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Thread: davek: double vs 6 deck

  1. #1
    davek
    Guest

    davek: double vs 6 deck

    I "know" you have better odds the fewer the decks, even if you play straight basic strategy, but when a friend of mine asked why I really could not articulate why and I don't recall anyone ever explaining why, at least in any plain english a layman could understand. I know it has to do with the fact there are more "bad" cards to draw from but that doesn't sound very scientific. Could someone here give me a better explanation?

    Thanks

    daveK

  2. #2
    Dancer
    Guest

    Dancer: More Blackjacks

    > I "know" you have better odds the
    > fewer the decks, even if you play straight
    > basic strategy, but when a friend of mine
    > asked why I really could not articulate why
    > and I don't recall anyone ever explaining
    > why, at least in any plain english a layman
    > could understand. I know it has to do with
    > the fact there are more "bad"
    > cards to draw from but that doesn't sound
    > very scientific. Could someone here give me
    > a better explanation?

    > Thanks

    > daveK

    The experts may weigh in with more esoteric reasons, but the most obvious is that you'll get more blackjacks with fewer decks.

    1 Deck Probabilities (to 3 significant figures)
    Ace on first card: 4/52
    Ten on second card: 16/51
    Ace first blackjack: 4/52 X 16/51 = .024

    Ten on first card: 16/52
    Ace on second card: 4/51
    Ten first blackjack: 16/52 X 4/51 = .024

    Probability of 1 deck blackjack: .024 + .024 = .048 (about 1 out of 20.8 hands)

    6 Deck Probabilities
    Ace on first card: 24/316
    Ten on second card: 96/315
    Ace first blackjack: 24/316 X 96/315 = .023

    Ten on first card: 96/316
    Ace on second card: 24/315
    Ten first blackjack: 96/316 X 24/315 = .023

    Probability of 6 deck blackjack: .023 + .023= .046 (about 1 out of 21.7 hands)

    Of course, the dealer gets more blackjacks as well, but he doesn't get paid 3:2 for his.

  3. #3
    Dancer
    Guest

    Dancer: Math Correction

    > The experts may weigh in with more esoteric
    > reasons, but the most obvious is that you'll
    > get more blackjacks with fewer decks.

    > 1 Deck Probabilities (to 3 significant
    > figures)
    > Ace on first card: 4/52
    > Ten on second card: 16/51
    > Ace first blackjack: 4/52 X 16/51 = .024

    > Ten on first card: 16/52
    > Ace on second card: 4/51
    > Ten first blackjack: 16/52 X 4/51 = .024

    > Probability of 1 deck blackjack: .024 + .024
    > = .048 (about 1 out of 20.8 hands)

    > 6 Deck Probabilities
    > Ace on first card: 24/316
    > Ten on second card: 96/315
    > Ace first blackjack: 24/316 X 96/315 = .023

    > Ten on first card: 96/316
    > Ace on second card: 24/315
    > Ten first blackjack: 96/316 X 24/315 = .023

    > Probability of 6 deck blackjack: .023 +
    > .023= .046 (about 1 out of 21.7 hands)

    > Of course, the dealer gets more blackjacks
    > as well, but he doesn't get paid 3:2 for
    > his.

    I somehow went brain dead and put 316 cards in 6 decks rather than 312. The actual numbers (to 5 significant figures) are:

    Probability of 1 deck BJ: 0.04827 (about 1 out of 20.72 hands)
    Probability of 6 deck BJ: 0.04749 (about 1 out of 21.06 hands)

  4. #4
    Sun Runner
    Guest

    Sun Runner: I'll take a shot

    The number one reason is .. fluxuation.
    (Man I hope that's right?!)

    Bigger faster swings in the count.

    SD, the count is up/down on every hand.
    8Ds, the count acts more like a lazy river.

    You better have your big bets ready and not be snoozin' when the count goes bad because the fewer the decks, the quicker it takes place.

    Right before your eyes.

  5. #5
    onetoomany
    Guest

    onetoomany: Re: double vs 6 deck

    I believe that with fewer decks there is much less chance that the dealer will get a blackjack at the same time a player gets one. The number of player blackjacks does increase slightly with fewer decks, but it isn't by a lot.

    Someone correct me on this if I have it wrong.

  6. #6
    Brick Waller
    Guest

    Brick Waller: Correction

    Who told you this?

    The dealers odds of blackjack are exactly the same. Why would it be any different? On the first 2 cards dealers have exactly the same odds as getting the same hand as anyone else,including all the stiffs.

    > I believe that with fewer decks there is
    > much less chance that the dealer will get a
    > blackjack at the same time a player gets
    > one. The number of player blackjacks does
    > increase slightly with fewer decks, but it
    > isn't by a lot.

    > Someone correct me on this if I have it
    > wrong.

  7. #7
    Fuzzy Math
    Guest

    Fuzzy Math: Re: Correction

    > Who told you this?

    > The dealers odds of blackjack are exactly
    > the same. Why would it be any different? On
    > the first 2 cards dealers have exactly the
    > same odds as getting the same hand as anyone
    > else,including all the stiffs.

