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Basic strategy and blackjack rule sets
Basic strategy is the set of playing decisions that maximizes expected return in blackjack under a stated rule set. Each decision uses two inputs, the player's hand and the dealer's exposed card, and some entries also depend on whether surrender, doubling or splitting is permitted at that table.
A quoted house edge is built on top of this chart and assumes it is followed on every hand. Deviate from it, or use a chart written for different rules, and the number no longer applies.
Why does the chart depend on the rules? Because rules shift the value of individual decisions. When the dealer hits soft seventeen, the dealer's final totals are distributed differently and a few borderline plays flip. When doubling after a split is barred, an option disappears from certain pair hands. Most cells on two charts can look identical while the ones that differ are exactly the ones that matter for [https://casinohouseedge.com/blackjack-house-edge/ blackjack basic strategy and house edge] at that table.
Strategy is also a different thing from a betting system. Strategy changes what is done inside a hand: hit, stand, double, split, surrender. A progression changes how much money goes out between hands. In a game whose rules stay fixed, raising the bet after a loss adds nothing to expected value; choosing the better available action does.
So a figure quoted "with basic strategy" describes a specific chart on a specific rule card, played without error. Change either half and the figure needs recomputing.