Black Jack Appendix 9
This is the table of contents for all my composition dependent expected return tables.
- One deck, dealer stands on soft 17
- One deck, dealer hits on soft 17
- Two decks, dealer stands on soft 17
- Two decks, dealer hits on soft 17
- Four decks, dealer stands on soft 17
- Four decks, dealer hits on soft 17
- Six decks, dealer stands on soft 17
- Six decks, dealer hits on soft 17
- Eight decks, dealer stands on soft 17
- Eight decks, dealer hits on soft 17
I used a recursive program to make the optimal strategy at every decision
point according to the exact deck composition. The expected values for splits
were based on one hand only and weighted by the expected number of other similar
hands the player would obtain. This is a very close approximation but not 100%
accurate. The program would have taken many days to run had it played out each
resplit hand individually.
Other sources for these expected values are Cacarulo's at http://www.bjmath.com/bjmath/ev/ev.htm
and Cindy's at http://www.gamblingtools.net/bj/ppbj.html.
Neither of these sources agree with me, and do not agree with each other, on the
expected value of split hands, although we are all very close. For example here
are the expected value for splitting eights against a dealer 10 under these
rules: single deck, dealer hits soft 17, double after split not allowed.
Wizard: -.457220
Cacarulo: -.45784
Cindy: -.4586
The greater the number of decks the less the differences are. In my opinion
these differences should not be interpreted that at least two of us are wrong,
but that we all use slightly different methodologies.
