Gambling GuideTotal 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.
"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
