Exact Calculation of Expected Values for Splitting Pairs in Blackjack

TL;DR

This paper introduces a highly efficient algorithm for exact calculation of pair splitting expected values in blackjack, enabling precise results for single-deck games and improving upon prior approximate methods.

Contribution

A novel algorithm significantly reduces computation time for exact pair splitting calculations, allowing for the first complete results in single-deck blackjack and improved resplitting approximations.

Findings

Exact pair splitting results for single-deck blackjack obtained.

Prior approximate theories are accurate generally but fail for resplitting tens.

New approximation method improves accuracy for all resplitting scenarios.

Abstract

Computer calculations for most exact expected values in blackjack have been available since the 1960's, but exact results for pair splitting and resplitting have previously been too computer intensive. This paper describes a new algorithm for exact pair-splitting. By using dealer probability caching methods and revising the method for recursively generating possible player hands, the estimated calculation time compared to standard methods was reduced by five orders of magnitude. The resulting algorithm was used to calculate the first exact and complete pair splitting results for a single deck game. The exact results were compared to prior approximate theories for resplitting. The prior theories are accurate for many calculations, but inaccurate for resplitting tens. A new approximation method was developed that is accurate for all resplitting calculations.