[Home] → Blackjack software and Expected Values by John A. Nairn
Updated: 14 NOV 2008
This web site describes a free Blackjack software package that does many exact calculations of blackjack expected values. Its unique feature is that it can even do exact calculations for pair splitting. Until recent algorithm development by the author, these calculations have not been possible. Although exact splitting calculations are now possible, they are time consuming. This web site, therefore, also 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 free Blackjack software. You can visit the software web site to download the source code and read instructions on how to compile and run the calculations. This software is a command-line tool that can be compiled and run on any platform that supports standard C++ development.
The exact calculation of pair splitting is much more time consuming then all other expected value calculations combined. An estimate predicted that non-optimized or conventional blackjack software methods would take about 11,000 years of computer time to complete all splitting calculations. 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 reduces to 45 days of computer time. The paper also describes an new approximate method that do get accurate splitting results in much less time. The Blackjack software can do both the exact and the approximate methods.
The paper describing the splitting work has recently been submitted to the journal "Journal of Statistical Computation & Simulation." The paper is titled "Exact Calculation of Expected Values for Splitting Pairs in Blackjack" by John A. Nairn. You can download a draft of the submitted paper here.
You can run the Blackjack software to complete exact expected values, 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 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.