Martingale System:
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Originally, martingale referred to a class of betting strategies popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Since a gambler with infinite wealth will with probability 1 eventually flip heads, the Martingale betting strategy was seen as a sure thing by those who practised it. Of course, none of these practitioners in fact possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt those who choose to use the Martingale. Moreover, it has become impossible to implement in modern casinos, due to the betting limit at the tables. Because the betting limits reduce the casino's short term variance, the Martingale system itself does not pose a threat to the casino, and many will encourage its use, knowing that they have the house advantage no matter when or how much is wagered. (WIKI)
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Anti-martingale system:
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In a classic martingale betting style, gamblers will increase their bets after each loss in hopes that an eventual win will recover all previous losses. The anti-martingale approach instead increases bets after wins, while reducing them after a loss. The perception is that in this manner the gambler will benefit from a winning streak or a "hot hand", while reducing losses while "cold" or otherwise having a losing streak. This general idea of increasing bets when conditions are believed to be favorable can improve the odds in games with a memory by using a strategy like card counting. But in a true random memoryless game there is no such thing as a winning streak or losing streak (these notions are gambler's fallacy) so this strategy can't improve the expected winnings in such situations. (WIKI)
In a classic martingale betting style, gamblers will increase their bets after each loss in hopes that an eventual win will recover all previous losses. The anti-martingale approach instead increases bets after wins, while reducing them after a loss. The perception is that in this manner the gambler will benefit from a winning streak or a "hot hand", while reducing losses while "cold" or otherwise having a losing streak. This general idea of increasing bets when conditions are believed to be favorable can improve the odds in games with a memory by using a strategy like card counting. But in a true random memoryless game there is no such thing as a winning streak or losing streak (these notions are gambler's fallacy) so this strategy can't improve the expected winnings in such situations. (WIKI)
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HINT: Both systems don't work unless you have unlimited amounts of money to throw away!!
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HINT 2: The concept of martingale in probability theory was introduced by Paul Pierre Lévy, and much of the original development of the theory was done by Joseph Leo Doob. Part of the motivation for that work was to show the impossibility of successful betting strategies!!!! (WIKI)
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