A position sizing strategy which incorporates the martingale technique is basically any strategy which increases the trade size as a trade moves against the trader or after a losing trade. On the flip side a position sizing strategy which incorporates the anti martingale technique is basically any strategy which increases the trade size as the trade moves in the traders favor or after a winning trade.
The most basic martingale strategy is one in which the trader trades a set position size at the beginning of his trading strategy and then double’s the size of his trades after each unprofitable trade, returning back to the original position size only after a profitable trade. Using this strategy no matter how large the string of losing trades a trader faces, on the next winning trade they will make up all their losses plus a profit equal to the profit on their original trade size.
At first glance the above method can seem very sound and people often point to their perception that the chances of having a winning trade increase after a string of losing trades. Mathematically however the large majority of strategies work like flipping a coin, in that the chances of having a profitable trade on the next trade is completely independent of how many profitable or unprofitable trades one has leading up to that trade. As when flipping a coin no matter how many times you flip heads the chances of flipping tails on the next flip of the coin are still 50/50.
The second problem with this method is that it requires an unlimited amount of money to ensure success.
So while the pure martingale strategy and variations of it can produce successful results for extended periods of time, odds are that it will eventually end up in blowing ones account completely.
With this in mind the large majority of successful traders that I have seen follow anti martingale strategies which increase size when trades are profitable, never when unprofitable.