[QUIZ] Studying Blackjack (#151)

Discussion in 'Ruby' started by Ruby Quiz, Jan 4, 2008.

  1. Ruby Quiz

    Ruby Quiz Guest

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    -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

    The majority of the strategy in Blackjack hinges around the dealer's hand. The
    reasons are likely obvious to most of you: that's the hand you have to beat and
    the dealer plays by fixed rules we can predict.

    For those unfamiliar with Blackjack, you only need to know a tiny bit about the
    game for the purposes of this exercise. The goal for both the player and the
    dealer is to draw cards to make a hand with the highest total possible, without
    going over 21. Going over 21 is called "busting" and it means you lose the
    hand. Face cards count for ten, aces are one or eleven (whichever is better for
    the hand), and all other cards count for their face value. You start with two
    cards and, if they happen to be a ten valued card and an ace (a count of 21),
    the hand is called a "natural." A natural is an automatic win in most cases.

    The dealer begins with one of his two cards face up and one face down. We call
    the former the "upcard." The dealer will "hit" or take more cards until he
    reaches a count of 17 or higher. After that he will "stand" or leave the hand
    where it is. That tells us that there are only seven possible outcomes for the
    dealer: get dealt a natural, bust, or hit to a total of 17, 18, 19, 20, or 21.

    We start every hand knowing half of what the dealer holds thanks to the upcard.
    Believe it or not, you can make pretty reliable guesses about how the hand will
    go with just that knowledge.

    Write a Ruby program that shows the percent chance of a dealer reaching each
    possible outcome based on the upcard showing.

    I'll give you some hints to verify your results. Basic Blackjack strategy
    teaches that we should assume the dealer "has a ten in the hole" (as the face
    down card). It's not always true, of course, but 17 is a common outcome for a
    dealer with an upcard of seven. Finally, we call five and six "the dealer's
    bust cards" for reasons that will become obvious if you are outputting correct
    percentages.

    In the casinos Blackjack is often played with more than one deck shuffled
    together. One, two, six, and eight deck games are common. You may want to
    offer the option to adjust the deck size your program uses. Either way, let's
    default to two decks as an average of what a player will face.
    Ruby Quiz, Jan 4, 2008
    #1
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  2. > Write a Ruby program that shows the percent chance of a dealer
    > reaching each
    > possible outcome based on the upcard showing


    Are we able to post partial / full outcomes within the 48 hours?

    Cheers,
    Dave
    Sharon Phillips, Jan 4, 2008
    #2
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  3. Ruby Quiz

    James Gray Guest

    On Jan 4, 2008, at 4:27 PM, Sharon Phillips wrote:

    >> Write a Ruby program that shows the percent chance of a dealer
    >> reaching each
    >> possible outcome based on the upcard showing

    >
    > Are we able to post partial / full outcomes within the 48 hours?


    You bet. Feel free.

    James Edward Gray II
    James Gray, Jan 4, 2008
    #3
  4. Ruby Quiz

    Chris Guest

    Re: Studying Blackjack (#151)

    > > Are we able to post partial / full outcomes within the 48 hours?
    > You bet.  Feel free.


    Here's mine so far, my first ruby quiz !

    Upcard Bust 17 18 19 20 21 Natural
    c1 26.20% 16.80% 13.00% 14.20% 13.90% 15.90% 0.00%
    c2 38.80% 14.60% 11.40% 11.00% 12.30% 11.90% 0.00%
    c3 40.50% 14.40% 13.40% 11.20% 12.00% 8.50% 0.00%
    c4 38.00% 15.20% 14.30% 11.70% 10.70% 10.10% 0.00%
    c5 42.30% 12.80% 12.30% 11.80% 9.20% 11.60% 0.00%
    c6 39.10% 23.50% 10.30% 10.00% 8.80% 8.30% 0.00%
    c7 25.60% 35.40% 14.00% 10.70% 6.50% 7.80% 0.00%
    c8 23.70% 13.00% 33.60% 16.20% 6.20% 7.30% 0.00%
    c9 21.90% 10.50% 11.90% 35.90% 12.90% 6.90% 0.00%
    ct 19.40% 12.50% 10.90% 11.20% 31.70% 5.10% 9.20%
    cj 19.70% 14.40% 10.60% 12.30% 29.90% 5.80% 7.30%
    cq 18.90% 13.50% 10.90% 10.30% 32.20% 6.60% 7.60%
    ck 19.50% 12.30% 12.80% 11.10% 31.90% 6.00% 6.40%
    ca 14.00% 13.40% 14.40% 13.10% 12.60% 4.10% 28.40%


    Seems to satisfy the hints given in the quiz, but I'm still not sure
    if I deal with the case where the dealer gets dealt two or more aces
    correctly.

