Appendices
1: Total dependent expected return table for an infinite deck
2a: Probabilities of dealer blackjack after peek
2b: Probabilities of dealer blackjack before peek
3a: Exceptions to single-deck S17 basic strategy
3b: Exceptions to double-deck S17 basic strategy
3c: Exceptions to single-deck H17 basic strategy
4: Blackjack standard deviation details
5: Infinite deck expected return by player hand and dealer upcard
6: Fine points of when to surrender
7: Effect of card removal
8: Analysis of blackjack side bets
9: Composition-dependent expected returns for 1 to 8 decks
10: Continuous shuffling machine vs. cut card
11: Value and strategy for 678 and 777 bonuses
12: Risk of ruin statistics
13: Probabilities in the first four cards
14: Value of each initial player card
15: House edge using total-dependent vs. composition-dependent basic strategy
16: Basic strategy when dealer exposes both cards
17: The Ace-Five card counting method
18: Basic strategy exceptions for three to six cards
19: Blackjack splitting strategy when a back-player is betting
20: Blackjack doubling strategy when doubling after splitting aces is allowed
21: Details on the Wizard\’s Simple Strategy
Miscellaneous
My comments on the movie "21"
Australian Blackjack
Introduction to Card Counting
Rule Variations
Blackjack "Charlie" Rule
Rummy (Blackjack variant popular in Costa Rica)
External Links
Macau Blackjack rules
Simple Blackjack Explanation
Total Dependent vs. Composition Dependent Basic
Introduction
Most blackjack basic strategy charts are said to be "total dependent." That means the total of the player's cards is considered, but not the specific composition. Total dependent basic strategy also considers whether the hand is soft or hard, and whether doubling, splitting, or surrender is possible. The following links are to total dependent strategy charts.
1 deck - total dependent
2 decks - total dependent
4 or more decks - total dependent
"Composition dependent" is used to describe blackjack strategy where the player makes use of not just the total of his cards but the composition as well. The fewer the decks the more beneficial using composition dependent basic strategy is. For example in single-deck blackjack the player should normally stand with 12 against a 4. However if the 12 is composed of a 10 and a 2 the odds favor hitting. Here is a link to a composition dependent strategy.
1 deck - composition dependent
This appendix addresses the question of how much benefit is there to using composition dependent strategy compared to total dependent. The following table shows the house edge both ways under 32 sets of rules. In all cases surrender is not allowed and the player may not resplict aces.
Total Dependent and Composition Dependent Basic Strategy House Edge
| Decks | Dealer Stands on Soft 17 |
Double after Split |
Total Dependent |
Composition Dependent |
Difference |
|---|---|---|---|---|---|
| 1 | N | N | 0.1881% | 0.1518% | 0.0364% |
| 1 | N | Y | 0.0438% | 0.0077% | 0.0361% |
| 1 | Y | N | -0.0026% | -0.0416% | 0.039% |
| 1 | Y | Y | -0.1442% | -0.1829% | 0.0387% |
| 2 | N | N | 0.5365% | 0.5253% | 0.0113% |
| 2 | N | Y | 0.3911% | 0.3799% | 0.0112% |
| 2 | Y | N | 0.335% | 0.321% | 0.014% |
| 2 | Y | Y | 0.1923% | 0.1783% | 0.014% |
| 3 | N | N | 0.6505% | 0.644% | 0.0065% |
| 3 | N | Y | 0.5053% | 0.4988% | 0.0066% |
| 3 | Y | N | 0.4424% | 0.4342% | 0.0082% |
| 3 | Y | Y | 0.3001% | 0.2918% | 0.0083% |
| 4 | N | N | 0.7067% | 0.7021% | 0.0046% |
| 4 | N | Y | 0.5617% | 0.5572% | 0.0045% |
| 4 | Y | N | 0.4951% | 0.4896% | 0.0055% |
| 4 | Y | Y | 0.353% | 0.3475% | 0.0055% |
| 5 | N | N | 0.7404% | 0.7369% | 0.0035% |
| 5 | N | Y | 0.5957% | 0.5922% | 0.0035% |
| 5 | Y | N | 0.5268% | 0.5228% | 0.004% |
| 5 | Y | Y | 0.3849% | 0.3808% | 0.004% |
| 6 | N | N | 0.7629% | 0.7602% | 0.0028% |
| 6 | N | Y | 0.6184% | 0.6156% | 0.0028% |
| 6 | Y | N | 0.548% | 0.5449% | 0.0031% |
| 6 | Y | Y | 0.4062% | 0.4031% | 0.0031% |
| 7 | N | N | 0.779% | 0.7768% | 0.0023% |
| 7 | N | Y | 0.6346% | 0.6324% | 0.0023% |
| 7 | Y | N | 0.5631% | 0.5607% | 0.0024% |
| 7 | Y | Y | 0.4214% | 0.419% | 0.0024% |
| 8 | N | N | 0.7911% | 0.7892% | 0.0019% |
| 8 | N | Y | 0.6468% | 0.6449% | 0.0019% |
| 8 | Y | N | 0.5744% | 0.5725% | 0.0019% |
| 8 | Y | Y | 0.4329% | 0.431% | 0.0019% |
The table above shows that using composition dependent strategy gives the player an extra 0.036% with a single deck. That will result in one extra bet about once every 2,800 hands. The benefit quickly tapers off after one deck.
Acknowledgements
I would like to extend much thanks to blackjack genius Scott E. for the above table, which is in close agreement to my own figures on this topic.