strategy based on cards

Sure, it would certainly beat basic strategy, which only considers the cards you currently see in your hand, not all the cards that have been played so far. This could overcome the house edge and give you a nice advantage in any a game with very good rules.

Card counting is an approximation of this (but being easy enough to do in your head).

More important would be to vary your bets based on how favorable the remaining cards are. This is where you gain most of your advantage when card counting. Bet more when there are mostly good cards left. Changing when you hit/stand and such is just icing on the cake.

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