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Sawasdee Kap K. Chusak,
In my view (and nobody should claim they hold a monopoly on the right answer in forex), the simplest way to differentiate the two is this:
* in a Martingale strategy, if your original Trade A goes against you, your next Trade B tends to be a multiplier of Trade A. For instance, if the multiplier = 2x; then the trades A, B, C, D and E for a BUY EURUSD could go like this, when EURUSD goes against you (ie EURUSD goes down): 0.01, 0.02, 0.04, 0.08 and 0.16. Total open trades at that point = 0.31 = the total of open trades in EURUSD. The idea here is that eventually, EURUSD will retrace/recover in the opposite direction, and your larger, later trades (e.g. 0.16, 0.08) will close out quicker because its size is much bigger than the earlier trades (e.g. 0.01, 0.02) when the EURUSD goes up a bit. All this is great in theory, if you have UNLIMITED monies, but as you would know, sometimes your luck runs out, and if you have limited funds, then your account can blow.
* In a grid approach, if your original Trade A goes against you, your next Trade B tends to be a not a multiplier of Trade A, but a 'step'. For instance, your step setting is 0.02. So in the same case as above, if you started a BUY EURUSD at 0.01 lot size, and the EURUSD goes down, your next trade would be 0.03, then 0.05, then 0.07 and 0.09. At that point, your total is 0.25. Your total open Trades for BUY EURUSD at that point in a Grid could be smaller than in a Martingale setting.
In some ways they are the same concept, but the difference is in money and risk management.
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