card probability

Hi, Im trying to calculate the probability of the dealer beeating 4
hands when you know what the players hands are. Im using an Infinete
Deck. So far Ive managed to calculate probabilitys when there is an
intial scenario and a 2nd scenerio dependant on an open hand, for
example the Dealer has 5 6 4 =15. players 1 to 4 are standing on 20,
16, 18, 19. So the dealer has to beat 20. The dealers possible hands
are: (from infinite deck)
5 6 4 2 S 17
5 6 4 3 S 18
5 6 4 4 S 19
5 6 4 5 S 20
5 6 4 6 S 21
5 6 4 7 B 22
5 6 4 8 B 23
5 6 4 9 B 24
5 6 4 T B 25
5 6 4 A H 16
5 6 4 J B 25
5 6 4 Q B 25
5 6 4 K B 25 which is the first scenario and :
5 6 4 A 2 S 18
5 6 4 A 3 S 19
5 6 4 A 4 S 20
5 6 4 A 5 S 21
5 6 4 A 6 B 22
5 6 4 A 7 B 23
5 6 4 A 8 B 24
5 6 4 A 9 B 25
5 6 4 A T B 26
5 6 4 A A B 17
5 6 4 A J B 26
5 6 4 A Q B 26
5 6 4 A K B 26 which is the second scenario.
The calcs Ive used as adviced prev are:

Only 2 of the possible 13 scenarios (out of 1st turn of card) make the
dealer a winner ( cards 5 and 6), 1 cards leaves the game open: A, and
the other 10 cards kill the game making the dealer a loser.

So P1 = 2/13 = 0.1538 ( winner in 2 out of 13 scenarios) .
when an Ace was dealt there is 13 additional scenarios: In 5 the dealer
is a winner ( A, 2, 3, 4, 5), in the other 8, the dealer is a loser.

P2 = 5/13 * 1/13. ( 5 winners out of 13) depends in getting an initial
ace ( 1 out of 13 cards)

P2 = 5/13 * 1/13 = 0.0296.

Ptotal = P1 + P2 (probability of any of the two cases happening) =
0.1538 + 0.0296 = 0.1834

OddsTotal = 1/Ptotal = 1/ 0.1834 = 5.45

This I can do, my problem is with this example the additional scenario
depended on one card the ace. If I have a low card like 2, and it needs
to beat 20, my additional cards are 2 through to king, as a turn on
the first round does not cause a stand or bust. How do I take
additional scenarios into consideration. Also a 5cards charlie beets
blackjack so Im assuming that I must consider this in the calcs as
well.

I hope Ive explained my problem ok. VBasically Ive an infinete deck and
whats the probability of the dealer having a 2, going on to beat a
players 20.

Regards Robert

.

Relevant Pages

  • Re: OT: Blackjack
    ... with an 11 for all dealer cards, EXCEPT an ace. ... Given that 8 deck shoes are less favorable to the player than a 6 deck ...
    (rec.gambling.poker)
  • Re: OT: Blackjack
    ... with an 11 for all dealer cards, ... S17, Dealer peek, NoSurrender table that pays 3 to 2. ... Given that 8 deck shoes are less favorable to the player than a 6 deck ... If there was no dealer peek on an ace then I'd just hit. ...
    (rec.gambling.poker)
  • Re: A blackjack story...
    ... random as a shuffled deck can be). ... mind concerning their play. ... the dealer to every player and themselves. ... player breaks the cards are collected. ...
    (alt.vacation.las-vegas)
  • Re: what are the odds?
    ... a deck of cards and carefully shuffle it. ... man idea and then caculates the probability of that. ... the probability that all the necessary mutations took place is ...
    (talk.origins)
  • Re: what are the odds?
    ... a deck of cards and carefully shuffle it. ... The thing that creationists attempting probability never understand is ... have designed imperfect replicators. ...
    (talk.origins)