  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.