    If there are 2 cards removed from 2 decks and there are 7 aces remaining, is the dealer's chance of getting an ace the same as if 2 cards were removed from 6 decks and only 23 aces remain?

  8. #8
    Parker
    Guest

    Parker: No

    > I believe that with fewer decks there is
    > much less chance that the dealer will get a
    > blackjack at the same time a player gets
    > one. The number of player blackjacks does
    > increase slightly with fewer decks, but it
    > isn't by a lot.

    > Someone correct me on this if I have it
    > wrong.

    Um, you have it wrong.

    As Dancer illustrated, the player will get more blackjacks with fewer decks.

    Since the dealer is dealt the cards at the same time, the dealer will also get more blackjacks.

    Now, if the player and the dealer are both getting more blackjacks, then it stands to reason that they will also get more of them at the same time.

    However, (again as Dancer pointed out), the 3:2 BJ payout means that the player will come out ahead for the ones that do not occur at the same time. When the player and the dealer both have blackjack it is a push, so it doesn't hurt anything.

    Note that the 3:2 blackjack payout is central to all of this. This is why it screws the game up so badly when the casinos start messing with the blackjack payout, a la 6:5 games.

  9. #9
    onetoomany
    Guest

    onetoomany: Re: No

    Hi Parker,

    My reasoning was something like this:

    Heads-up game, 1 deck, I get an ace and something else, dealer has a 3/50 chance of getting an ace. (3 aces left in deck, 50 cards left in deck). So there is a 6% chance he will get an ace on the same round as I.

    In 6 deck, he would have a 23/310 chance, about 7.4%.

    I know the dealer has the same chance as any player to get a blackjack. The comment was that there is less chance the dealer will get a blackjack in the same round that a player does, when there are fewer decks.

    Are you saying that the number of decks does not affect the chance of a dealer matching a player's blackjack on the same round?

    I'm ready to be edgeamacated........

  10. #10
    Parker
    Guest

    Parker: No ... really

    > Hi Parker,

    > My reasoning was something like this:

    > Heads-up game, 1 deck, I get an ace and
    > something else, dealer has a 3/50 chance of
    > getting an ace. (3 aces left in deck, 50
    > cards left in deck). So there is a 6% chance
    > he will get an ace on the same round as I.

    > In 6 deck, he would have a 23/310 chance,
    > about 7.4%.

    Except that the cards aren't dealt like that. The dealer gives everyone a first card, including him/herself, and then deals the second card.

    Sure, if you get an ace, the dealer is less likely to get a blackjack, but what about the times when the dealer gets the first ace? They cancel out.

    > I know the dealer has the same chance as any
    > player to get a blackjack. The comment was
    > that there is less chance the dealer will
    > get a blackjack in the same round that a
    > player does, when there are fewer decks.

    > Are you saying that the number of decks does
    > not affect the chance of a dealer matching a
    > player's blackjack on the same round?

    No, I'm saying that the dealer is more likely to match a player's blackjack in a game with fewer decks, and it doesn't mean anything.

  11. #11
    Norm Wattenberger
    Guest

    Norm Wattenberger: Actally, this is interesting

    Although it is more likely for a BJ to appear in single deck, it is less likely for two BJs at the same time. Look at it this way, it is unlikely to see five BJs in one round in six decks. It is impossible in SD.


  12. #12
    onetoomany
    Guest

    onetoomany: Re: Actally, this is interesting

    This is what I'd thought, that with fewer decks you are less likely to have your blackjack canceled by the dealer getting one also on the same round. With a player holding an ace there are simply fewer of them left in deck for dealer to get one on the same round, and the effect is more pronounced in single deck than 6 deck. To me it's kinda like the reason you don't hit a pair of sevens in single deck against dealer 10. I agree that the dealer has the same chance as a player to get a blackjack overall in any given game, but the chances of a player and the dealer both getting blackjacks in the same round are lower when there are fewer decks, right?


  13. #13
    Dancer
    Guest

    Dancer: Well...

    > I'm saying that the dealer is more
    > likely to match a player's blackjack in a
    > game with fewer decks.

    I was firmly in your camp on this one, Parker. I consulted CVData, though, and now I'm not so sure. According to the stats below, the probability of pushing with a BJ increases with the number of decks. The data comes from 2 sims of 250 million hands each. Both played BS, so pen shouldn't be an issue.

    1 Deck (Pen 75%)
    Probability of being dealt BJ: 4.786% (about 1 every 20.89 hands)
    Probability of BJ push vs. dealer's 10: .061
    Probability of BJ push vs. dealer's A: .303
    Total probability of BJ push: .036 (About 1 out of every 27.78 BJ's)

    6 Deck (Pen 83% - 5/6)
    Probability of being dealt BJ: 4.745% (about 1 every 21.07 hands)
    Probability of BJ push vs. dealer's 10: .074
    Probability of BJ push vs. dealer's A: .308
    Total probability of BJ push: .046 (About 1 out of every 21.74 BJ's)

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