exactly 1%, and there is the original max win for JD.
You could check the wiki page about it for details. http://en.wikipedia.org/wiki/Kelly_criterion