How often should you get a BlackJack?
  • According to statistics or probability, how often should you get a BlackJack?

    I thought I read somewhere that you should get a BlackJack something like 1 out of every 21 hands or something like that.

    Anybody know or heard of this?
  • Thats approx. right. Depends on the number of decks but thats a close approximation.
  • all you need to do is remember some basic stats... the probability of two events happening is the product of the probability for each event.

    single-deck game. BJ requires an ace and a ten. probability of getting an ace is 4/52 (hope it is obvious where that comes from) and the probability of getting a ten is 16/51 (because one card has already been dealt, your ace).. So the probability of gettng an Ace-Ten is 64 / 2652 or .024... But you are only half done, because you can also get a BJ by getting a ten first. The probability of a 10-A BJ is therefore 16/52 * 4/51, or .024 (same number as before you will notice. So the probability of getting either is the sum of both probabilities, or .048.

    To use that to answer your question, just compute the reciprocal of .048 (1 / .048) and you get 20.83, which means you should get a BJ in a 52 card came once every 21 hands roughly...

    You can use the above to compute the odds for getting any hand, just don't forget that some hands have many ways to arrive at them. BTW a shortcut is N * P(hand) where P(hand) is the probability of getting that hand any single way and N is the number of possible ways to get that hand...
  • However on a shoe it is so possed to be slight less often that you will get blackjack on a shoe. The second deal of a single deck can produce blackjack much more often if an ace has not been dealt out on the first deal. Single deck one in 20.2 six decks one in 21!
  • Thanks for your answers.

    And special thanks to Stainless Steel Rat for explaining the math behind it all.
    You explained it very well so I could follow it.
  • LTC: BJ on the second round is not precisely calculatable, unless you specify exactly which cards appeared on the first round.

    But for 6D vs 1D games, the EOR (effect of removal) for any one card is less pronounced. For example, in a single-deck game, once a single ace falls, the probability of getting another ace is 3/51. While in a 6d shoe, it would be 23/311. In a single-deck game, that means P(2nd ace) is .0588 while in the shoe it would be .074... That's because removing one of 24 cards has less effect than removing one of four...

    By the same token, I much prefer to play SD/DD games, because the EOR is more pronounced and counting is more effective...
  • Now that you've had your math lesson,please remember that just because you should get a BJ on average every 20-21 hands,there is no such thing as an overdue BJ.I've seen plenty of players raise their bets after going 25 hands or so,in the expectation of catching the BJ.Assuming you are not tracking cards,the odds of you getting a BJ on any one hand doesn't change if you've gone thirty hands without one,or if you just recieved two in a row.
  • Unlike roulette cards do have memory so if you are playing and don't get a blackjack the first hand if they don't shuffle you are more likely to get a blackjack!!! If you do get a blackjack the next hand you are less likely to get a blackjack!!! Lets say you go one round without seeing any aces and very few tens pop out as well you are more likely on the next round to get a blackjack than the round before it!!! Why because casinos don't play from an infinate deck that is reshuffled every time unless you are playing online!!! Remember that blackjack cards are dependant trails!!!
  • NYB said:
    Now that you've had your math lesson,please remember that just because you should get a BJ on average every 20-21 hands,there is no such thing as an overdue BJ.I've seen plenty of players raise their bets after going 25 hands or so,in the expectation of catching the BJ.Assuming you are not tracking cards,the odds of you getting a BJ on any one hand doesn't change if you've gone thirty hands without one,or if you just recieved two in a row.



    NYB- Thanks for the reminder. Just like you're not due a win after losing x many hands in a row, I see you're also not "due" to get a BJ after so many non-BJ hands.
  • all you can say after playing 500 consecutive rounds without getting a blackjack are the following:

    (1) I'm an unlucky SOB.

    (2) I have about a 1 in 21 chance of getting a BJ on the next round...

    Now if you are counting cards, (2) is not exactly correct as you might be aware that all the aces have been dealt so that 1 in 21 chance becomes 0.0 probability... Or you might know there are nothing but aces and 10's left, but you still have a big chance of getting a 20 rather than a 21. But 1/21 is the general number no matter what has happened in the past...
  • Last year,at The Edgewater in Laughlin,they had a promo where you got a slip every $5 or better BJ.Collect 7 and you can exchange them for an envelope with pizes,some of which were really nice.
    My first night,I get 13,so I need 1 more in the morning to qualify for 2 prizes.Took almost 2 hours for my first BJ.
    Went to lunch and then got another 7 tickets in about 15 minutes.Only thing thats certain in this game is if you play 21 gazillion hands,you should get about a gazillion naturals.
  • You get blackjacks more often than in multideck blackjack games!!! Lets say for example on the first round no tens or aces appear and you go through ten cards on the next round a blackjack is going to happen 1 in 13.5 hands instead of the usual 21 hands. 52-10=42 16/42*2=.7619*(4/41)=.0743 You will get a blackjack that in that scenario about 7.43% of the time in multi deck games it drops of significantly!!!
  • How often should you get a blackjack? P= 2*(4/13)*(4n/(52n-1)) for any number of decks. n=1,2,3,4,5,6,7,8, etc

    Decks:

    1= .4826
    2= .4779
    6= .4748
    8= .4751
    etc

    But, there is more to it than that because I could easily play 100 hands without a single blackjack, and have. Or play 95 hands without a blackjack and then get 5 in a row or 1 or perhaps 2.

    Sometimes card removal is such that your chance to get a BJ is improved. Other times your chance is reduced. Every card that is played changes the odds.

    The small difference in 1 to 8 deck blackjacks illustrates the importance of card removal as you move down in number of decks. Basic strategy is more accurate and so is variations in basic strategy, etc

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