    Chris
    Chris, Jan 5, 2008
    #4
  5. Ruby Quiz

    Eric I. Guest

    Re: Studying Blackjack (#151)

    Here are my results. I combined the 10 and the face cards in one row
    since they're essentially equivalent. And the data was generated by
    doing 10,000 deals per upcard.

    upcard bust 17 18 19 20 21
    natural
    ------ ------- ------- ------- ------- ------- -------
    -------
    2 | 35.95% 13.32% 13.17% 13.34% 12.44% 11.78%
    0.00%
    3 | 37.85% 13.41% 12.93% 11.69% 12.51% 11.61%
    0.00%
    4 | 40.14% 13.24% 11.86% 12.03% 11.48% 11.25%
    0.00%
    5 | 41.80% 12.82% 12.32% 11.41% 11.34% 10.31%
    0.00%
    6 | 41.76% 17.65% 10.59% 10.36% 10.04% 9.60%
    0.00%
    7 | 26.77% 36.23% 13.53% 8.29% 7.88% 7.30%
    0.00%
    8 | 24.96% 12.84% 35.69% 12.73% 7.04% 6.74%
    0.00%
    9 | 22.98% 12.27% 10.69% 35.47% 12.22% 6.37%
    0.00%
    10 | 21.61% 11.21% 11.68% 11.23% 32.97% 3.55%
    7.75%
    ace | 11.60% 12.33% 13.03% 13.06% 13.43% 5.27%
    31.28%

    I do wonder, though, whether the deck is biased somehow when the
    dealer deals him/herself since all the players are dealt beforehand.
    For example, it seems a player is more likely to consume a sequence of
    low cards through consecutive hits than a sequence of high cards. So
    depending on the number of players at the table, the cards the dealer
    is likely to get may change somewhat. And perhaps the dealer's odds
    change further the deeper into the shoe the table gets. Does anyone
    know?

    Eric

    ====

    Are you interested in on-site Ruby training that uses well-designed,
    real-world, hands-on exercises? http://LearnRuby.com
    Eric I., Jan 5, 2008
    #5
  6. Ruby Quiz

    Joe Guest

    Re: Studying Blackjack (#151)

    I didn't think it was supposed to be run a specific number of times,
    but go over all possibilities.

    I was thinking something like this: (with 2 decks of cards)
    2 2 2 2 2 2 2 2 3 - 19
    2 2 2 2 2 2 2 2 4 - 20
    2 2 2 2 2 2 2 2 5 - 21
    2 2 2 2 2 2 2 2 6 - bust
    2 2 2 2 2 2 2 2 7 - bust

    also would these be considered different hands or the same?
    2 2 2 2 2 2 2 2 3
    2 2 2 2 2 2 2 3 2

    I may be wrong though. If that's the case someone correct me.

    Joe

    On Jan 4, 2008 8:55 PM, Eric I. <> wrote:
    > Here are my results. I combined the 10 and the face cards in one row
    > since they're essentially equivalent. And the data was generated by
    > doing 10,000 deals per upcard.
    >
    > upcard bust 17 18 19 20 21
    > natural
    > ------ ------- ------- ------- ------- ------- -------
    > -------
    > 2 | 35.95% 13.32% 13.17% 13.34% 12.44% 11.78%
    > 0.00%
    > 3 | 37.85% 13.41% 12.93% 11.69% 12.51% 11.61%
    > 0.00%
    > 4 | 40.14% 13.24% 11.86% 12.03% 11.48% 11.25%
    > 0.00%
    > 5 | 41.80% 12.82% 12.32% 11.41% 11.34% 10.31%
    > 0.00%
    > 6 | 41.76% 17.65% 10.59% 10.36% 10.04% 9.60%
    > 0.00%
    > 7 | 26.77% 36.23% 13.53% 8.29% 7.88% 7.30%
    > 0.00%
    > 8 | 24.96% 12.84% 35.69% 12.73% 7.04% 6.74%
    > 0.00%
    > 9 | 22.98% 12.27% 10.69% 35.47% 12.22% 6.37%
    > 0.00%
    > 10 | 21.61% 11.21% 11.68% 11.23% 32.97% 3.55%
    > 7.75%
    > ace | 11.60% 12.33% 13.03% 13.06% 13.43% 5.27%
    > 31.28%
    >
    > I do wonder, though, whether the deck is biased somehow when the
    > dealer deals him/herself since all the players are dealt beforehand.
    > For example, it seems a player is more likely to consume a sequence of
    > low cards through consecutive hits than a sequence of high cards. So
    > depending on the number of players at the table, the cards the dealer
    > is likely to get may change somewhat. And perhaps the dealer's odds
    > change further the deeper into the shoe the table gets. Does anyone
    > know?
    >
    > Eric
    >
    > ====
    >
    > Are you interested in on-site Ruby training that uses well-designed,
    > real-world, hands-on exercises? http://LearnRuby.com
    >
    >
    Joe, Jan 5, 2008
    #6
  7. Ruby Quiz

