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Math Help - drawing a striaght in texas holdem

  1. #1
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    drawing a striaght in texas holdem

    if you have 4,5 in your hand and the board is 6,7,A, what is the chance of hitting your run? i thought with 8 cards to hit and 2 chances to hit them that would mean 47/16 but im told this is wrong...
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  2. #2
    hpe
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    Quote Originally Posted by mrconfused
    if you have 4,5 in your hand and the board is 6,7,A, what is the chance of hitting your run? i thought with 8 cards to hit and 2 chances to hit them that would mean 47/16 but im told this is wrong...
    There are 47 cards left, of which 8 are in your favor. So it's 8/47, about 17%.
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    u misread the question... there are 2 chances to hit... i thought the answer would be 47/(8*2) but have been told its wrong which i accept but i cant get my head how the formula for probability is arrived.
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    hpe
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    Quote Originally Posted by mrconfused
    u misread the question... there are 2 chances to hit... i thought the answer would be 47/(8*2) but have been told its wrong which i accept but i cant get my head how the formula for probability is arrived.
    I guess I was confused (thinking Omaha )

    You'll end up with a straight if one of the following two possibilities occur:

    1. The turn card or the river card is a 8. This results in 4 5 6 7 8.
    2. The turn card or the river card is a 3. This results in 3 4 5 6 7.

    You could also see a 2 and a 3, allowing the straight A 2 3 4 5, but you wouldn't do this, since the 3 4 5 6 7 straight is higher in this case.

    Altogether, there are 47 possibilities for the turn card and 46 for the river card, since you have already seen five cards. This gives 47*46 ways in which these two cards can be dealt. Since the order in which they are dealt doesn't matter for the end result, there are 47*46/2 = 1081 possibilities.

    So now let's find the number of ways in which you might lose, i.e. no 3 and no 8 among turn or river card. There are 39 cards you don't want to see, and 39*38/2 = 741 ways to deal only these. All 340 other cases include at least one 8 or one 3. Therefore the probability is 340/1081, about 31.5%.
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    What if you wanted to include the possibility of the bicycle (A-2-3-4-5)?
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    hpe
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    Quote Originally Posted by MathGuru
    What if you wanted to include the possibility of the bicycle (A-2-3-4-5)?
    Isn't 3 4 5 6 7 higher? We're not playing lowball.
    Last edited by hpe; November 14th 2005 at 07:33 PM.
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    a straight is a straight

    It is a lower straight but it is still a straight. And a straight would still be a very good hand. That low straight might beat another player with 3 of a kind or two pair.
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  8. #8
    hpe
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    Quote Originally Posted by MathGuru
    It is a lower straight but it is still a straight. And a straight would still be a very good hand. That low straight might beat another player with 3 of a kind or two pair.
    Right. But if the community cards are 2 3 6 7 A (and that's the only case that's relevant here) and you are holding 4 5, you' be foolish not to go for the better straight 3 4 5 6 7, which is evidently also possible.
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    Thumbs up

    You are absolutely right!
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