The term ‘Martingale’ when in reference to the subject of betting systems and tweaks, refers to any system which originated in 18th century France.
Perhaps the most basic and in turn worthy of mentioning system of the martingale class is that which involves ‘doubling up’. To put it as simply as possible, this systems maintains that in a game of 50/50 probability (betting red/black in roulette, for example) a player may recuperate any loss made by doubling up on the next round (or in the case of roulette, the next spin). Statistically speaking, the player will eventually win and earn all of the money lost prior to that moment.
As you can imagine, this was considered for a long time to be one of the surest things in gambling, though many eventually fell victim to its apparent simplicity. While a gambler with an infinite amount of money in their possession will at some point cash in and win all of their money back, most would be surprised at just how quickly even the most handsome of table-side stashes can be depleted- especially if each bet is double to the previous.
In this light, the martingale system is fail safe in the case of an infinite wealth to bet with. However, if a player is limited to only a certain amount of money (no matter how much it may be) it acts as no more of a guarantee than playing without the use of a any form of system at all.