    James Gray Guest

    Re: Studying Blackjack (#151)

    On Jan 4, 2008, at 8:22 PM, Joe wrote:

    > I didn't think it was supposed to be run a specific number of times,
    > but go over all possibilities.
    >
    > I was thinking something like this: (with 2 decks of cards)
    > 2 2 2 2 2 2 2 2 3 - 19
    > 2 2 2 2 2 2 2 2 4 - 20
    > 2 2 2 2 2 2 2 2 5 - 21
    > 2 2 2 2 2 2 2 2 6 - bust
    > 2 2 2 2 2 2 2 2 7 - bust
    >
    > also would these be considered different hands or the same?
    > 2 2 2 2 2 2 2 2 3
    > 2 2 2 2 2 2 2 3 2
    >
    > I may be wrong though. If that's the case someone correct me.


    I think I've heard about two different, but very interesting
    strategies to solve this problem. I can't wait to see the code. ;)

    James Edward Gray II
    James Gray, Jan 5, 2008
    #7
  8. Ruby Quiz

    James Gray Guest

    Re: Studying Blackjack (#151)

    On Jan 4, 2008, at 6:35 PM, Chris wrote:

    >>> Are we able to post partial / full outcomes within the 48 hours?

    >> You bet. Feel free.

    >
    > Here's mine so far, my first ruby quiz !


    Welcome to the quiz. Glad to have you.

    > =85but I'm still not sure if I deal with the case where the dealer =20
    > gets dealt two or more aces correctly.


    If a dealer has two aces, the first one would be 11 and the second one =20=

    a 1 for a total of twelve. Any aces added into the mix would be =20
    another one. The original aces would drop to a one if keeping it at =20
    11 takes the dealer over 21.

    James Edward Gray II=
    James Gray, Jan 5, 2008
    #8
  9. Ruby Quiz

    James Gray Guest

    Re: Studying Blackjack (#151)

    On Jan 4, 2008, at 7:55 PM, Eric I. wrote:

    > I do wonder, though, whether the deck is biased somehow when the
    > dealer deals him/herself since all the players are dealt beforehand.


    I believe what you say is true, though I think it's a detail typically
    ignored in this kind of strategic analysis.

    Google the "cut card effect blackjack" for some interesting (and I
    *think* semi-related) reading.

    James Edward Gray II
    James Gray, Jan 5, 2008
    #9
  10. Ruby Quiz

    tho_mica_l Guest

    Re: Studying Blackjack (#151)

    > Write a Ruby program that shows the percent chance of a dealer
    > reaching each possible outcome based on the upcard showing.


    I'm sorry for asking this dummy question (and I hope not to spoil it
    for
    anyone) but all this jargon makes me feel strange and it's early in
    the
    morning. Do I understand the game right in that:

    1. The dealer gets a card
    2. If the sum of his cards is < 17, repeat step #1
    3. If the sum is >= 17, the result is registered
    4. If the dealer has 6 + Ace, he stops and doesn't try to get a 4
    or
    something lower?

    The set of possible cards is limited to 2 decks, i.e. 2 * 13 (2..10,
    B,
    D, K, A) cards by default.

    A set of two card decks contains two 2s?

