A String of Naturals
March 25th, 2015 at 7:28:16 AM
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Dear Wizard,
I have been playing casino blackjack nearly weekly for several years. Until this week, the most consecutive blackjacks I had seen dealt (it was to me) was 4. This week I was dealt 5 consecutive blackjacks. Neither the dealer, the other players, nor the floor had ever seen this happen. Just how rare is this occurrence?
Love your work...have lurked around your site for years!
Lisa
I have been playing casino blackjack nearly weekly for several years. Until this week, the most consecutive blackjacks I had seen dealt (it was to me) was 4. This week I was dealt 5 consecutive blackjacks. Neither the dealer, the other players, nor the floor had ever seen this happen. Just how rare is this occurrence?
Love your work...have lurked around your site for years!
Lisa
March 25th, 2015 at 8:13:53 AM
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How many decks of cards were in play?
May the cards fall in your favor.
March 25th, 2015 at 8:50:55 AM
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Let the games begin.Quote: DieterHow many decks of cards were in play?
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
March 25th, 2015 at 8:51:02 AM
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Let the games begin.Quote: DieterHow many decks of cards were in play?
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
March 25th, 2015 at 9:47:43 AM
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Quote: AxelWolfLet the games begin.
You can say that again!
March 25th, 2015 at 10:07:02 AM
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With replacement after each hand, it looks to me like the odds are about 1:4.2MM.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
March 25th, 2015 at 10:19:20 AM
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Sorry, folks...I should have noted that there were 8 decks in play.
March 25th, 2015 at 12:18:21 PM
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Welcome to the forums, Lisa.
Odds of Blackjack... 2* (Odds of Ace)*(Odds of 10 valued card). For 8 decks:
(Odds of Ace, in 8 decks) = 32/416 = 0.0769
(Odds of '10', in 8 decks) = 128/415 = 0.3084
Odds of getting 1 Blackjack = 2 * .0769 * .3084 = .0474, or 4.74%.
Now, we're going to assume after every hand the dealer reshuffled the 8 decks. I know they don't do that, and the math would only differ slightly, but this should be a fairly close estimate...
Odds of getting 5 Blackjacks in a row = .0474^5 = 2.393*e-7 = .0000002393, about 1 in 4.2 million =)
The Wizard Says the odds of a blackjack for n decks is: 2*(4/13)*(4n/(52*n-1))
Simplifying the Wizards formula a bit: 32n / 13(52*n-1) = 256 / 5395 = .0475 = 4.75%. If we again assume a shuffled deck each go it would be .0475^5 = 2.418*e-7 = .0000002418, or close to 1 in 4.2 million as previously described.
Odds of Blackjack... 2* (Odds of Ace)*(Odds of 10 valued card). For 8 decks:
(Odds of Ace, in 8 decks) = 32/416 = 0.0769
(Odds of '10', in 8 decks) = 128/415 = 0.3084
Odds of getting 1 Blackjack = 2 * .0769 * .3084 = .0474, or 4.74%.
Now, we're going to assume after every hand the dealer reshuffled the 8 decks. I know they don't do that, and the math would only differ slightly, but this should be a fairly close estimate...
Odds of getting 5 Blackjacks in a row = .0474^5 = 2.393*e-7 = .0000002393, about 1 in 4.2 million =)
The Wizard Says the odds of a blackjack for n decks is: 2*(4/13)*(4n/(52*n-1))
Simplifying the Wizards formula a bit: 32n / 13(52*n-1) = 256 / 5395 = .0475 = 4.75%. If we again assume a shuffled deck each go it would be .0475^5 = 2.418*e-7 = .0000002418, or close to 1 in 4.2 million as previously described.
Playing it correctly means you've already won.
March 25th, 2015 at 12:22:36 PM
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Hey Romes - check the decimals on your ace odds...
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
March 25th, 2015 at 12:27:33 PM
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Quote: rdw4potusHey Romes - check the decimals on your ace odds...
lol I knew I'd get called out. As soon as I reviewed and saw "omg 23% chance for BJ?!?!" I was like, okay where's the decimal...
Playing it correctly means you've already won.
March 25th, 2015 at 1:21:13 PM
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Quote: Romeslol I knew I'd get called out. As soon as I reviewed and saw "omg 23% chance for BJ?!?!" I was like, okay where's the decimal...
lol. right? I think there's still one small issue. You need to multiply by 2, since order doesn't matter. odds of 1 BJ are 2* 2.37%...
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
March 25th, 2015 at 1:53:29 PM
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Quote: rdw4potuslol. right? I think there's still one small issue. You need to multiply by 2, since order doesn't matter. odds of 1 BJ are 2* 2.37%...
Yeah, I got caught up at work and said F it, I'll leave it wrong (with the Wiz's correct math below it) for an hour or two =P. Ty though for pointing it out, I would hate to have mislead someone with a simple math mistake!
Playing it correctly means you've already won.
March 25th, 2015 at 3:12:47 PM
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I would be good at math if there weren't letters involved. WTF, why are their letters. I am great at non lettered math.
Expect the worst and you will never be disappointed.
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