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Blackjack Player: You are player number 1035 Description: Blackjack is one of the most popular Casino games black jack casino - Tips :
THE BLACK JACK DEALER'S EXACT PERCENTAGE TAKE-2
It is, of course, not feasible to figure the exact percentage against individual players because their play differs so much. Some players will stay on 12, 13 and 14; some will draw on 15 and 16; others stay on 15 or more; and there's always the dub who will draw to an ace and nine.
However, since the dealer has no choice whether to stay or draw, because the rules predetermine this, we can calculate the exact percentage working in his favor. It isn't easy, but it can be done. We know first that the banker's hidden advantage lies in the fact that the player must play first, and if dealer and player both bust at a count above 21 the player loses his bet. If it were not for this (and if, when the dealer's face-up card was dealt face down the bank paid off a natural at even-money odds, and a player could not split pairs or double down) the game would be an even-up proposition.
There is also another complication. Unlike the bank's P.C. at Craps and Roulette, which doesn’t vary, the bank’s P.C. at Black Jack changes considerably during the play? It goes up or down as each card is dealt. The following analysis therefore must be based on a full-deck composition. We assume, for purposes of analysis, that all 52 cards are present, none having yet been dealt.
Next, we find out how many dealer busts may be expected in the long run. We make use of the standard permutation and combination formulas, plus some straight thinking and simple arithmetic. We calculate how many different ways (using a 52-card deck) the dealer's initial two face-down cards can produce all the possible counts. Like this:
We find that the dealer's first two cards can produce the counts from 2 through 21 in 1,326 different ways. Note that the player can count an ace as either 1 or 11, but the dealer must count the ace as 11 in all soft hands with a count of 17 or more; the above table is figured on that premise. We won't try to calculate how many hands out of these 1,326 the dealer will bust, because we'll run into too many fractions. We11 discover what we need to know, however, and avoid most of the fractions, if we multiply 1,326 X 169 to get a common multiple of 224,094. Now suppose your favorite dealer dealt this many hads and suppose each combination of two cards appeared exactly as often as probability theory predicts it will in the long run
Two-card counts of 17, 18, 19, 20 and 21 will show up 462 times out of 1,326, which is 462/1326 X 224,094 = 78,078 times. The Black Jack rules demand that the dealer must stay on all these hands, so he cannot bust on any of them.
Two-card counts of 12, 13, 14, 15 and 16 will be held by the dealer 514 times out of 1,326 or 514/1,326 X 224,094 = 86,866 times.
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