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Math Help - Some probability in the game Big 2

  1. #1
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    Some probability in the game Big 2

    Big 2 is a card game commonly played in Asia.
    Big Two - Wikipedia, the free encyclopedia

    There are 4 playeers and each is dealt 13 cards. The trump cards in this game is 2, hence the name Big 2. My question is:
    What's the probability of 1 player dealt 4 '2's?

    Method 1:
    {{48 \choose 9} \over {52 \choose 13}} = {11 \over 4165}


    Method 2:
    Using the ball-and urn model championed by William Feller,
    we imagine 4 people as 4 urns, and the 4 '2's to be dealt as 4 balls:
    So now, we are asking what's the probability of all 4 balls landing inside 1 urn:

    The probability of 4 balls inside 1 urn(and not 3 others): ({1 \over 4})^4 = {1 \over 256}

    Since it can be any of the 4 urns, we multiply by 4 and get {4 \over 256}

    Now, why don't the 2 methods tally?
    Can anyone please explain?

    Much appreciated!
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  2. #2
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    Quote Originally Posted by chopet View Post
    There are 4 playeers and each is dealt 13 cards. The trump cards in this game is 2, hence the name Big 2. My question is: What's the probability of 1 player dealt 4 '2's?

    Method 1:
    {{48 \choose 9} \over {52 \choose 13}} = {11 \over 4165}
    That is the correct probability if one hand, 13 cards, are dealt.
    Last edited by Plato; November 12th 2007 at 10:27 AM.
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  3. #3
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    Quote Originally Posted by Plato View Post
    That is the correct probability if one hand, 13 cards, are dealt.
    I think the problem lies with Method 2, not Method 1.
    I am treating each placement as independent, when in fact, they are not.
    Or are they? Urgh. I am confused.
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