Even without deviations in strategy based on index numbers (the importance of which decreases as the number of decks and/or the necessity of camouflaging oneself increase) such as taking insurance, standing on 15 or 16 versus a dealer 10, or splitting 10s versus 5s and 6s, there are still other sources of asymmetry which provide excess value for the player under a high count.
For example, (as John already pointed out) the player receives a payout of 3:2 on BJ (while the dealer only receives 1:1), and the dealer is required to hit on hard totals of 16 or less while the player is under no such obligation.
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