    The probabilities for 10, B, D, K should be all the same since they
    all
    count 10 and removing them from the card set results in the same
    probability
    to get another card with a value of 10 for each of them?
    tho_mica_l, Jan 5, 2008
    #10
  11. Ruby Quiz

    tho_mica_l Guest

    Re: Studying Blackjack (#151)

    > The set of possible cards is limited to 2 decks, i.e. 2 * 13 (2..10,
    > B,
    > D, K, A) cards by default.


    It's * 4 because there are 4 colours.
    tho_mica_l, Jan 5, 2008
    #11
  12. [Note: parts of this message were removed to make it a legal post.]

    On 4 Jan 2008, at 22:31, James Gray wrote:

    > On Jan 4, 2008, at 4:27 PM, Sharon Phillips wrote:
    >
    >>> Write a Ruby program that shows the percent chance of a dealer
    >>> reaching each
    >>> possible outcome based on the upcard showing

    >>
    >> Are we able to post partial / full outcomes within the 48 hours?

    >
    > You bet. Feel free.
    >
    > James Edward Gray II
    >


    Here's my results so far. I don't completely trust them yet since I'm
    not sure I understand the blackjack rules properly (I'm assuming the
    dealer has to use an ace as 11 unless they bust).

    /dh

    $ ./blackjack.rb
    Odds for each dealer outcome based on initial upcard (2 deck game)
    17 18 19 20 21 BUST
    A 12.58% 12.82% 12.75% 12.85% 36.07% 12.93%
    2 13.93% 13.33% 13.07% 12.39% 11.92% 35.36%
    3 13.27% 13.06% 12.45% 12.18% 11.53% 37.50%
    4 13.07% 12.02% 12.10% 11.63% 11.31% 39.88%
    5 12.10% 12.28% 11.73% 10.90% 10.73% 42.25%
    6 16.62% 10.62% 10.67% 10.12% 9.75% 42.21%
    7 37.05% 13.82% 7.80% 7.88% 7.34% 26.11%
    8 12.97% 36.12% 12.90% 6.89% 6.96% 24.16%
    9 12.09% 11.20% 35.41% 12.11% 6.10% 23.09%
    10 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    J 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    Q 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    K 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    Denis Hennessy, Jan 5, 2008
    #12
  13. Re: Studying Blackjack (#151)

    Hi Chris,

    You have an extra card in your hand (a '1' as well as an ace).

    /dh

    On 5 Jan 2008, at 00:35, Chris wrote:

    >>> Are we able to post partial / full outcomes within the 48 hours?

    >> You bet. Feel free.

    >
    > Here's mine so far, my first ruby quiz !
    >
    > Upcard Bust 17 18 19 20 21 Natural
    > c1 26.20% 16.80% 13.00% 14.20% 13.90% 15.90% 0.00%
    > c2 38.80% 14.60% 11.40% 11.00% 12.30% 11.90% 0.00%
    > c3 40.50% 14.40% 13.40% 11.20% 12.00% 8.50% 0.00%
    > c4 38.00% 15.20% 14.30% 11.70% 10.70% 10.10% 0.00%
    > c5 42.30% 12.80% 12.30% 11.80% 9.20% 11.60% 0.00%
    > c6 39.10% 23.50% 10.30% 10.00% 8.80% 8.30% 0.00%
    > c7 25.60% 35.40% 14.00% 10.70% 6.50% 7.80% 0.00%
    > c8 23.70% 13.00% 33.60% 16.20% 6.20% 7.30% 0.00%
    > c9 21.90% 10.50% 11.90% 35.90% 12.90% 6.90% 0.00%
    > ct 19.40% 12.50% 10.90% 11.20% 31.70% 5.10% 9.20%
    > cj 19.70% 14.40% 10.60% 12.30% 29.90% 5.80% 7.30%
    > cq 18.90% 13.50% 10.90% 10.30% 32.20% 6.60% 7.60%
    > ck 19.50% 12.30% 12.80% 11.10% 31.90% 6.00% 6.40%
    > ca 14.00% 13.40% 14.40% 13.10% 12.60% 4.10% 28.40%
    >
    >
    > Seems to satisfy the hints given in the quiz, but I'm still not sure
    > if I deal with the case where the dealer gets dealt two or more aces
    > correctly.
    >
    > Chris
    >
    >
    >
    Denis Hennessy, Jan 5, 2008
    #13
  14. Ruby Quiz

    Sander Land Guest

    On Jan 5, 2008 12:25 PM, Denis Hennessy <> wrote:
    > Here's my results so far. I don't completely trust them yet since I'm
    > not sure I understand the blackjack rules properly (I'm assuming the
    > dealer has to use an ace as 11 unless they bust).


