Only a fool (with an unlimited cash supply) uses a Martingale-based approach (whether in a casino or the market). Sure, if you're an Arab sheik and can keep doubling your bet EVENTUALLY you'll win and get everything back (assuming you're at a no limit table).
But that puts you in the position of perhaps betting a million dollars just to win (net) a buck. Hardly the smart thing to do.
In the casino, I've used an inverse-Martingale betting approach that usually works where you're basically using a structured sequence of increasing your bets in a staggered manner while you're winning. This has worked well at craps and roulette. For blackjack I still prefer to vary the bet size based on the card count. In either case, your goal is to be betting with the house's money not playing catch up.
BUT, the market isn't really analogous to a craps table - although a lot of people seem to trade/invest like gamblers. The objective in trading is to cut your losses quickly and let your winners run.
You profit as much from risk management/mitigation as you do from stock picking. For instance, using incremental profit taking to take money off the table as your position goes green and moving your stop accordingly to mitigate position risk.
Example - you buy 800 shares of XYZ @ 40 with a 1 point initial stop (initial risk is $800 so you're capital needs to be at least $40K to maintain a 2% capital risk). Now when the stock moves to say +1/2, you dump 400 shares and move your stop to a net breakeven point at 39 1/2. At this point you have mitigated the risk of the position. If the stock gets to +1, you dump 200 more shares and move the stop on the remaining position to breakeven at 40. You have now locked in $600 in profits and have almost no risk in the remaining position. You then ride the remainder as far as you can while periodically trailing up the stop (although you may want to set another profit taking target to lock in additional profits).
Obviously, the initial stop size and profit taking targets will be based on the specific analysis of the stock and especially the expected layout of it's support/resistance zones (you usually want to plan your initial stop below a support zone and plan your profit taking just ahead of resistance zones).
The one analogy to a casino with this approach is that by incrementally taking profits you quickly move a position to the point where you've essentially mitigated its risk and you're playing with the "house's money".
Good luck.