phoebeanne
phoebeanne
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March 19th, 2017 at 5:12:39 PM permalink
I am seeking what the odds are of a very, very unusual blackjack hand!!! Ready for this scenario??

A six deck blackjack table. (Dealer hits on 16, standard blackjack.)

A player is dealt two aces (A1 & A2). She splits.
A1 is dealt a face card (blackjack #1, henceforth known as BJ1). A2 is dealt an ace (A3) - so she splits again.
(Review: there are now three aces in front of the player, one has been made into BJ1).
A2 is dealt a face card (blackjack #2, henceforth known as BJ2). A3 is dealt an ace (A4) - so she splits again.
(Review: there are now four aces in front of the player, two have been made into BJ1 & BJ2).
A3 is dealt a face card (blackjack #3, henceforth known as BJ3).
A4 is dealt a ten (blackjack #4, aka BJ4).
(Review: there are now four aces in front of the player, all four have been made into BJ1, BJ2, BJ3, and BJ4).

What are the odds of this happening?
Last edited by: phoebeanne on Mar 19, 2017
teliot
teliot
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phoebeanne
March 19th, 2017 at 5:51:11 PM permalink
Assuming by "Ten" for BJ4 and "Face Card" for BJ1, BJ2, and BJ3 you are referring to any ten-valued card and not specifically to JQK for the first 3 blackjacks and T for the 4-th blackjack, the answer is 4,034,212-to-1.

You may be asking more generally about the question, "how often do Aces split to 4 hands and make blackjack on each hand," but I have no idea if that's what you are really asking, so I will just answer the question you asked (with an assumption about Tens and Face Cards).
phoebeanne
phoebeanne
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March 19th, 2017 at 6:02:22 PM permalink
WOW - thanks! No, I was not asking that general question, so thank you! How in the world does one go about figuring that out??
Deucekies
Deucekies
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March 19th, 2017 at 6:31:16 PM permalink
Quote: teliot

Assuming by "Ten" for BJ4 and "Face Card" for BJ1, BJ2, and BJ3 you are referring to any ten-valued card and not specifically to JQK for the first 3 blackjacks and T for the 4-th blackjack, the answer is 4,034,212-to-1.



Wow, that much? That's up there in Seven Card Straight Flush territory.
Casinos are not your friends, they want your money. But so does Disneyland. And there is no chance in hell that you will go to Disneyland and come back with more money than you went with. - AxelWolf and Mickeycrimm
RS
RS
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phoebeanne
March 19th, 2017 at 6:37:24 PM permalink
Quote: phoebeanne

WOW - thanks! No, I was not asking that general question, so thank you! How in the world does one go about figuring that out??



Chance of getting an ace as your first card is 24/312 (24 aces, 312 cards). Chance of an ace on your second card is 23/311 (23 aces remaining out of 311 cards). Then 64/310 for the face card. Then 22/309 for the next ace. And so on. Multiply all them numbers up and you get your answer.

(24*23*22*21*96*95*94*93) / (312*311*310*309*308*307*306*305)
:.
http://m.wolframalpha.com/input/?i=%28%2824*23*22*21*96*95*94*93%29+%2F+%28312*311*310*309*308*307*306*305%29%29&x=0&y=0
:.
http://m.wolframalpha.com/input/?i=1%2F%28%2824*23*22*21*96*95*94*93%29+%2F+%28312*311*310*309*308*307*306*305%29%29&x=0&y=0

= 1 in 4,034,212
"should of played 'Go Fish' today ya peasant" -typoontrav
billryan
billryan
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March 19th, 2017 at 7:12:34 PM permalink
Of course, the player had no blackjacks as a two card 21 after a split is simply a 21, not a blackjack.
It's what you do and not what you say If you're not part of the future then get out of the way
phoebeanne
phoebeanne
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March 19th, 2017 at 8:58:53 PM permalink
Billryan,
Depends on the casino, definitions vary by casino. The place my friend was at considered her four amazing deals blackjacks (and paid appropriately).
RS
RS
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March 19th, 2017 at 11:28:17 PM permalink
Quote: phoebeanne

Billryan,
Depends on the casino, definitions vary by casino. The place my friend was at considered her four amazing deals blackjacks (and paid appropriately).


I think I may have heard of this rare rule, many moons ago.....where split A's with a T count as a 3:2 BJ.



I remember once playing blackjack with my brother. He got aces, split, got a T on one of them. When dealer paid him even money, he tried to get paid 3:2 on it (he thought it was considered a blackjack). At first I thought he was joking, but then realized he was serious. He tried getting the pit boss over and I was telling him the dealer was right, it pays even money. He thought we all missed the obvious.
"should of played 'Go Fish' today ya peasant" -typoontrav
billryan
billryan
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March 19th, 2017 at 11:35:54 PM permalink
From what I have read, that rule has been effect since casinos first adapted to Ed Thorpe in the early Sixties.
Anyone want to chime in with a casino that treats split 21s as a BJ?
When BJ pays 3-2, of course. I've seen video BJ machines that will say Blackjack when it happens but they pay even money.
It's what you do and not what you say If you're not part of the future then get out of the way
phoebeanne
phoebeanne
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March 20th, 2017 at 8:37:42 AM permalink
The casino we were at is an Indian casino in Arizona. She was paid even money. I was wrong earlier when I said she got 3-2.

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