6 cards straight Flush probability
July 28th, 2015 at 9:27:20 AM
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Hello,
Would somebody please show me how to calculate the probability of getting a 6 cards straight Flush in a 8 decks game? Similar to the 3 card poker's 6 card Bonus bet that I see all over Vegas..
Thanks,
Tommy
Would somebody please show me how to calculate the probability of getting a 6 cards straight Flush in a 8 decks game? Similar to the 3 card poker's 6 card Bonus bet that I see all over Vegas..
Thanks,
Tommy
July 28th, 2015 at 9:47:03 AM
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Not sure which game you're talking about, but I can do it for 6 cards off the top of an 8 deck shoe. Probability I got is 1 in 40,000.
Possible combinations: 416choose6 = 6.94e12 hands
Winning combinations: 9straights^8decks*4suits = 1.72e8
Probability: 1.72e8/6.94e12 = .000025 = 1 in 40,318
Winning combinations: 9straights^8decks*4suits = 1.72e8
Probability: 1.72e8/6.94e12 = .000025 = 1 in 40,318
July 28th, 2015 at 10:11:11 AM
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Thank you Studmuffn! that was quick haha I was still playing with this formula and then I got stuck. Perhaps, I did it completely wrong lol
(52/416)*(12/415)*(11/414)*(10/413)*(9/412)*(8/411) I was like ehhhhhh. Thanks for your quick reply again I really appreciate that.
(52/416)*(12/415)*(11/414)*(10/413)*(9/412)*(8/411) I was like ehhhhhh. Thanks for your quick reply again I really appreciate that.
July 28th, 2015 at 11:09:05 AM
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Quote: tommyngo215Thank you Studmuffn! that was quick haha I was still playing with this formula and then I got stuck. Perhaps, I did it completely wrong lol
(52/416)*(12/415)*(11/414)*(10/413)*(9/412)*(8/411) I was like ehhhhhh. Thanks for your quick reply again I really appreciate that.
It's not as simple as that. Since there is no 'wrap around' straight flush, the first card matters.... a deuce is less likely to produce a six card straight flush than a 7 as an example. (j, q, k, A, 2, 3) does not count as a 6 card straight flush)
July 28th, 2015 at 11:22:09 AM
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Quote: studmuffnNot sure which game you're talking about, but I can do it for 6 cards off the top of an 8 deck shoe. Probability I got is 1 in 40,000.
Possible combinations: 416choose6 = 6.94e12 hands
Winning combinations: 9straights^8decks*4suits = 1.72e8
Probability: 1.72e8/6.94e12 = .000025 = 1 in 40,318
Your winning combinations is off. It's 9*4*8^6 ( 9 straights * 4 suits * 8 cards for each of the 6 ranks)
“Man Babes” #AxelFabulous
July 28th, 2015 at 12:48:56 PM
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Quote: mipletYour winning combinations is off. It's 9*4*8^6 ( 9 straights * 4 suits * 8 cards for each of the 6 ranks)
Hm that's not how I see it. I stand by the exponent being the number of decks in the shoe because a low straight in spades could have n different AoS, 8 different deuces, etc.
The length of the straight (6) only factors into the combinatorial and the number of possible straights (here it can start with Ace thru 9). In your equation, a straight of 13 is more than certain.
July 28th, 2015 at 5:34:19 PM
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Miplet is right.
I heart Crystal Math.
July 29th, 2015 at 9:08:16 AM
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Ok, I think I understand. straights*suits*decks^ranks
That makes sense, thanks for the correction.
I guess that puts OPs probability even lower, down to 1 in 736,000
That makes sense, thanks for the correction.
I guess that puts OPs probability even lower, down to 1 in 736,000
July 29th, 2015 at 12:46:06 PM
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Thanks so much everybody for your replies.
