Posted by COSMICOOMPH

Feb 25, 2013

Feb 25, 2013

## What is the standard deviation of a Q high pai gow or what is the % of occurence between set # hands

What is the percentage of times a Q high pai gow occurs between 52 and 62 hands played, and the following:47 and 67 hands

42 and 72 hands

Thanks.

cosmicoomph

## Comments

The q-high pai-gow happens 1.7643% of the time. So, you should expect to see it about 1 time in all of your example ranges.

"What is the standard deviation of a Q high pai gow"

Nice question

(I answered the range one in your thread and you may need more explanation on that.)

For the Binomial Standard Deviation (and NOT the $SD)

Simple

square root of (P*Q)

P=probability of success = 0.0176426992376174 (1/56.68) this is rounded

Q = 1-P = probability of failure

You will get 0.1316 = standard deviation

How to use this??

Well, say 100 hands for the Dealer

Expected # of successes = 100*P or 1.76

The SD for 100 trials = square root of 100 (10) * 0.1316 = 1.316

But because of the low probability of 1 in 57

The curve at 100 and even 200 is NOT a normal one. Not even close. You can see this from a simple histogram.

At 1000 it looks to be.

A simple test if the sample size could be normal is

N*P and N*Q are both over 5 (sometimes must be over 10)

1.76 and 98.2

It fails the normal distribution test (Just the SD value should tell you this)

Now do not get a probability and an average mixed up.

They are two different values.

N = sample size (all the possible outcomes)

n = number of successes

A Probability (between 0 and 1 or as a percentage) is n/N

An average (a number) is N/n

Apples and Oranges using the same data

May I suggest not amusing people who blog to ask questions? It is not the proper use of a blog and I have come to believe 99% of the time it is just some impatient person joining and who typically does not even come back to see what someone has written.

Does it matter? yes, because those of us who post proper blog posts often would like for them to 'stay up' so we have a chance to get comments.

I agree with the above. Please make gambling questions a post, not a blog entry.