Video Poker Distributions are Not Normal

[New2vp]

What would be great is if everyone reading this walked away with at least the ability to calculate standard deviations.Seriously, Frank, most don't really want to do homework, sometimes even at the cost of a lower grade.  So probably not many will want to do this.In my experience, I found that many people shied away from this measure simply because it is too difficult to understand and it has that awful square root sign in its formula.  To start with, "standard deviation" is a classical example of an oxymoron with standard often meaning "usual" and deviation denoting the "unusual."  To help with understanding, standard deviation can be thought of as the typical distance that an individual observation in your data is from the average of your data.  Large standard deviations mean large, more spread out data, while small standard deviations denote just the opposite.Now, going along with Frank's program to get everyone to be able to calculate a standard deviation, if you don't like to do such work manually, in this day and age, EXCEL can do this for you.  In the formula bar of the cell where you want the standard deviation of a list of numbers:1.  Type in the eight keystrokes that follow =STDEVP(2.  Highlight the list of numbers3.  Type in the closing parenthesis  ) and then hit the ENTER key.---------------------------------------------------------------------------------------------------------------------------If you were going to follow Frank's formula, in the days of pencil and paper, there is an easier equivalent way to calculate the standard deviation by hand, called the "computational" formula.  The reason the computational formula is easier to apply is because the average may typically contain a fraction even if all the numbers in your list are integers.  It is a lot easier to square whole numbers than square a bunch of fractions.  With the computational formula often you have to square only one fraction instead of an entire list of fractions.  (Of course, with computers, it's equally easy to do either.)Computational formula:First make a mean average of all
the results; then square it and save for step 4.
Then square each individual
result.
Average all the squared individual results.
Subtract the result in Step 1 from the result in Step 3; you're done.If this seems harder, try it both ways and see which is easier for you.  If you don't get the same answer, then you made a mistake (or we did in our explanations!)  Experience says there will be fewer mistakes made with the computational formula.(Nevertheless, I almost always use a computer these days; I have a much more difficult time finding pencil and paper than finding my computer...or phone...or...)

[Frank Kneeland]

Perhaps what we need to get the ball rolling is some numbers people can play around with.Here's some heights of basket ball players I just made up. Your job is to figure out the standard deviation in height.5' 11" / 6' / 6' 1" / 5' 10" / 6' 2" / 6' 4" / 6' 11" / 7' / 6' 8" / 6' 5"~FK

[New2vp]

Frank, I'm not really sure where you are going with this.  You know that the whole idea of this thread is that video poker distributions are not normal.  Hey, that's its title!  And I think you even suggested that I start this new thread!That being said, I do not want to stop anyone from learning.  So if you want to do this problem, please do.But, unfortunately, the value of knowing how to do standard deviations will not really help much in determining probabilities of ranges of outcomes of video poker distributions, which is the point of this thread.  At least not until after millions of hands.I would think that the last 4 points in your Relevance post are more pertinent to the thread than the how-to on standard deviations.  And, perhaps, there is just not that much more to say on that subject.  Just my opinion.

[Frank Kneeland]

I think it's relevant since a person can't a appreciate not-normal, if they don't know what normal is. You have to start somewhere.

[New2vp]

Perhaps what we need to get the ball rolling is some numbers people can play around with.Here's some heights of basket ball players I just made up. Your job is to figure out the standard deviation in height.5' 11" / 6' / 6' 1" / 5' 10" / 6' 2" / 6' 4" / 6' 11" / 7' / 6' 8" / 6' 5"~FKThat was very nice of you to make the average height work out to be an integer, so that the calculations are easy however you plan on attacking this problem.  Of course, there's a 10% probability that it came out this way simply by chance, but...

[BillyJoe]

Nice curve.. 
Here's an easy way to think of the relevance of all this to the "average" VP player.
How many pencil dots can you fit UNDER THE PINK CURVE to the left of the Zero line versus to the right of the Zero line? Each pencil dot represents a possible outcome of a "session", which for your curve is 700 hands on that game with that pay table. This is a measure of how often I would lose versus how often I would win. It is NOT a measure of "how much", just "how often".
I think that you can see that there will be more pencil dots to the left. Hence, you would have the OPPORTUNITY for more losing sessions than winning sessions. But there is room for a few pencil dots way to the right of the Zero line. So the OPPORTUNITY for profit over many sessions is there, provided you are able, in one or more of your sessions, to get pencil dots out there to the right.
That's when VP is fun...

[New2vp]

Great points and accurate ones, billyjoe, about the pencil dots telling you the chances of winning or losing.  The distance that the pencil dots are left or right of the zero line will tell you how much you have won or lost.

[Frank Kneeland]

I guess what we have here is another "catch square root of 484".People don't understand how useful this information can be, but to realize that they'd have to understand it.~FK

[Quad Deuces]

How Video Poker for Winners displays the same information:My session at South Point today floated between about even and 400-coin down until a late but very welcome 22622.  2500 hands.  Pencil dot right.

[BillyJoe]

Great points and accurate ones, billyjoe, about the pencil dots telling you the chances of winning or losing.  The distance that the pencil dots are left or right of the zero line will tell you how much you have won or lost.
Understood, New2VP. I just wanted to point out, though, that your curve is representative of a 700 hand "session". I am not sure that most players count their hands, so I thought that I would keep it simple with just "did I win ?". If you used your curve, marked the spots at the end of each 700 hand session, and then added them all up (plus and minus), then you could see if you made or lost money on that machine.