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Strategies for playing blackjack
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Provided by The Wizard of Odds

BlackJack Apppendix 3c
In single deck blackjack every card that is played has a considerable impact on the distribution of the remaining cards. The following lists will show exactly how to play your cards immediately after a shuffle in a single deck game where the dealer hits a soft 17.

To use this guide first go to the list according to the number of cards in your hand. Then note the basic strategy changes and finally the exceptions to the changes. For example if you have a 16 composed of a 10, 4, and 2 against a 10 look under the 3 card list. You will see that with three cards you should stand on 16 against 10. Going further you will see there are some exceptions, for example with a 16 composed of a 6, 6, and 4 you should hit. If your hand is not listed as an exception so you should stand. It should not be interpreted that this is a card counting guide. Everything is based on exact cards and no numbers represent a count.

Two Cards

Basic Strategy Changes: None

Exceptions:

  1. 8 (6+2) vs 6 = Hit
  2. 12 (7+5) vs 3 = Stand
  3. 12 (8+4) vs 3 = Stand
  4. 12 (10+2) vs 4 = Hit

Three Cards

Basic Strategy Changes:
  1. 12 vs 3 = Stand
  2. 16 vs 10 = Stand
Exceptions:
  1. 15 (5+5+5) vs 10 = Stand
  2. 15 (6+5+4) vs 10 = Stand
  3. 15 (6+6+3) vs 10 = Stand
  4. 16 (6+5+5) vs 9 = Stand
  5. 16 (8+4+4) vs 9 = Stand
  6. 16 (8+5+3) vs 9 = Stand
  7. 16 (6+6+4) vs 10 = Hit
  8. 16 (7+6+3) vs 10 = Hit
  9. 16 (8+6+2) vs 10 = Hit
  10. 16 (9+6+A) vs 10 = Hit

Four Cards

Basic Strategy Changes:
  1. 12 vs 3 = Stand
  2. 16 vs 10 = Stand
Exceptions:
  1. 12 (2+2+2+6) vs 3 = Hit
  2. 12 (2+2+3+5) vs 3 = Hit
  3. 12 (2+3+3+4) vs 3 = Hit
  4. 15 (A+4+5+5) vs 10 = Stand
  5. 15 (A+3+5+6) vs 10 = Stand
  6. 15 (A+2+6+6) vs 10 = Stand
  7. 16 (6+6+2+2) vs 10 = Hit
  8. 16 (6+6+3+A) vs 10 = Hit
  9. 16 (7+6+2+A) vs 10 = Hit
  10. 16 (8+6+A+A) vs 10 = Hit
  11. 16 (10+2+2+2) vs 10 = Hit
  12. 16 (4+4+4+4) vs 9 = Stand
  13. 16 (5+4+4+3) vs 9 = Stand
  14. 16 (5+5+3+3) vs 9 = Stand
  15. 16 (5+5+4+2) vs 9 = Stand
  16. 16 (5+5+5+A) vs 9 = Stand
  17. 16 (6+4+4+2) vs 9 = Stand
  18. 16 (6+5+4+A) vs 9 = Stand
  19. 16 (8+3+3+2) vs 9 = Stand
  20. 16 (8+4+2+2) vs 9 = Stand
  21. 16 (8+4+3+A) vs 9 = Stand
  22. 16 (8+5+2+A) vs 9 = Stand
  23. 16 (9+5+A+A) vs 9 = Stand
  24. 16 (9+4+2+A) vs 9 = Stand

Five Cards

Basic Strategy Changes:
  1. 12 vs 3 = Stand
  2. 16 vs 10 = Stand
  3. 16 vs 9 = Stand
Exceptions:
  1. 12 (A+2+2+2+5) vs 3 = Hit
  2. 12 (A+2+2+3+4) vs 3 = Hit
  3. 12 (A+2+3+3+3) vs 3 = Hit
  4. 12 (2+2+2+2+4) vs 3 = Hit
  5. 12 (2+2+2+3+3) vs 3 = Hit
  6. 15 (A+A+A+6+6) vs 10 = Stand
  7. 15 (A+A+3+5+5) vs 10 = Stand
  8. 16 (6+3+3+2+2) vs 10 = Hit
  9. 16 (7+6+A+A+A) vs 10 = Hit
  10. 16 (10+2+2+A+A) vs 10 = Hit
  11. 16 (6+6+2+A+A) vs 10 = Hit
  12. 16 (10+3+A+A+A) vs 9 = Hit
  13. 16 (7+6+A+A+A) vs 9 = Hit
  14. 16 (10+2+2+A+A) vs 9 = Hit
  15. 16 (7+5+2+A+A) vs 9 = Hit
  16. 16 (6+6+2+A+A) vs 9 = Hit
  17. 16 (7+4+3+A+A) vs 9 = Hit
  18. 16 (7+4+2+2+A) vs 9 = Hit
  19. 16 (7+3+3+2+A) vs 9 = Hit
  20. 16 (6+3+3+3+A) vs 9 = Hit
  21. 16 (7+3+2+2+2) vs 9 = Hit
  22. 16 (6+3+3+2+2) vs 9 = Hit

Six Cards

Basic Strategy Changes:
  1. 12 vs 3 = Stand
  2. 16 vs 9 = Stand
  3. 16 vs 10 = Stand
Exceptions:
  1. 12 (3+3+3+A+A+A) vs 3 = Hit
  2. 12 (3+3+2+2+A+A) vs 3 = Hit
  3. 12 (3+2+2+2+2+A) vs 3 = Hit
  4. 15 (6+5+A+A+A+A) vs 10 = Stand
  5. 16 (6+6+A+A+A+A) vs 10 = Hit
  6. 16 (6+3+2+2+2+A) vs 10 = Hit
  7. 16 (6+6+A+A+A+A) vs 9 = Hit
  8. 16 (7+3+3+A+A+A) vs 9 = Hit
  9. 16 (7+3+2+2+A+A) vs 9 = Hit
  10. 16 (7+2+2+2+2+A) vs 9 = Hit
  11. 16 (6+3+2+2+2+A) vs 9 = Hit

Methodology

The fine points of basic strategy was determined using a combinatronic and recursive program that made the optimal play at every step considering the exact distribution of remaining cards. This program was also used to create the basic strategy charts for one and multiple decks.

Go back to blackjack.
Blackjack appendix 3A: basic strategy exceptions for single deck, dealer stands on soft 17.
Blackjack appendix 3B: basic strategy exceptions for double deck, dealer stands on soft 17.
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