The computer
technique of altering normal decks so as to produce
rich or lean mixtures for investigating different
situations has not always incorporated an accurate
alteration of conditional probabilities corresponding
to the extreme values of the parameter assumed. The
proper approach can be derived from bivariate normal
assumptions and consists of maintaining the usual
density for zero valued cards and displacing the other
denominations in proportion to their assigned point
values, rather than just their algebraic signs. [A]
As an
example of the technical difficulties still to be
encountered consider a +8126 Hi Opt i deck. Computer
averaging of all possible decks with this count leaves
us with a not surprising "ideal" deck of
tilve tens, one each three, four, five, and six, and
two of everything else. it is by no means likely,
hoiver, that the favorabilities for this "ideal"
deck will be precisely the average of those from all
possible +8126 decks (of which the non-ideal far outnumber
the ideal). it would, for instance, be impossible
to be dealt a pair of threes from such an ideal deck;
a more reasonable estimate of the probability of this
is 1/26 x 3/25 x 3/15, but even this is imprecise
in the 3/25 which complete analysis shows to be 3.17828/25.
There is at present no completely satisfactory resolution
of such quandaries and even the most carefully computerized
critical indices have an element of faith in them. |

Stud
eight-or-better is dealt almost exactly the almost
as the high version with a few minor exceptions. Normally
the low card still makes the bring-in (games that
use a high-card bring-in are not unheard of, but are
rare), but that's often not the burden that it is
in high-only stud; low cards can be very valuable
in stud eight-or-better. Also, there is no "double
bet on an open pair" option in stud eight-or-better.
The first two rounds are played at the single bet
level and the final three at the double bet level,
regardless of what cards are out. |