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

• rsala004
In summary: For this conversation, you would need to use the Hypergeometric distribution to calculate the probability of getting a given hand in a single deal. The Binomial distribution can be used to calculate the probability of a certain hand, like pocket rockets, or AA in Texas Holdem.
rsala004
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 occurring equally?

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

any topics i should look up?

thanks a lot!

rsala004 said:
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 occurring equally?

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

any topics i should look up?

thanks a lot!

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

rsala004 said:
my question is how would you represent how likely something is over the average or expected?
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.

## 1. How can I calculate the probability of a specific series of dealt cards?

The probability of a specific series of dealt cards can be calculated by multiplying the probabilities of each individual card being dealt in that specific order. For example, if you are interested in the probability of getting a specific hand in poker, you would multiply the probability of getting each card needed for that hand in the specific order.

## 2. What is the significance level for determining if a series of dealt cards is very unlikely?

The significance level is a measure of how unlikely an event is. It is usually expressed as a percentage and is used to determine the threshold for rejecting the null hypothesis. In the context of checking if a series of dealt cards is very unlikely, a significance level of 5% is commonly used as a threshold.

## 3. Can I use a statistical test to determine if a series of dealt cards is very unlikely?

Yes, you can use a statistical test to determine if a series of dealt cards is very unlikely. The most commonly used test for this purpose is the chi-square test, which compares the observed frequencies of the dealt cards to the expected frequencies based on the null hypothesis.

## 4. What is the null hypothesis when checking if a series of dealt cards is very unlikely?

The null hypothesis is that the series of dealt cards is random and follows the expected probabilities of each card being dealt. In other words, there is no significant difference between the observed and expected frequencies of the dealt cards.

## 5. What sample size is needed to accurately determine if a series of dealt cards is very unlikely?

The sample size needed to accurately determine if a series of dealt cards is very unlikely depends on the level of significance and the expected probability of each card being dealt. Generally, a larger sample size is needed for a more accurate determination, but a rule of thumb is to have at least 20 observations for each category of cards being dealt.

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