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How to check if a series of dealt cards are very unlikely

  1. Dec 3, 2009 #1
    I am trying to make a basic little program where i can input a large set of texas holdem hands (2 cards) and check to see how Unlikely/likely these cards were to be dealt. (to show that no tampering was done...ie. show its random enough)

    For example, it is VERY unlikely that a player receives AA hundreds of times in a small sample.

    I have some basic questions I was wondering if someone could help me get started?

    I do have minimal experience with stats though.

    my question is how would you represent how likely something is over the average or expected?

    I figure there are (52 choose 2) card combinations...and each card combination should be expected equally, so over an extremely large sample all card combinations should be roughly occuring equally?

    In statistics how do you show how far something is from normal?

    any topics i should look up?

    thanks a lot!
  2. jcsd
  3. Dec 3, 2009 #2


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    Cards dealt at random from a deck are a "selection without replacement". For this, you want to use the Hypergeometric distribution; this essentially can be used to you a probability of obtaining a given hand in a single deal.

    To get the expected mean and standard deviation for the number of times you get a certain hand in repeated independent deals, you want the Binomial distribution.

    Getting the probability of a certain hand (like pocket rockets, or AA in Texas Holdem) is just a matter of getting the number of ways for have that hand divided by the total number of hands. This is 6 / 1326, or 1 / 216, which is about 0.004524887

    In a large number of repeated hands n, the expected number of times you will get AA is given by the binomial distribution, which is np, and the standard deviation is sqrt(np(1-p)).

    For example, in one million hands, the number of times you get AA is about 4525, and the standard deviation is about 67

    Cheers -- sylas
  4. Dec 3, 2009 #3

    D H

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    The general name for this type of question is "statistical hypothesis testing". In short, is some set of observations consistent or inconsistent with what would be expected given some distribution? In long, this is the subject of books, multiple books. You will get an inkling of what needs to be done by googling "statistical hypothesis testing", but if you want to get serious about this topic you will need to read one of the books you run across during your search.
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