8 card 21
June 29th, 2025 at 12:20:39 PM
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Last week while playing Blackjack, on the first hand of the show, the dealer got an eight card 21. Can one of you better than me math guys calculate the odds of this happening? Six deck shoe, dealer hits soft 17. Thanks!
June 29th, 2025 at 12:35:41 PM
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Somewhere north of 200,000 to 1, if I remember correctly.
The older I get, the better I recall things that never happened
June 30th, 2025 at 4:14:49 PM
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I am not 100% confident about this, but for exactly 8 cards, I get 1 in 2,882,126
June 30th, 2025 at 5:19:37 PM
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I knew I answered this somewhere. Ask the Wizard #128 says the probability of exactly 8 is 1 in 79,000.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 30th, 2025 at 5:30:47 PM
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Quote: WizardI knew I answered this somewhere. Ask the Wizard #128 says the probability of exactly 8 is 1 in 79,000.
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That's for any hand of 17-21. The OP asked for an 8-card 21.
June 30th, 2025 at 7:00:25 PM
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Thanks everyone, for what it’s worth an AI LLM came up with this after a long discussion of probabilities , assumptions:and math computations:
The probability of the dealer achieving an eight-card 21 in a six-deck shoe, hitting on a soft 17, is approximately 0.00001 (or ( 1 \times 10^{-5} )), based on combinatorial estimation and adjusted for typical blackjack simulation results. For precise values, a Monte Carlo simulation would be needed, but this provides a reasonable order-of-magnitude estimate.
The probability of the dealer achieving an eight-card 21 in a six-deck shoe, hitting on a soft 17, is approximately 0.00001 (or ( 1 \times 10^{-5} )), based on combinatorial estimation and adjusted for typical blackjack simulation results. For precise values, a Monte Carlo simulation would be needed, but this provides a reasonable order-of-magnitude estimate.
June 30th, 2025 at 8:00:51 PM
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For what it's worth, I did a simulation on a well-known commercial software package which does not have an option for exactly 8 cards, but does have an option for greater than 7 cards, and it came out to 1 in 632115. This will include all the dealer 21s of more than 8 cards too. 6D, H17.
I could probably do an exact sim by setting up the player to play by dealer rules up to 7 cards and stop on the 8th card, and see how often he has 21.
I could probably do an exact sim by setting up the player to play by dealer rules up to 7 cards and stop on the 8th card, and see how often he has 21.
July 1st, 2025 at 12:31:37 AM
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I lost to a a 8 card 21 on double deck on Bellagio 6-7 years ago.
July 1st, 2025 at 1:42:57 AM
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Quote: ThatDonGuyI am not 100% confident about this, but for exactly 8 cards, I get 1 in 2,882,126
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I get 1 in 656,359.
For all 21s with at least 8 cards: 1 in 633,951
| Total/Cards | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bust | n/a | 5.78 | 11.19 | 48.85 | 379 | 4,663 | 86,745 | 2,450,682 | 109,949,376 | 8,343,095,906 | 1,213,023,668,212 | 448,764,604,396,277 |
| 21 | 21.06 | 19.02 | 53.94 | 297.72 | 2,629 | 34,187 | 656,359 | 18,980,146 | 868,413,812 | 67,191,896,915 | 9,972,546,764,362 | 3,746,208,871,481,960 |
| 20 | 9.45 | 18.60 | 54.90 | 305.35 | 2,658 | 34,404 | 659,483 | 18,987,054 | 861,604,315 | 65,880,705,729 | 9,651,778,337,472 | 3,590,116,835,170,220 |
| 19 | 16.85 | 18.23 | 55.99 | 311.22 | 2,686 | 34,856 | 670,424 | 19,299,118 | 872,152,834 | 66,168,030,727 | 9,628,665,841,453 | 3,590,116,835,170,220 |
| 18 | 15.37 | 18.15 | 57.15 | 315.73 | 2,726 | 35,724 | 695,970 | 20,335,076 | 928,614,978 | 70,457,123,485 | 9,972,546,764,362 | 3,590,116,835,170,220 |
| 17 | 16.85 | 19.01 | 56.12 | 305.32 | 2,695 | 36,125 | 720,211 | 21,780,040 | 1,059,278,794 | 89,082,974,516 | 15,003,473,341,010 | 6,627,908,003,391,170 |
“Man Babes” #AxelFabulous
July 1st, 2025 at 6:55:37 AM
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Fascinating. We have Wizard, ThatDonGuy, AutomaticMonkey, Miplet and an AI Source all disagreeing with everyone else.
I wlll wager $20 on Miplet having the correct answer versus the field.
I wlll wager $20 on Miplet having the correct answer versus the field.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
July 1st, 2025 at 7:17:15 AM
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Say, here's a crazy idea: how about calculating the value based on "dealer hits on 16 and below, or soft 17" instead of "dealer hits on 15 and below, or soft 16"?
The corrected solution is 1 in 656,359 (specifically, 12,053,386,992 / 7,911,348,676,656,425). Wizard, if I have any beers owed to me, give one of them to Miplet.
Note that my solution is based solely on the dealer playing out the hand from a full shoe, and not taking into account cards taken by other players - or, for that matter, hands not being played because all of the other players had blackjack and/or busted.
The corrected solution is 1 in 656,359 (specifically, 12,053,386,992 / 7,911,348,676,656,425). Wizard, if I have any beers owed to me, give one of them to Miplet.
Note that my solution is based solely on the dealer playing out the hand from a full shoe, and not taking into account cards taken by other players - or, for that matter, hands not being played because all of the other players had blackjack and/or busted.
July 1st, 2025 at 8:03:49 AM
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Quote: ThatDonGuyThat's for any hand of 17-21. The OP asked for an 8-card 21.
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Ooops.
However, I was asked in Ask the Wizard #231 about the probability of a dealer 8-card 21. This was relevant because there was a jackpot at the Barona casino if this happened.
My answer was 0.00000152356 = 1 in 656,357.
Same as Miplet!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
