February 26th, 2018 at 3:58:01 PM
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Quote:BlackjackGuy123Depends, how many players are playing?

If it is just heads up and we are talking about a shoe where there is 1 decks cut off out of six, then we can expect to get 52 rounds in playing heads up. So the odds of not getting blackjack in one trial is 95.17%.

.9517 to the 52nd power is 7.6%

But at a crowded table the probability would be much higher.

On the other hand, getting at least one blackjack in 52 rounds –

“The probability of at least one success in 52 trials for an event of probability p=0.0483 is 92.38% or 1 in 1.08.” (courtesy of SuperFormula.exe).

The chance in a complete 6D shoe is overwhelmingly in favor of at least one blackjack (better than 10 to 1). Playing through 10 shoes as mcavanaugh8 did is overwhelmingly highly favorable to at least one blackjack. That is 520 trials!!!

“The probability of at least one success in 520 trials for an even of probability p=0.0483 is 0.9999999999.”

Its like tossing the coin 5000 times to get b0th heads/tails at least once. mcavanaugh8 didn’t get that virtually certain outcome!!! I BLAME the automatic shufflers… again… and again… 520 times!

Ok this is for heads-up play. The probability you get a blackjack is very high even with 7 players at the table and plying 10 shoes.

February 26th, 2018 at 6:09:54 PM
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"52 trials in a 6 deck shoe" assumes 100% penetration and one on one play.

With 4 decks dealt per shoe and a full table (7 players) I think there would be about 9-10 hands dealt per shoe. So ten shoes would be roughly 100 hands. Odd s of not getting at least one blackjack in ten shoes would be on the order of 0.035% -approximately 1 in 3,000.

With 4 decks dealt per shoe and a full table (7 players) I think there would be about 9-10 hands dealt per shoe. So ten shoes would be roughly 100 hands. Odd s of not getting at least one blackjack in ten shoes would be on the order of 0.035% -approximately 1 in 3,000.

So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.

February 26th, 2018 at 7:38:53 PM
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I find that the odds of not getting it grows exponentially when you're down to your last bet.

"I should have bet black." - Winston Churchill .

February 27th, 2018 at 8:37:27 AM
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@gordonm888

Your penetration is 66%. So if you play through 10 6D shoes a day it takes 3000 days to be in a no blackjack situation. That would be 8 years of daily play and in one of those days you wont hit a blackjack.

Your penetration is 66%. So if you play through 10 6D shoes a day it takes 3000 days to be in a no blackjack situation. That would be 8 years of daily play and in one of those days you wont hit a blackjack.

February 27th, 2018 at 8:38:04 AM
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“I find that the odds of not getting it grows exponentially when you're down to your last bet.”

Sarcastic but just about every player says it’s true.

Sarcastic but just about every player says it’s true.

February 27th, 2018 at 9:39:03 AM
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agreeQuote:weezrDASvegasOn the other hand, getting at least one blackjack in 52 rounds –

“The probability of at least one success in 52 trials for an event of probability p=0.0483 is 92.38% or 1 in 1.08.” (courtesy of SuperFormula.exe).

about 12 out of 13 in 52 rounds

round X | prob NO BJ | 1 in | prob at least 1 BJ | 1 in | out of |
---|---|---|---|---|---|

