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3 Flopped Flushes and Set over Set over Set Probability Questions

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  1. Davio Davio is offline

    Antwerp
    Belgium

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    Dec 7th, 2006 (12/7/2006 3:36am)

    Give your answers in the form '1 in x' or 'y to 1'.

    1)a) In a 3-handed game, given the fact that all 3 people have cards of the same suit, what is the chance of 3 of that suit flopping?

    You don't have to account for any straight flush possibilities.

    b) Does anything change if it was a 9-handed game?

    2) If 3 people have pocket pairs in a 3-handed game (none shared) what is the chance of all 3 people flopping a set?
  2. twosovertens twosovertens is offline

    United Kingdom

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    Dec 7th, 2006 (12/7/2006 4:27am) in reply to Davio

    Im pretty rubbish at poker, but ok at maths, so:

    1a) 7 remaining cards in the suit, 46 unknown cards -- 7*6*5/(46*45*44)= 0.0023

    1 in about 430

    b) Unless you have any more information about the other hands then nothing changes.

    2) 6*4*2/(46*45*44) = 0.0005

    about 1 in 1900
  3. Staple Gun Staple Gun is offline

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    Dec 7th, 2006 (12/7/2006 5:58am) in reply to twosovertens

    ^^ He pretty much nailed it.
  4. Leet8s Leet8s is offline usausausausausa

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    Dec 7th, 2006 (12/7/2006 7:09am) in reply to Staple Gun

    for b, wouldnt it just be

    2^3 / (46 X 45 X 44)???

    everyone has 2 cards to make a set, but the total deck decreases by one each time.

    or basically 2/46 X 2/45 X 2/44?
     
  5. twosovertens twosovertens is offline

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    Dec 7th, 2006 (12/7/2006 7:41am) in reply to Leet8s

    Doing it like that orders the cards as well - initially there are 6 possible cards to make a set, then once one of them is done there are 4 more for the remaining 2 sets and finally 2 cards to make the last set.
  6. Leet8s Leet8s is offline usausausausausa

    New York City, NY
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    Dec 7th, 2006 (12/7/2006 8:10am) in reply to twosovertens

    ahhh, now i see, thank you
     
  7. bdluss bdluss is offline

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    Dec 7th, 2006 (12/7/2006 11:32am) in reply to Davio

    When I answered, I looked at the possibilty of this happening at the start of the hand. Flush over flush over flush in a 3 handed game. Basically 12/51*11/50*10/49*9/48*8/47*7/46*6/45*5/44 which comes to 19958400/2567428617600. This is approximately 1,312,698 to 1 in a 3 handed game.

    For the set over set in a 3 handed game. 1/17 (i wont use exact # for odds of a pocket pair but it is approximately that) * 1/17*1/17*1/8 (once again apprimate for hitting a set) *1/8*1/8 which is 1 in 2,515,456. Once again the 3 handed stuff is easier to do.
     
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