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Exercise If utility

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.

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Table Talk
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.