How to calculate standard deviation for fpdw

Hello..I wanna make sure Im doing the math right..so lets say I played 480hands of .5c fpdw and I lost $19(obv. no royals or deuces)
So I multiply 480h x .25 to get my c/i which is 120. And then I divide 19/120 and that equals 0.1583333
so my sd for this session is 5.83? which is a little higher than the long term average 5.08? tks.

Somebody with a little more expertise in statistics than I have can explain it better, but I think you're using the term "standard deviation" in the wrong way.

FPDW has a mean return value of 1.00762 (that is, for every $1 put in, you can expect to get $1.00762 back out), and a standard deviation (if I calculated it correctly) of 5.08306. This means that the actual return amount can be within 5.08306 of the mean (i.e. anywhere between -4.07544 and +6.09068, but of course the return amount cannot be less than zero, unless somebody has invented a machine with a vacuum hose that sucks up your money when you're not looking) 68.27% of the time, and within two times that number, or 10.16612, 95.45% of the time.

Your returned value was (120 - 19)/120 = 101/120; 1.00762 - 101/120 = 0.16595 = 5.08306 x 0.03265, or 0.03265 standard deviations from the mean.

I think...could somebody confirm/correct this? That SD that I calculated seems a bit high.

Doing the math in bets ($.25) makes it a little easier.

Essentially you made 480 bets and wound up down 76.

The return of FPDW is about 100.7% and the variance is about 26.

So your expected return is .007*480~3. Your actual return was -76 for a difference of -79.

The formula for the standard deviation of N independent identical bets = sqrt(N*Variance)=sqrt(480*26) ~112

To calculate your Z Score (how many standard deviations you are above or below average) just divide the 2 numbers. Z=-79/112=-0.71

So your actual results were about .71 SD's below expectation, which is pretty typical.

One thing to note about video poker is that the standard deviation isn't as meaningful as in other games. If you asked about blackjack or baccarat then we'd tell you that about 70% of the time your results will be between -1 and +1 SD, but this isn't true for video poker because the royal and 4 deuces payouts skew it so much. FPDW is a strange game where you'll lose the majority of sessions but make money overall.

Tks for the responses DonGuy and Tortoise..makes me feel better to not put too much stock into sd when it comes to vp.

Quote: bstillmatic

Hello..I wanna make sure Im doing the math right..so lets say I played 480hands of .5c fpdw and I lost $19(obv. no royals or deuces)
So I multiply 480h x .25 to get my c/i which is 120. And then I divide 19/120 and that equals 0.1583333
so my sd for this session is 5.83? which is a little higher than the long term average 5.08? tks.

Nice try i say
others i think have shown the math on how to do this
do not know how accuarte their math is but the process looks correct, in me opinion

but
1st
any normal distribution calculations (expected value and variance and confidence intervals)
for video poker less than 100,000 hands played is really totally meaningless, in other words
useless

so i say never go there...

unless you want to calculate exactly the exact distribution of 480 hands played
(computers help to do this but a program like Video poker for winners will not)
and then compare that to your normal calcs and see what the difference is

i would have to be paid to do just that, and lots of cash
in my opinion
what a waste of time and effort Sally...
==============================
here is what some people think is normal for the eyes
when the mean, mode and median are about the same (math is fun if you need to study)
480 fair coin flips


480 hands fpdw
HEY!


and together

have fun and good luck

the probability of losing 76 units or more over 480 hands played = 9.337% (rounded)
a cumulative view
about 9.3% chance also is for ending up at least 150 units
so it is what it is

math for this using the normal approximation becomes meaningless
math rules and is fun!


so
what does that mean?
does it help out?
i also show the probability of a 480 hand session loss = 0.63966803
and the average loss = -44.06348641 units (i think this can be seen)
that leaves a probability of not a loss = 0.36033197
and the average NO loss = 88.14964886 units gained

simple to convolve the paytable for this
why estimate with the CLT other than for practice?

Sally

Quote: Tortoise

The formula for the standard deviation of N independent identical bets = sqrt(N*Variance)=sqrt(480*26) ~112

This is what I couldn't seem to find online anywhere. Is there an online source for this bit of knowledge?

Quote: ThatDonGuy

This is what I couldn't seem to find online anywhere. Is there an online source for this bit of knowledge?

You should be able to find it in any introductory stats course, it's usually called the Variance Sum Law.

http://www.utstat.utoronto.ca/~radford/sta247.F11/lec7.html

@mustangsally: You showed interesting graphics in your post. What is the name of the software ?

Quote: mpower

@mustangsally: You showed interesting graphics in your post.

well thank you
i think they are lifeless (no color flavor)
compared to the ones i make in Excel

Quote: mpower

What is the name of the software ?

Gamblers Odds 1.3
the website is gone but can be found in archives

it is freeware on some sites now but who knows what you get
(unless you love to download and install any software)

i did find many errors in using that program, some very large errors (shhhh)
would be nice to get the source code to make it even better
maybe

it is why i like Excel
i can C how 2 + 3 = 6

Sally

Quote: mustangsally

the website is gone but can be found in archives

where is the archives?

Quote: Walker2050

where is the archives?

i use here
http://wayback.archive.org/web/20140702044045/http://www.gamblecraft.com/

my online folder has the GO1.3
OddsSetup.exe file
see me blog for the link

have fun!
most errors I have found in the program is risk of ruin and chance of success
i have found others and have entered wrong data in the games info too
Sally