1 | 0.9517 | 1.051 | 0.0483 | 20.704 | . |

2 | 0.90573289 | 1.104 | 0.09426711 | 10.608 | . |

3 | 0.861985991 | 1.160 | 0.138014009 | 7.246 | . |

4 | 0.820352068 | 1.219 | 0.179647932 | 5.566 | . |

5 | 0.780729063 | 1.281 | 0.219270937 | 4.561 | . |

6 | 0.743019849 | 1.346 | 0.256980151 | 3.891 | . |

7 | 0.707131991 | 1.414 | 0.292868009 | 3.415 | . |

8 | 0.672977516 | 1.486 | 0.327022484 | 3.058 | . |

9 | 0.640472702 | 1.561 | 0.359527298 | 2.781 | . |

10 | 0.60953787 | 1.641 | 0.39046213 | 2.561 | . |

11 | 0.580097191 | 1.724 | 0.419902809 | 2.382 | . |

12 | 0.552078497 | 1.811 | 0.447921503 | 2.233 | . |

13 | 0.525413105 | 1.903 | 0.474586895 | 2.107 | . |

14 | 0.500035652 | 2.000 | 0.499964348 | 2.000 | . |

15 | 0.47588393 | 2.101 | 0.52411607 | 1.908 | 1.1 out of 2.1 |

16 | 0.452898736 | 2.208 | 0.547101264 | 1.828 | 1.21 out of 2.21 |

17 | 0.431023727 | 2.320 | 0.568976273 | 1.758 | 1.32 out of 2.32 |

18 | 0.410205281 | 2.438 | 0.589794719 | 1.696 | 1.44 out of 2.44 |

19 | 0.390392366 | 2.562 | 0.609607634 | 1.640 | 1.56 out of 2.56 |

20 | 0.371536415 | 2.692 | 0.628463585 | 1.591 | 1.69 out of 2.69 |

21 | 0.353591206 | 2.828 | 0.646408794 | 1.547 | 1.83 out of 2.83 |

22 | 0.336512751 | 2.972 | 0.663487249 | 1.507 | 1.97 out of 2.97 |

23 | 0.320259185 | 3.122 | 0.679740815 | 1.471 | 2.12 out of 3.12 |

24 | 0.304790666 | 3.281 | 0.695209334 | 1.438 | 2.28 out of 3.28 |

25 | 0.290069277 | 3.447 | 0.709930723 | 1.409 | 2.45 out of 3.45 |

26 | 0.276058931 | 3.622 | 0.723941069 | 1.381 | 2.62 out of 3.62 |

27 | 0.262725285 | 3.806 | 0.737274715 | 1.356 | 2.81 out of 3.81 |

28 | 0.250035653 | 3.999 | 0.749964347 | 1.333 | 3 out of 4 |

29 | 0.237958931 | 4.202 | 0.762041069 | 1.312 | 3.2 out of 4.2 |

30 | 0.226465515 | 4.416 | 0.773534485 | 1.293 | 3.42 out of 4.42 |

31 | 0.215527231 | 4.640 | 0.784472769 | 1.275 | 3.64 out of 4.64 |

32 | 0.205117265 | 4.875 | 0.794882735 | 1.258 | 3.88 out of 4.88 |

33 | 0.195210102 | 5.123 | 0.804789898 | 1.243 | 4.12 out of 5.12 |

34 | 0.185781454 | 5.383 | 0.814218546 | 1.228 | 4.38 out of 5.38 |

35 | 0.176808209 | 5.656 | 0.823191791 | 1.215 | 4.66 out of 5.66 |

36 | 0.168268373 | 5.943 | 0.831731627 | 1.202 | 4.94 out of 5.94 |

37 | 0.16014101 | 6.244 | 0.83985899 | 1.191 | 5.24 out of 6.24 |

38 | 0.1524062 | 6.561 | 0.8475938 | 1.180 | 5.56 out of 6.56 |

39 | 0.14504498 | 6.894 | 0.85495502 | 1.170 | 5.89 out of 6.89 |

40 | 0.138039308 | 7.244 | 0.861960692 | 1.160 | 6.24 out of 7.24 |

41 | 0.131372009 | 7.612 | 0.868627991 | 1.151 | 6.61 out of 7.61 |

42 | 0.125026741 | 7.998 | 0.874973259 | 1.143 | 7 out of 8 |

43 | 0.118987949 | 8.404 | 0.881012051 | 1.135 | 7.4 out of 8.4 |

44 | 0.113240832 | 8.831 | 0.886759168 | 1.128 | 7.83 out of 8.83 |

45 | 0.107771299 | 9.279 | 0.892228701 | 1.121 | 8.28 out of 9.28 |

46 | 0.102565946 | 9.750 | 0.897434054 | 1.114 | 8.75 out of 9.75 |

47 | 0.09761201 | 10.245 | 0.90238799 | 1.108 | 9.24 out of 10.24 |

48 | 0.09289735 | 10.765 | 0.90710265 | 1.102 | 9.76 out of 10.76 |

49 | 0.088410408 | 11.311 | 0.911589592 | 1.097 | 10.31 out of 11.31 |

50 | 0.084140186 | 11.885 | 0.915859814 | 1.092 | 10.88 out of 11.88 |

51 | 0.080076215 | 12.488 | 0.919923785 | 1.087 | 11.49 out of 12.49 |

52 | 0.076208533 | 13.122 | 0.923791467 | 1.082 | 12.12 out of 13.12 |

53 | 0.072527661 | 13.788 | 0.927472339 | 1.078 | 12.79 out of 13.79 |

54 | 0.069024575 | 14.488 | 0.930975425 | 1.074 | 13.49 out of 14.49 |

55 | 0.065690688 | 15.223 | 0.934309312 | 1.070 | 14.22 out of 15.22 |

56 | 0.062517828 | 15.995 | 0.937482172 | 1.067 | 15 out of 16 |

57 | 0.059498217 | 16.807 | 0.940501783 | 1.063 | 15.81 out of 16.81 |

