Mathematically Optimal Decisions for Each Rule Set
Basic strategy identifies the decision that maximizes the expected value of a hand — or minimizes the expected loss — given the player’s cards, the dealer’s upcard and the exact table rules.
It is not a betting system and does not guarantee that a single hand or session will end in profit. It does, however, prevent decisions that unnecessarily increase the house edge.
The first systematic calculations were published in 1956 by Roger R. Baldwin, Wilbert E. Cantey, Herbert Maisel and James P. McDermott. Edward O. Thorp later expanded the mathematical study of Blackjack and popularized advantage play through card counting.
Reference Rule Set
The following chart is constructed for this rule set:
6 decks; S17; DOA; DAS; RSA; classic ENHC; no surrender; Blackjack paid 3:2.
Under these conditions, the house edge with correct basic strategy is approximately 0.55%.
These differences materially affect optimal strategy. The following chart is therefore valid only for the stated rule set.
Legend
- H: Hit.
- S: Stand.
- D/H: Double if allowed, otherwise Hit.
- D/S: Double if allowed, otherwise Stand.
- P: Split.
Hard Hands
| Hand | Decision |
|---|---|
| 8 or less | H |
| 9 | D/H against 3–6; otherwise H |
| 10 | D/H against 2–9; H against 10 and Ace |
| 11 | D/H against 2–9; H against 10 and Ace |
| 12 | S against 4–6; otherwise H |
| 13–16 | S against 2–6; otherwise H |
| 17 or more | S |
Soft Hands
| Hand | Decision |
|---|---|
| A,2 and A,3 | D/H against 5–6; otherwise H |
| A,4 and A,5 | D/H against 4–6; otherwise H |
| A,6 | D/H against 3–6; otherwise H |
| A,7 | S against 2, 7 and 8; D/S against 3–6; H against 9, 10 and Ace |
| A,8 and A,9 | S |
| A,10 | Blackjack on the first two cards; after a split it is an ordinary 21 |
Pairs
| Pair | Decision |
|---|---|
| 2,2 and 3,3 | P against 2–7; otherwise H |
| 4,4 | P against 5–6; otherwise H |
| 5,5 | do not split; play as hard 10 |
| 6,6 | P against 2–6; otherwise H |
| 7,7 | P against 2–7; otherwise H |
| 8,8 | P against 2–9; H against 10 and Ace |
| 9,9 | P against 2–6 and 8–9; S against 7, 10 and Ace |
| 10,10 | S |
| A,A | P against 2–10; H against Ace |
The Three Most Important ENHC Adjustments
- 11 against 10: Hit, not Double;
- 8,8 against 10 or Ace: Hit, not Split;
- A,A against Ace: Hit, not Split.
With OBO, which returns additional wagers, these adjustments are not required.
Total-Dependent and Composition-Dependent Strategy
The chart uses a total-dependentstrategy based on the hand total. Composition-dependent refinements exist, especially in games with few decks, but total-dependent strategy remains the clearest reference for an introductory page.
Insurance and Even Money
Under basic strategy, insurance and even money are not accepted. These decisions change only when reliable information about the composition of the remaining cards is available.
Final Considerations
Basic strategy does not automatically make Blackjack positive. It reduces the mathematical cost of the game under the conditions imposed by the table. card counting, Shuffle Tracking and other advanced methods require ordinary playing decisions to be executed correctly first.
Before using any chart, always verify the table rules and payouts.
Calculate strategy for the table rules
Generate the matrix directly with the Blackjack Basic Strategy Generator and, for a specific hand and remaining composition, compare actions with the Blackjack EV Calculator.