    I think that's correct.
    >
    > /dh
    >
    > $ ./blackjack.rb
    > Odds for each dealer outcome based on initial upcard (2 deck game)
    > 17 18 19 20 21 BUST
    > A 12.58% 12.82% 12.75% 12.85% 36.07% 12.93%
    > 2 13.93% 13.33% 13.07% 12.39% 11.92% 35.36%
    > 3 13.27% 13.06% 12.45% 12.18% 11.53% 37.50%
    > 4 13.07% 12.02% 12.10% 11.63% 11.31% 39.88%
    > 5 12.10% 12.28% 11.73% 10.90% 10.73% 42.25%
    > 6 16.62% 10.62% 10.67% 10.12% 9.75% 42.21%
    > 7 37.05% 13.82% 7.80% 7.88% 7.34% 26.11%
    > 8 12.97% 36.12% 12.90% 6.89% 6.96% 24.16%
    > 9 12.09% 11.20% 35.41% 12.11% 6.10% 23.09%
    > 10 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    > J 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    > Q 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    > K 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%


    Those last four lines are identical. Are you calculating the
    probabilities and not simulating, or do you just output the last run
    four times?

    Here are my results, 2 decks and 1_000_000 deals each.

    $ ruby1.9 blackjack.rb
    upcard: 2
    17 18 19 20 21 bust
    13.9% 13.4% 13.1% 12.4% 11.9% 35.3%
    upcard: 3
    17 18 19 20 21 bust
    13.3% 13.1% 12.5% 12.2% 11.5% 37.4%
    upcard: 4
    17 18 19 20 21 bust
    13.1% 12.0% 12.1% 11.7% 11.3% 39.8%
    upcard: 5
    17 18 19 20 21 bust
    12.1% 12.3% 11.7% 10.9% 10.7% 42.1%
    upcard: 6
    17 18 19 20 21 bust
    16.6% 10.7% 10.7% 10.1% 9.8 % 42.1%
    upcard: 7
    17 18 19 20 21 bust
    36.8% 13.9% 7.9 % 8.0 % 7.3 % 26.1%
    upcard: 8
    17 18 19 20 21 bust
    13.0% 36.0% 12.9% 6.9 % 7.0 % 24.3%
    upcard: 9
    17 18 19 20 21 bust
    12.1% 11.2% 35.3% 12.2% 6.1 % 23.1%
    upcard: 10
    17 18 19 20 21 bust
    11.3% 11.2% 11.3% 33.6% 11.3% 21.3%
    upcard: 11
    17 18 19 20 21 bust
    12.6% 12.8% 12.7% 12.9% 36.0% 13.0%
    Sander Land, Jan 5, 2008
    #14
  15. Ruby Quiz

    Chris Lowis Guest

    Re: Studying Blackjack (#151)

    > You have an extra card in your hand (a '1' as well as an ace).

    Thank you, well spotted !

    Chris
    Chris Lowis, Jan 5, 2008
    #15
  16. Ruby Quiz

    Chris Lowis Guest

    Re: Studying Blackjack (#151)

    > You have an extra card in your hand (a '1' as well as an ace).

    Here's my updated results using a two-deck deck and 5000 simulated
    hands per upcard.

    Upcard Bust 17 18 19 20 21 Natural
    2 35.14% 13.66% 13.80% 13.18% 12.10% 12.12% 0.00%
    3 37.96% 13.02% 12.72% 12.98% 12.10% 11.22% 0.00%
    4 39.98% 13.40% 12.70% 11.70% 11.58% 10.64% 0.00%
    5 40.70% 12.86% 12.66% 11.12% 11.94% 10.72% 0.00%
    6 43.02% 16.74% 10.30% 10.20% 9.78% 9.96% 0.00%
    7 26.36% 37.44% 13.18% 8.02% 7.84% 7.16% 0.00%
    8 24.52% 12.68% 35.78% 13.42% 6.72% 6.88% 0.00%
    9 23.64% 11.52% 11.98% 34.42% 11.88% 6.56% 0.00%
    t 21.60% 11.60% 10.90% 11.22% 33.36% 3.98% 7.34%
    j 21.30% 11.84% 10.94% 11.68% 32.84% 3.88% 7.52%
    q 21.78% 11.26% 10.94% 11.20% 34.08% 3.68% 7.06%
    k 20.60% 10.96% 10.34% 11.82% 34.60% 3.54% 8.14%
    a 12.48% 13.40% 13.20% 12.82% 12.86% 4.84% 30.40%

