#1
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Prob. of flush in 7 card stud with three-flush after 4th street?
In The Theory of poker on page 95, Sklansky says that there is 9-to-1 chance against making flush (spades) when you have a 3-flush (spades) after 4th street. In the example sited, there is only 1 opponent, and you see two of his exposed cards- both cards are not spades.
I am not sure why my math is incorrect. I have {10/46 * 9/45 * 44/44) *3! = 26.1% - a very different result!! Anyone know the correct math. |
#2
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Re: Prob. of flush in 7 card stud with three-flush after 4th street?
There are many combinations which you count a lot of times in that.
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#3
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Re: Prob. of flush in 7 card stud with three-flush after 4th street?
Well, 10/46*9/45 is 4.34%, not 26%, for a start.
Counting more carefully to avoid duplicates: You can get three spades, 10/46*9/45*8/44 = 0.79% Or, you can get spade spade plain suit, or spade plain suit spade, or plain suit spade spade: 10/46*9/45*36/44 = 3.56% each of three ways, for a total of 0.79+3x3.56=11.5%. That's about 9 in 1 or 8 to 1. It will move by about 0.4% for each additional non-spade you see. |
#4
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Re: Prob. of flush in 7 card stud with three-flush after 4th street?
(edit: the answer below provides the wrong answer... though I don't quite understand why)
10/46 * (9/45 + 9/44) which is 8.79%, or 1 in 11.37. |
#5
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Re: Prob. of flush in 7 card stud with three-flush after 4th street?
spade spade plain = 10/46 * 9/45 * 36/44 = 3.557%
spade plain spade = 10/46 * 37/45 * 9/44 = 3.656% plain spade spade = 38/46 * 10/45 * 9/44 = 3.755% spade spade spade = 10/46 * 9/45 * 8/44 = 0.791% total: 11.047%, or 1 in 9.05. Clearly this is the correct answer. Can someone point out to me why my earlier answer is wrong, though? Why doesn't that provide the correct result? mdb: Does the book actually say "9 to 1"? It's 8 to 1, or 1 in 9... it's a mistake in the book if it says 9 to 1. |
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