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Thread: Question on the mathematics of Blackjack

  1. #1


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    Post Question on the mathematics of Blackjack

    This is my first post and I am curious to know how things work, including gambling. In SCARNE ON CARDS HOW TO WIN 1974 edition, third printing 1977, page 289, he states

    "...We'll discover...if we multiply 1,326 X 169 to get a common multiple of 224,094....."

    Where does the term 169 come from?

    And thanks for allowing me to post. I can't figure out how to submit a brief bio at my profile.

  2. #2
    Random number herder Norm's Avatar
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    I wouldn't trust Scarne on anything related to blackjack math.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    Quote Originally Posted by tjkoko View Post
    This is my first post and I am curious to know how things work, including gambling. In SCARNE ON CARDS HOW TO WIN 1974 edition, third printing 1977, page 289, he states

    "...We'll discover...if we multiply 1,326 X 169 to get a common multiple of 224,094....."

    Where does the term 169 come from?

    And thanks for allowing me to post. I can't figure out how to submit a brief bio at my profile.

    169 represents the number of possible starting situations in a game of blackjack. Here's how it breaks down:

    • The player can have 13 different starting hands:
      • Ten different hard totals (4 through 13)
      • One soft hand (A,2 through A,9 are all considered "soft 13" through "soft 20")
      • Pair of Aces
      • Any pair except Aces (treated as one category)

    • The dealer can have 13 possible up-cards:
      • Ace through 10 (with 10, Jack, Queen, and King all counting as 10)

    Therefore, 13 (player hands) x 13 (dealer up-cards) = 169 possible starting situations.
    This number is crucial in blackjack strategy and analysis because:

    • It forms the basis for creating basic strategy charts.
    • It's used in probability calculations for different game outcomes.
    • It's a fundamental component in more advanced blackjack mathematics, including card counting systems.

    Understanding these 169 situations and the optimal play for each is key to mastering basic blackjack strategy. Advanced players and analysts often use this as a starting point for more complex calculations and strategy development.

  4. #4
    Random number herder Norm's Avatar
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    Glad I'll never start with a hard 16.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  5. #5


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    Quote Originally Posted by Norm View Post
    I wouldn't trust Scarne on anything related to blackjack math.
    That made me chuckle
    Chance favors the prepared mind

  6. #6


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    Talking

    Quote Originally Posted by Archvaldor View Post
    169 represents the number of possible starting situations in a game of blackjack. Here's how it breaks down:

    • The player can have 13 different starting hands:
      • Ten different hard totals (4 through 13)
      • One soft hand (A,2 through A,9 are all considered "soft 13" through "soft 20")
      • Pair of Aces
      • Any pair except Aces (treated as one category)

    • The dealer can have 13 possible up-cards:
      • Ace through 10 (with 10, Jack, Queen, and King all counting as 10)


    Therefore, 13 (player hands) x 13 (dealer up-cards) = 169 possible starting situations.
    This number is crucial in blackjack strategy and analysis because:

    • It forms the basis for creating basic strategy charts.
    • It's used in probability calculations for different game outcomes.
    • It's a fundamental component in more advanced blackjack mathematics, including card counting systems.

    Understanding these 169 situations and the optimal play for each is key to mastering basic blackjack strategy. Advanced players and analysts often use this as a starting point for more complex calculations and strategy development.
    Thank you for the very informed reply!

  7. #7
    Random number herder Norm's Avatar
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    The response was very odd. But it wouldn't surprise me if Scarne said it. But then Scarne did say he created card counting -- a few years after he died. Scarne is a good read on the history of many games. But ignore him on blackjack.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  8. #8


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    Quote Originally Posted by Norm View Post
    The response was very odd. ......
    Whose response. Explain.

  9. #9
    Random number herder Norm's Avatar
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    The lengthy one by Archvaldor.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    Quote Originally Posted by Norm View Post
    The response was very odd. ........
    Why odd???

  11. #11


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    Quote Originally Posted by Archvaldor View Post
    169 represents the number of possible starting situations in a game of blackjack. Here's how it breaks down:

    • The player can have 13 different starting hands:
      • One soft hand (A,2 through A,9 are all considered "soft 13" through "soft 20")


    .................
    On the soft hand, it seems that there are 8 combinations excluding BJ. Why then is it counted as one soft hand?

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    Quote Originally Posted by tjkoko View Post
    Why odd???
    Norm, was being polite. Others might have said, "The response was wrong."

    Don

  13. #13
    Random number herder Norm's Avatar
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    I don't agree with a single word. As a start, here are the starting hands in normal blackjack. You can ignore some of the rows for strategy decisions in normal methods of play. Hard 4 is always a pair, although any pair can be treated otherwise. Different pairs and soft hands must be treated separately, not as a group. 16vT is ignored for some reason.

    shands.jpg
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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