    Chris
    Chris Lowis, Jan 5, 2008
    #16
  17. On 5 Jan 2008, at 13:45, Sander Land wrote:
    >> 9 12.09% 11.20% 35.41% 12.11% 6.10% 23.09%
    >> 10 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    >> J 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    >> Q 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%
    >> K 11.29% 11.22% 11.30% 33.56% 11.31% 21.32%

    >
    > Those last four lines are identical. Are you calculating the
    > probabilities and not simulating, or do you just output the last run
    > four times?


    I'm calculating (based on every permutation of remaining cards) rather
    than simulating. Hence I only do one run. I guess I could have
    duplicated the last four lines and saved a few CPU cycles but it runs
    reasonably fast anyway so I didn't bother.
    >
    > Here are my results, 2 decks and 1_000_000 deals each.
    >


    I'm guessing that you used a simulation approach instead. It's
    interesting, and reassuring, that we got the same results.

    /dh
    Denis Hennessy, Jan 5, 2008
    #17
  18. Re: Studying Blackjack (#151)

    On Jan 4, 2008 11:37 PM, James Gray <> wrote:

    > Google the "cut card effect blackjack" for some interesting (and I
    > *think* semi-related) reading.


    Interesting. This seems to have to do with the Casinos doing away
    from using a cut card and using a new machine which continuously
    reshuffles used cards back into the "deck". The traditional way for
    casinos to deal blackjack is to shuffle several decks together, place
    them into a shoe, insert a cut card towards the back of the deck, put
    used cards at the back of the shoe, and reshuffle the whole deck when
    the cut card gets near the front.

    Of course, the real reason they do this is to minimize losses to card
    counters. In the old-way players could gather information as cards
    were removed from play, of course it's quite a skill to remember the
    information and be able to mentally keep track of the effect on the
    odds. The one article I just read on the "cut card effect didn't
    mention that but only talked about the effect it has on players who
    just use a "basic" strategy based on what's in their current hand, and
    what the dealer (and others at the same table) are showing currently.

    --
    Rick DeNatale

    My blog on Ruby
    http://talklikeaduck.denhaven2.com/
    Rick DeNatale, Jan 5, 2008
    #18
  19. Ruby Quiz

    James Gray Guest

    Re: Studying Blackjack (#151)

    On Jan 5, 2008, at 2:05 AM, tho_mica_l wrote:

    >> Write a Ruby program that shows the percent chance of a dealer
    >> reaching each possible outcome based on the upcard showing.

    >
    > I'm sorry for asking this dummy question (and I hope not to spoil it
    > for
    > anyone) but all this jargon makes me feel strange and it's early in
    > the
    > morning.


    No worries. I probably didn't explain it well.

    > Do I understand the game right in that:
    >
    > 1. The dealer gets a card
    > 2. If the sum of his cards is < 17, repeat step #1
    > 3. If the sum is >= 17, the result is registered
    > 4. If the dealer has 6 + Ace, he stops and doesn't try to get a 4
    > or
    > something lower?


    Yes to all of the above.

    The forth rule actually varies somewhat in the casinos. Some tables
    allow a dealer to hit on "soft 17" (a total of 17 involving an ace
    used as an eleven). I left that out to keep this exercise simple.

    > The set of possible cards is limited to 2 decks, i.e. 2 * 13 (2..10,
    > B,
    > D, K, A) cards by default.
    >
    > A set of two card decks contains two 2s?


    I meant to do the experiment using two full decks shuffled together.
    That would be a total of 104 cards and include eight twos, threes, etc.

    I hope that clears things up.

    James Edward Gray II
    James Gray, Jan 6, 2008
    #19
  20. Ruby Quiz

    James Gray Guest

    On Jan 5, 2008, at 5:25 AM, Denis Hennessy wrote:

    > (I'm assuming the dealer has to use an ace as 11 unless they bust).


    Correct.

    James Edward Gray II
    James Gray, Jan 6, 2008
    #20
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