# Thread: Question on the mathematics of Blackjack

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## 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.

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I wouldn't trust Scarne on anything related to blackjack math.

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Originally Posted by tjkoko
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.

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Originally Posted by Norm
I wouldn't trust Scarne on anything related to blackjack math.

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Originally Posted by Archvaldor
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!

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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.

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

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The lengthy one by Archvaldor.

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

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

Don

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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

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