Cryptologic composition-dependent exceptions



Two cards
Three cards
Four cards
Five cards
Six cards



In single deck blackjack, the effect of the removal of certain cards in certain situations is sufficiently great to enable strategic alterations to be made that marginally improve the expected return. For example: basic strategy says to stand on a 12 against a dealer 4. However, if the 12 is composed of a ten and a two, that ten card reduces by 25% the chance of busting with the draw of another card - there now being only three 10 cards remaining in the deck as opposed to four. Hence, although basic strategy says to stand, "composition dependent" strategy says to hit.

The sum total of all the composition-dependent variations doesn't amount to more than a few tenths of a percent, but in the context of the Cryptologic single deck game the house edge is already sufficiently low for a few tenths extra to make a respectable difference in context. It's quite a hard slog to learn ALL the variations, but if you want to shave the house edge down to the bare minimum it's well worth it. If nothing else, learn a few of the simpler ones such as the two-card and three-card alterations - it makes the game more fun.

(I'm indebted to The Wizard Of Odds for permission for the use of his charts here)

H17 exceptions:

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 (A+5+5+5) vs 7 = Stand
8. 16 (2+4+5+5) vs 7 = Stand
9. 16 (3+3+5+5) vs 7 = Stand
10. 16 (3+4+4+5) vs 7 = Stand
11. 16 (4+4+4+4) vs 7 = Stand
12. 16 (A+5+5+5) vs 8 = Stand
13. 16 (2+4+5+5) vs 8 = Stand
14. 16 (3+3+5+5) vs 8 = Stand
15. 16 (3+4+4+5) vs 8 = Stand
16. 16 (4+4+4+4) vs 8 = Stand
17. 16 (4+4+4+4) vs 9 = Stand
18. 16 (5+4+4+3) vs 9 = Stand
19. 16 (5+5+3+3) vs 9 = Stand
20. 16 (5+5+4+2) vs 9 = Stand
21. 16 (5+5+5+A) vs 9 = Stand
22. 16 (6+4+4+2) vs 9 = Stand
23. 16 (6+5+4+A) vs 9 = Stand
24. 16 (8+3+3+2) vs 9 = Stand
25. 16 (8+4+2+2) vs 9 = Stand
26. 16 (8+4+3+A) vs 9 = Stand
27. 16 (8+5+2+A) vs 9 = Stand
28. 16 (9+5+A+A) vs 9 = Stand
29. 16 (9+4+2+A) vs 9 = Stand
30. 16 (6+6+2+2) vs 10 = Hit
31. 16 (6+6+3+A) vs 10 = Hit
32. 16 (7+6+2+A) vs 10 = Hit
33. 16 (8+6+A+A) vs 10 = Hit
34. 16 (10+2+2+2) vs 10 = Hit
35. Soft 18 (3+2+2+A) vs 10 = Stand
36. Soft 18 (3+2+2+A) vs A = 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 (A+A+4+5+5) vs 7 = Stand
9. 16 (A+2+3+5+5) vs 7 = Stand
10. 16 (A+2+4+4+5) vs 7 = Stand
11. 16 (A+3+3+4+5) vs 7 = Stand
12. 16 (A+3+4+4+4) vs 7 = Stand
13. 16 (2+2+2+5+5) vs 7 = Stand
14. 16 (2+2+3+4+5) vs 7 = Stand
15. 16 (2+2+4+4+4) vs 7 = Stand
16. 16 (2+3+3+3+5) vs 7 = Stand
17. 16 (2+3+3+4+4) vs 7 = Stand
18. 16 (3+3+3+3+4) vs 7 = Stand
19. 16 (A+A+4+5+5) vs 8 = Stand
20. 16 (A+2+3+5+5) vs 8 = Stand
21. 16 (A+2+4+4+5) vs 8 = Stand
22. 16 (A+3+3+4+5) vs 8 = Stand
23. 16 (A+3+4+4+4) vs 8 = Stand
24. 16 (2+2+2+5+5) vs 8 = Stand
25. 16 (2+2+3+4+5) vs 8 = Stand
26. 16 (2+2+4+4+4) vs 8 = Stand
27. 16 (2+3+3+3+5) vs 8 = Stand
28. 16 (2+3+3+4+4) vs 8 = Stand
29. 16 (3+3+3+3+4) vs 8 = Stand
30. 16 (10+3+A+A+A) vs 9 = Hit
31. 16 (7+6+A+A+A) vs 9 = Hit
32. 16 (10+2+2+A+A) vs 9 = Hit
33. 16 (7+5+2+A+A) vs 9 = Hit
34. 16 (6+6+2+A+A) vs 9 = Hit
35. 16 (7+4+3+A+A) vs 9 = Hit
36. 16 (7+4+2+2+A) vs 9 = Hit
37. 16 (7+3+3+2+A) vs 9 = Hit
38. 16 (6+3+3+3+A) vs 9 = Hit
39. 16 (7+3+2+2+2) vs 9 = Hit
40. 16 (6+3+3+2+2) vs 9 = Hit
41. 16 (6+3+3+2+2) vs 10 = Hit
42. 16 (7+6+A+A+A) vs 10 = Hit
43. 16 (10+2+2+A+A) vs 10 = Hit
44. 16 (6+6+2+A+A) vs 10 = Hit

Six Cards


Basic Strategy Changes:
1. 12 vs 3 = Stand
2. 16 vs 7 = Stand
3. 16 vs 9 = Stand
4. 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 (A+A+A+A+3+9) vs 7 = Hit
6. 16 (A+A+A+A+6+6) vs 7 = Hit
7. 16 (A+A+A+2+2+9) vs 7 = Hit
8. 16 (A+A+A+3+5+5) vs 8 = Stand
9. 16 (A+A+2+2+5+5) vs 8 = Stand
10. 16 (A+A+2+3+4+5) vs 8 = Stand
11. 16 (A+A+2+4+4+4) vs 8 = Stand
12. 16 (A+A+3+3+3+5) vs 8 = Stand
13. 16 (A+A+3+3+4+4) vs 8 = Stand
14. 16 (A+2+2+2+4+5) vs 8 = Stand
15. 16 (A+2+2+3+3+5) vs 8 = Stand
16. 16 (A+2+2+3+4+4) vs 8 = Stand
17. 16 (A+2+3+3+3+4) vs 8 = Stand
18. 16 (2+2+2+2+3+5) vs 8 = Stand
19. 16 (2+2+2+2+4+4) vs 8 = Stand
20. 16 (2+2+2+3+3+4) vs 8 = Stand
21. 16 (2+2+3+3+3+3) vs 8 = Stand
22. 16 (6+6+A+A+A+A) vs 9 = Hit
23. 16 (7+3+3+A+A+A) vs 9 = Hit
24. 16 (7+3+2+2+A+A) vs 9 = Hit
25. 16 (7+2+2+2+2+A) vs 9 = Hit
26. 16 (6+3+2+2+2+A) vs 9 = Hit
27. 16 (6+6+A+A+A+A) vs 10 = Hit
28. 16 (6+3+2+2+2+A) vs 10 = Hit


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