[Editor's Note: The following answer is supplied by Arnold Snyder, one of the world's foremost experts on blackjack.]
Continuous shuffle machines (CSMs) have no effect on basic strategy, only on card counting.
If you use an accurate 2-deck basic strategy against a game shuffled via CSM, you'll be playing accurately for that game and diminish the house edge as much as possible. (Depending on the exact rules of the game, there may be slight differences between a perfect 2-deck basic strategy and a strategy for four, six, or eight decks. But these differences are so minor that most experts, including most professional players, simply use a generic multiple-deck basic strategy for all games dealt from more than one deck.)
Basic strategy for blackjack was initially devised by using computer simulations that mimicked CSM games (even though CSMs didn’t even exist when blackjack basic strategy was first developed). The programmers figured out basic strategy by testing each playing decision off the top of the freshly shuffled deck(s). That’s precisely what the game is when you play against a CSM.
Card counting is useless versus CSMs, because you never have a chance for the count to go up (or down), enabling you to make more accurate betting or playing decisions based on your count. If multiple players are at the table in a game shuffled via CSM, occasionally enabling the count to rise enough by the time the counter must make a playing decision, he might enjoy a very slight advantage over a strict basic strategy player, but this trivial edge will never be enough to get him over the house edge.
For example, if the count rises at all when a player is holding a total of 16 vs. a dealer ten-valued card, it would be more correct for a player to stand, as opposed to following basic strategy and hitting. But the actual value of the few deviations from basic like this that have minor value to you as a player won’t affect your overall expectation from the game more than a few cents per hour.
If you don’t mind giving up the house edge on a game, but you just want to play as accurately as possible with correct basic strategy, don’t worry about the CSM. Just stick to basic and you’ll do just as well as when you use basic in a hand-shuffled game. And you’ll be miles ahead of players who play their hunches or make betting and playing decisions based on trends.