58 | 0.056624453 | 17.660 | 0.943375547 | 1.060 | 16.66 out of 17.66 |

59 | 0.053889492 | 18.556 | 0.946110508 | 1.057 | 17.56 out of 18.56 |

60 | 0.05128663 | 19.498 | 0.94871337 | 1.054 | 18.5 out of 19.5 |

61 | 0.048809485 | 20.488 | 0.951190515 | 1.051 | 19.49 out of 20.49 |

62 | 0.046451987 | 21.528 | 0.953548013 | 1.049 | 20.53 out of 21.53 |

63 | 0.044208356 | 22.620 | 0.955791644 | 1.046 | 21.62 out of 22.62 |

64 | 0.042073093 | 23.768 | 0.957926907 | 1.044 | 22.77 out of 23.77 |

65 | 0.040040962 | 24.974 | 0.959959038 | 1.042 | 23.97 out of 24.97 |

66 | 0.038106984 | 26.242 | 0.961893016 | 1.040 | 25.24 out of 26.24 |

67 | 0.036266416 | 27.574 | 0.963733584 | 1.038 | 26.57 out of 27.57 |

68 | 0.034514749 | 28.973 | 0.965485251 | 1.036 | 27.97 out of 28.97 |

69 | 0.032847686 | 30.444 | 0.967152314 | 1.034 | 29.44 out of 30.44 |

70 | 0.031261143 | 31.989 | 0.968738857 | 1.032 | 30.99 out of 31.99 |

71 | 0.02975123 | 33.612 | 0.97024877 | 1.031 | 32.61 out of 33.61 |

72 | 0.028314245 | 35.318 | 0.971685755 | 1.029 | 34.32 out of 35.32 |

73 | 0.026946667 | 37.110 | 0.973053333 | 1.028 | 36.11 out of 37.11 |

74 | 0.025645143 | 38.994 | 0.974354857 | 1.026 | 37.99 out of 38.99 |

75 | 0.024406483 | 40.973 | 0.975593517 | 1.025 | 39.97 out of 40.97 |

76 | 0.02322765 | 43.052 | 0.97677235 | 1.024 | 42.05 out of 43.05 |

77 | 0.022105754 | 45.237 | 0.977894246 | 1.023 | 44.24 out of 45.24 |

78 | 0.021038046 | 47.533 | 0.978961954 | 1.021 | 46.53 out of 47.53 |

79 | 0.020021909 | 49.945 | 0.979978091 | 1.020 | 48.95 out of 49.95 |

80 | 0.01905485 | 52.480 | 0.98094515 | 1.019 | 51.48 out of 52.48 |

81 | 0.018134501 | 55.144 | 0.981865499 | 1.018 | 54.14 out of 55.14 |

82 | 0.017258605 | 57.942 | 0.982741395 | 1.018 | 56.94 out of 57.94 |

83 | 0.016425014 | 60.883 | 0.983574986 | 1.017 | 59.88 out of 60.88 |

84 | 0.015631686 | 63.973 | 0.984368314 | 1.016 | 62.97 out of 63.97 |

85 | 0.014876676 | 67.219 | 0.985123324 | 1.015 | 66.22 out of 67.22 |

86 | 0.014158132 | 70.631 | 0.985841868 | 1.014 | 69.63 out of 70.63 |

87 | 0.013474294 | 74.215 | 0.986525706 | 1.014 | 73.22 out of 74.22 |

88 | 0.012823486 | 77.982 | 0.987176514 | 1.013 | 76.98 out of 77.98 |

89 | 0.012204112 | 81.940 | 0.987795888 | 1.012 | 80.94 out of 81.94 |

90 | 0.011614653 | 86.098 | 0.988385347 | 1.012 | 85.1 out of 86.1 |

91 | 0.011053665 | 90.468 | 0.988946335 | 1.011 | 89.47 out of 90.47 |

92 | 0.010519773 | 95.059 | 0.989480227 | 1.011 | 94.06 out of 95.06 |

93 | 0.010011668 | 99.883 | 0.989988332 | 1.010 | 98.88 out of 99.88 |

94 | 0.009528105 | 104.953 | 0.990471895 | 1.010 | 103.95 out of 104.95 |

95 | 0.009067897 | 110.279 | 0.990932103 | 1.009 | 109.28 out of 110.28 |

96 | 0.008629918 | 115.876 | 0.991370082 | 1.009 | 114.88 out of 115.88 |

97 | 0.008213093 | 121.757 | 0.991786907 | 1.008 | 120.76 out of 121.76 |

98 | 0.0078164 | 127.936 | 0.9921836 | 1.008 | 126.94 out of 127.94 |

99 | 0.007438868 | 134.429 | 0.992561132 | 1.007 | 133.43 out of 134.43 |

100 | 0.007079571 | 141.252 | 0.992920429 | 1.007 | 140.25 out of 141.25 |

the median looks to be at

14 rounds of play

Now, that seems too low by my lifetime of play

of course

over a lifetime of BJ play one can get close to the expectation

over a weekend of play

0 Bjs happens to many

enjoy the journey

enjoy the ride

Sally

I Heart Vi Hart

February 27th, 2018 at 10:29:25 AM
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This is all fascinating--thanks to everyone who's punching the numbers! Apparently it was even more improbable than I thought. I guess this means I'm due for a big win, right?! ;)