[Home] → Blackjack software and Expected Values by John A. Nairn
Updated: 22 SEP 2019
This web site posts results run using a public domain software package (which is available in a Blackjack project on GitHub) that does many exact calculations of blackjack expected values. The software's unique feature is that it can even do exact calculations for pair splitting. Until a recent algorithm developed by the author, these calculations have not been possible. Although exact splitting calculations are now possible, they are time consuming. This web site, therefore, has tables of exact expected values output from the software. You can use them without needing to download and run the software.
All tables of expected values given below were calculated using the public domain software package available in the Blackjack project on GitHub. You can clone that project to learn how to compile the code and run calculations.
The exact calculation of pair splitting is much more time consuming then all other expected value calculations combined. An estimate based on scaling effects with conventional blackjack software methods showed that a convential approach would take about 11,000 years of computer time (on 3GHz processors) to complete all splitting calculations for a single-deck game. Fortunately, it is possible to do better. The author of the Blackjack software has written a paper describing the process. The final result was that all splitting calculations were reduced to 45 days of computer time. The paper also describes an new approximate method that can get accurate splitting results in much less time. The Blackjack software can do both the exact and the approximate calculations.
The paper describing the new splitting methods is titled "Exact Calculation of Expected Values for Splitting Pairs in Blackjack" by John A. Nairn. A copy of the paper is included in the Blackjack project and posted here.
You can obtain and run the Blackjack software software to complete exact expected value calculations, but some of those calculations take a long time. The longest, by far, are the exact results for splitting. Alternatively, you can just look up many results in the tables listed below. These tables are direct output from the Blackjack software (formatted for nice display) for most expected values. Exact results for splitting have only been completed for the single deck game. All tables, however, include the new approximate, but accurate, splitting results.