See the top rated post in this thread. Click here

Page 1 of 2 12 LastLast
Results 1 to 13 of 16

Thread: What Are Odds of Winning 20 Blackjack Hands in a Row

  1. #1


    Did you find this post helpful? Yes | No

    What Are Odds of Winning 20 Blackjack Hands in a Row

    Pushes don't count as a win, but they don't break the streak either.

    DraftKings is having a blackjack promotion for longest winning streak in the month of June. Looks like 20 wins in a row is the top value. I won't say what my streak is, but its in the double digits.
    Last edited by Midwest Player; 06-29-2021 at 01:52 PM.

  2. #2
    Banned or Suspended
    Join Date
    Oct 2018
    Posts
    1,154


    0 out of 2 members found this post helpful. Did you find this post helpful? Yes | No
    Here is my calculation: (42%+8%)^20=0.0001%. My longest losing streak is 15 hands in a row.

  3. #3


    Did you find this post helpful? Yes | No
    aceside is wrong, as usual. A more interesting calculation is what are the odds of aceside making a correct statement once in a row?

    As pushes don't count, you are left with 91.2& of hands. Within that, the ratio of wins to losses is 47.5% to 52.5%. So 0.475% is the number you would raise exponentially. I'll leave the math to you.
    I suspect there are other mitigating factors if your goal is the longest win streak, rather than the highest EV, such as not doubling, splitting, etc. I'll leave those complexities to the more knowledgeable.

  4. #4
    Banned or Suspended
    Join Date
    Oct 2018
    Posts
    1,154


    Did you find this post helpful? Yes | No
    Quote Originally Posted by 21forme View Post
    aceside is wrong, as usual. A more interesting calculation is what are the odds of aceside making a correct statement once in a row?

    As pushes don't count, you are left with 91.2& of hands. Within that, the ratio of wins to losses is 47.5% to 52.5%. So 0.475% is the number you would raise exponentially. I'll leave the math to you.
    I suspect there are other mitigating factors if your goal is the longest win streak, rather than the highest EV, such as not doubling, splitting, etc. I'll leave those complexities to the more knowledgeable.
    It seems you are reasonable this time. Let me think harder.

  5. #5
    Banned or Suspended
    Join Date
    Oct 2018
    Posts
    1,154


    0 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    I recalculated this again, to consider the condition of Pushes don't count as a win, but they don't break the streak either. Here is the result:
    If we follow the suit of the rhythm, 42 wins-8 pushes-52 loses, winning 20 hands in a row corresponds to wins+pushes=23.8 hands.
    So my final result is 0.5^23.8=6.8E-8, that is, one in 15 million.


  6. #6


    Did you find this post helpful? Yes | No
    Am I crazy or wasn’t it just explained as .475^20?

  7. #7


    Did you find this post helpful? Yes | No
    Seeing the right answer won't stop aceside from attempting to come up with their own.

    Also, I wonder how basic strategy changes if you aim for the longest win(or push) streak. If you aren't concerned with the EV of the hand, maybe you shouldn't take as many risks, hit 11 so you can improve it, don't double soft 18, stand 16vT, things like that.

  8. #8
    Banned or Suspended
    Join Date
    Oct 2018
    Posts
    1,154


    0 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    Quote Originally Posted by PitBoss321 View Post
    Seeing the right answer won't stop aceside from attempting to come up with their own.
    For this problem, I insist I am correct. Let us wait for Norm and Don to judge it.

  9. #9
    Banned or Suspended
    Join Date
    Oct 2018
    Posts
    1,154


    Did you find this post helpful? Yes | No
    Quote Originally Posted by PitBoss321 View Post
    Seeing the right answer won't stop aceside from attempting to come up with their own.

    Also, I wonder how basic strategy changes if you aim for the longest win(or push) streak. If you aren't concerned with the EV of the hand, maybe you shouldn't take as many risks, hit 11 so you can improve it, don't double soft 18, stand 16vT, things like that.
    Dog Hand is an authority on this kind of problem. Let him jump in. I am not so confident anymore.

  10. #10


    2 out of 2 members found this post helpful. Did you find this post helpful? Yes | No
    When pushes are excluded, it depends on the rules as to what the win rate is. But 21forme is obviously right. I'd make the ultimate win rate for this problem a bit higher, because we can improve the outright rate for winning according to the discussions above. You never double except when you'd never hit more than once, and you never split when playing the hand out improves your outright win percentage, irrespective of e.v.

    You can find all these numbers in the appendices of BJA3. So, if you make the win rate, say, 0.48, then 20 hands in a row is 1 in 2.37 million.

    Don

  11. #11
    Banned or Suspended
    Join Date
    Oct 2018
    Posts
    1,154


    0 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    I studied a little online and considered this problem more carefully. We use the following probabilities for each initial hand from Wizard: Win 42.43%; Lose 49.09%; Push 8.48%.
    Of non-push hands, players win 46.36% and lose 53.64%. So the probability of wining exactly 20 hands in a row for this problem is
    0.4636^20X0.5364=1.13E-7, that is 1 in 8.9 million.

  12. #12
    Random number herder Norm's Avatar
    Join Date
    Dec 2011
    Location
    The mote in God's eye
    Posts
    12,461
    Blog Entries
    59


    Did you find this post helpful? Yes | No
    Keep in mind that when the deck is not shuffled after every hand; the odds are different as a win or loss alters the average shoe composition. Also, if there is a reshuffle in the middle of a string, cut card effect comes into the calculation.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  13. #13


    Did you find this post helpful? Yes | No
    Quote Originally Posted by Norm View Post
    Keep in mind that when the deck is not shuffled after every hand; the odds are different as a win or loss alters the average shoe composition. Also, if there is a reshuffle in the middle of a string, cut card effect comes into the calculation.
    In this case since it is an online blackjack game, the 8 decks are shuffled after every hand. DraftKings is offering about 10 of these different games, and all the win streaks are in the double digits so I doubt if its 1 in 8.9 million. I personally twice had streaks into the double digits. The standings are posted on the DraftKings casino web site.

Page 1 of 2 12 LastLast

Similar Threads

  1. Dealers Were Winning 80% of The Hands
    By Ianmark in forum General Blackjack Forum
    Replies: 2
    Last Post: 05-18-2019, 01:32 AM
  2. Average bet for winning versus loosing hands
    By Oneoffthecount in forum General Blackjack Forum
    Replies: 13
    Last Post: 05-24-2015, 01:40 AM
  3. How Do You React After Winning MAX BET Hands?
    By Mickey in forum General Blackjack Forum
    Replies: 32
    Last Post: 03-25-2015, 06:50 PM
  4. Tax from winning blackjack.
    By chang04133 in forum General Blackjack Forum
    Replies: 34
    Last Post: 01-14-2013, 12:52 PM
  5. al: winning hands
    By al in forum Blackjack Beginners
    Replies: 1
    Last Post: 03-31-2006, 08:03 PM

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  

About Blackjack: The Forum

BJTF is an advantage player site based on the principles of comity. That is, civil and considerate behavior for the mutual benefit of all involved. The goal of advantage play is the legal extraction of funds from gaming establishments by gaining a mathematic advantage and developing the skills required to use that advantage. To maximize our success, it is important to understand that we are all on the same side. Personal conflicts simply get in the way of our goals.