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Thread: It says odds of busting with 14 is 56% but 6/13 = 46%, why?

  1. #1


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    Question It says odds of busting with 14 is 56% but 6/13 = 46%, why?

    Why does every photo I search for says the probability of player to bust drawing another card while having 14 is 56% if the only cards you can bust with are 8, 9, 10, J, Q, K (6 cards)? 6/13 ~ 46%.


    There's a total of 13 cards in the deck (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K) and you won't be busted with A 2 3 4 5 6 7 (7 cards), so 7/13 ~ 53%.


    Here's one photo showing the odds of 46% (you can find a lot of them if u search 'player busting odds blackjack' on google):



    And here's another one, showing the odds of 56% with the same hand:

    Attached Images Attached Images

  2. #2


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    Probably because there are times where you hit again when you draw an Ace or 2.

  3. #3


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    Quote Originally Posted by ShipTheCookies View Post
    Probably because there are times where you hit again when you draw an Ace or 2.
    Thank you for your reply Most of the pictures on google search show the 56% chance of busting, only a few show 46%.

    Maybe the digit was misspelled, however, I'm not sure about that.

    So, the right player's chance of busting when hitting on 14 is 46% (without taking another card on 15 or 16), right?

    Things get a little weird when I think about the dealer's chance because the dealer stands on soft 17 and hits 16 and less. The dealer's odds of busting when hitting on 14 should be the same as the player's with additional hit on 15 or 16, so 56% may be an answer to both dealer's chance and player's when hitting until 17.

  4. #4


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    Quote Originally Posted by LukizKing View Post
    Thank you for your reply Most of the pictures on google search show the 56% chance of busting, only a few show 46%.

    Maybe the digit was misspelled, however, I'm not sure about that.

    So, the right player's chance of busting when hitting on 14 is 46% (without taking another card on 15 or 16), right?

    Things get a little weird when I think about the dealer's chance because the dealer stands on soft 17 and hits 16 and less. The dealer's odds of busting when hitting on 14 should be the same as the player's with additional hit on 15 or 16, so 56% may be an answer to both dealer's chance and player's when hitting until 17.
    That seems correct to me. 6/13 = 46 percent is the chance of busting a Hard 14 hand by the next card (provided that you neglect the visible cards, e.g. the player's own cards , the dealer upcard or other player cards on the table). The chance of busting the hand increases with additional cards. However, the second screenshot is wrong, since it states 56 percent by drawing the _next_ card. And when comparing player with dealer, remember that following Basic Strategy, the player will _not_ draw till 17 when the dealer has a low upcard of 2,3,4,5,6. I don't know if the 56 percent number takes this into account.
    Last edited by PinkChip; 11-16-2019 at 09:34 AM.

  5. #5


    1 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    Has it ever occurred to you that they're idiots who don't know what they're talking about?

    Don

  6. #6


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    It may be that they took the math from someone who took hand totals into consideration. For example, the most common configuration of a 16 is 10+6, which means that two potential cards that would bust a 16 are out of the deck. I'm sure those numbers are out there, but I'm pretty sure the people in the infographic just got the math wrong, as DSchles suggested.

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    It actually says "on the next card drawn", so it is flat out inaccurate. In fact only 6/13 ranks bust you with 14 on the next card, which is clearly lesser than 50%.

  8. #8


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    The sudden jump from 39% to 56% seems weird to me as well. Do you think the chance of bust when hitting on 15 or 16 for the dealer could increase the chance from 46% to 50%+? I'm not sure how to calculate it.

    Of course, we're talking about the fresh shoe, total dependent strategy and excluding card counting because the true count and composition dependent strategy could alter the outcome a little bit (that's why the Illustrious 18 table was created).
    Last edited by LukizKing; 11-16-2019 at 10:39 AM.

  9. #9


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    They say 100% bust rate for 21 which is not true. You can have a soft 21 and hit and not bust. (Think 8,2,Ace)

  10. #10


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    Quote Originally Posted by Midwest Player View Post
    They say 100% bust rate for 21 which is not true. You can have a soft 21 and hit and not bust. (Think 8,2,Ace)
    As far as I know, they don't let you hit or do anything on soft 21.

  11. #11


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    By the 6/13 + (6/13 * 1/13) + (6/13 * 1/13) calculation we get the odds of all the possible outcomes until we hit the soft 17, WHICH IS ~ 53%. Does that make sense?

    In the combinatorics, '*' means AND, while '+' means OR. Having 6/13 as our starting probability, we add the probability of getting the A or 2, resulting in the ~ 53% for the player or the dealer to bust.

    6/13 chance of hitting on 14 and busting.
    (6/13 * 1/13) chance of hitting on 14, getting 15, hitting and busting.
    (6/13 * 1/13) chance of hitting on 14, getting 16, hitting and busting.

    Correct me if I'm wrong
    Last edited by LukizKing; 11-16-2019 at 11:04 AM.

  12. #12


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    Quote Originally Posted by LukizKing View Post
    As far as I know, they don't let you hit or do anything on soft 21.
    I have hit soft 21 in error already, and have seen other folks do it quite often in error.

  13. #13


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    Quote Originally Posted by LukizKing View Post
    6/13 chance of hitting on 14 and busting.
    (6/13 * 1/13) chance of hitting on 14, getting 15, hitting and busting.
    (6/13 * 1/13) chance of hitting on 14, getting 16, hitting and busting.
    But in the second case (dealer gets an Ace, with probability of 1/13):
    when dealer has 15, his probability of busting by the next card is not 6/13 anymore.
    If he has Hard 15, there are now 7 cards which would him bust: 7,8,9,10,J,Q,K.
    So you must compute 1/13 * 7/13 in the second case.

    Analogously, 1/13 * 8/13 in the third case, since if the dealer has 16,
    he busts with 8 cards: 6,7,8,9,10,J,Q,K.

    It gets further complicated, since in the second case, if the dealer has 15,
    he could draw another Ace (1/13) and then get into the third case.
    In my opinion, the result of these overall four cases is

    6/13 (start on Hard 14 and draw 8,9,10,J,Q,K) +
    1/13 * 7/13 (start on Hard 14, then draw an Ace to Hard 15, then draw 7,8,9,10,J,Q,K) +
    1/13 * 8/13 (start on Hard 14, then draw a Two to Hard 16, then draw 6,7,8,9,10,J,Q,K) +
    1/13 * 1/13 * 8/13 (start on Hard 14, then draw two Aces to Hard 16, then draw 6,7,8,9,10,J,Q,K)

    = 6/13 + 7/169 + 8/169 + 8/2197
    = 1014/2197 + 91/2197 + 104/2197 + 8/2197
    = 1217/2197
    = 55.4 %
    Last edited by PinkChip; 11-16-2019 at 12:15 PM.

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