Total Dependent vs. Composition Dependent Basic (original) (raw)
- 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
- External Links
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Total Dependent vs. Composition Dependent Basic
Last updated: Oct 16, 2023
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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.
"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.
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.
Written by: Michael Shackleford