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Probability of getting 3 Blackjacks in a row?
| January 13th, 2011 at 2:47:56 PM permalink | |
| L8lori Member since: Jan 13, 2011 Threads: 1 Posts: 1 | Wizard, You have an awesome sight & I have enjoyed your articles for a few years now... thank you for giving us this web site. I am been running different numbers thru my head trying to come up with a way to compute the probabilities of getting 3 blackjacks in a row with a 6 deck continuous shuffle machine? Or even the odds of getting 5 blackjacks in a row with the same situation? Also... I saw a casino promotion where you got a drawing ticket every time you were dealt a red queen and a black ace... is there a way to calculate my odds of getting this type of hand in blackjack? Thank you L8lori |
| January 13th, 2011 at 3:40:53 PM permalink | |
| HKrandom Member since: Oct 1, 2010 Threads: 16 Posts: 126 | Odds of getting a blackjack are roughly 4/13*1/13*2 so the chances of that happening 3 times in a row are about 1 in 10,000 and the chances of getting 5 in a row are about 1 in 4,200,000. The chance of getting a red queen and a black ace is 2*2/52*2/52 or 1/338. |
| January 13th, 2011 at 4:17:14 PM permalink | |
| Ayecarumba Member since: Nov 17, 2009 Threads: 113 Posts: 2047 | From the Wizard of Odds Blackjack page, the probability of getting a blackjack on a six deck game is: 0.047489. The probability of this happening three times in a row is: (.047489)^3 = .00010709743 or 1 in 9,337 Edit: FYI, from the Wizard's Blackjack page, the general formula for calculating the odds of a blackjack in n decks is: 2*(4/13)*(4n/(52n-1)). |
| January 13th, 2011 at 4:28:58 PM permalink | |
| mkl654321 Member since: Aug 8, 2010 Threads: 65 Posts: 3412 |
I'm glad it's that low, because I ever actually got three blackjacks in a row, the earth would open up and swallow me and the casino. The fact that a believer is happier than a skeptic is no more to the point than the fact that a drunken man is happier than a sober one. The happiness of credulity is a cheap and dangerous quality.---George Bernard Shaw |
| January 13th, 2011 at 4:31:01 PM permalink | |
| ElectricDreams Member since: Sep 8, 2010 Threads: 4 Posts: 194 |
I got two in a row a few days ago. I was all like "yay! Blackjack again!" I think I colored up after that, because I wanted to leave on a high point ;-) |
| January 13th, 2011 at 4:59:59 PM permalink | |
| Ayecarumba Member since: Nov 17, 2009 Threads: 113 Posts: 2047 |
In a six deck shoe (or CSM) there are 12 red queens and 12 black aces. The odds of getting dealt one of each is (12/312)*(12/311) = .001484 or 1-in-674. |
| January 13th, 2011 at 5:20:30 PM permalink | |
| Ayecarumba Member since: Nov 17, 2009 Threads: 113 Posts: 2047 |
1-in-9,337 is not that unusual, when, according to the Wizard, the odds of getting a royal flush in VP, if all you did was try to get a Royal every draw are 1-in-23,081. |
| January 13th, 2011 at 5:44:29 PM permalink | |
| PapaChubby Member since: Mar 29, 2010 Threads: 9 Posts: 342 |
You neglected that the cards may be dealt in either order, so the probability is twice as great as you calculated. |
| January 13th, 2011 at 5:45:19 PM permalink | |
| PapaChubby Member since: Mar 29, 2010 Threads: 9 Posts: 342 | I don't think I have ever been dealt three blackjacks in a row, but I'm sure I've seen the dealer get 'em on several occasions. Sometimes the math just doesn't tell the whole story. |
| January 13th, 2011 at 6:22:59 PM permalink | |
| Ayecarumba Member since: Nov 17, 2009 Threads: 113 Posts: 2047 |
Thank you for the correction PapaChubby. This is my calculation: (24 (12 red Q's and 12 black A's) / 312 total cards in six decks) * (12 red Q's or black A's, depending on what was dealt first/311) = 1-in-337 |
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