vpFREE2 Forums

Full Pay Myth and Reality

#1

OK...let's try to clear things up...

Trying to define the "Long-term" is essentially meaningless, since of
course there is no point when you actually hit it. Think of your
results for now not in dollar amounts but as a percentage of coin
in. i.e. losing every hand is a 0% return and hitting royal flushes
evey hand is an 80,000% return (800 to 1 * 100%). One way to think
of the long term is the concept of probablility bands. Probability
bands are the "plus-or-minus 3%" that you hear when the results of a
poll are given. Let's take 2 video poker games, one with a 101%
return (maybe DW with .25% Cash back) and another with a 98% return.
Regardless of how many hands you play, the probabilities of the 101%
game will center around 101%, and the probabilities of the 98% game
will center around 98%. But there can still be huge overlap. For
example, (and these numbers are estimates), after 1000 hands, there
may be a 95% probability that your results on the good machine will
range from (111% to 91%), while your results on the bad machine will
range from (108% to 88%). Clearly, there is a lot of overlap, and in
addition, 5% of the time, your results will fall outside of that
range.

#2

One way to think
of the long term is the concept of probablility bands. Probability
bands are the "plus-or-minus 3%" that you hear when the results of a
poll are given.

The "probability bands" of +/- three percent that you speak of is the
Standard Deviation, and the overlap you mention is the normal distribution
inside or outside the SD, although the specific numbers you give are only
examples. But it does illustrate that long term results can fall within the
SD and still be negligible, which is pretty much a given I think. With a SD
of 1, for example, roughly 66% of results fall somewhere within the SD,
while the remainder (34%) fall outside, either high or low. I don't know the
specific SDs as applied to various vp games, but I'd be interested in seeing
them. My guess is that they're below 1.

lb

#3

Standard deviation is the root mean square of deviations from the
mean for a given frequency distribution, and its 'size' will vary
depending on the number of observations in that distribution. In
general, the larger the N the smaller the SD. For a normally
distributed population, 95% of the actual results will fall within
2SDs of the mean, but in probibalistic games of chance like video
poker with highly variable outcomes, this SD is likely to be quite
large, especially if only a small number of trials are conducted
(that's why you can win and lose big in the so-called short-term).In
terms of 'percent return', I would suspect that all VP games have SDs
much greater than 1% unless very large numbers of trials are
conducted.

CPC

The "probability bands" of +/- three percent that you speak of is

the

Standard Deviation, and the overlap you mention is the normal

distribution

inside or outside the SD, although the specific numbers you give

are only

examples. But it does illustrate that long term results can fall

within the

SD and still be negligible, which is pretty much a given I think.

With a SD

of 1, for example, roughly 66% of results fall somewhere within

the SD,

while the remainder (34%) fall outside, either high or low. I don't

know the

specific SDs as applied to various vp games, but I'd be interested

in seeing

···

them. My guess is that they're below 1.

lb

#4

Now you've gone and done it... Let me simplify all of this:

Whether you win or lose on any given day is 50/50, either you do, or you don't.

How much you win or lose is only relevant to the mass intake of alcohol. Now, that 50/50 figure can be adjusted by taking the square root of how many drinks you have, then multiply that by the alcohol percentage less, of course, the mean average of any free buffets you've had within the last 24 hours.

So, pay tables or how you play are all irrelevant. <G> As long as you can float within the standard deviation. If you find yourself outside the normal standard deviation, then increasing the blood alcohol level can offset most, if not all, the negative effects on your bankroll. If you are winning outside the standard deviation, it's called "celebrating". If you are losing outside the standard deviation, it's called "easing the pain".

And, always remember "If you win, it's skill. If you lose, it's bad luck."

ADR

···

At 09:20 AM 2/7/03, you wrote:

I don't know the specific SDs as applied to various vp games, but I'd be interested in seeing them. My guess is that they're below 1.

#5

That clarifies things, but correct me on a couple of points: my
understanding is that a higher SD predicts a greater probablity that the
results will fall within the range of averages, i.e. a SD or 1 is roughty
66% while a SD or 2 is a virtual certainty (the 95% that you mention).
Please correct me if that is not right.

Also, assuming a large number of trials, you seem to be saying that while
the "volitility" effects short term outcomes, the SD goes up as samples
increase. At the same time you say that as samples increase the SD goes
down. I'm a little confused.

And if anyone has the actual specific SDs as a function of some formula for
various vp games, please post an example. Based on previous posts by those
who say they've used the SD as a means of guaging their long term, it must
be floating around somewhere out there. Thanks.

lb

···

Standard deviation is the root mean square of deviations from the
mean for a given frequency distribution, and its 'size' will vary
depending on the number of observations in that distribution. In
general, the larger the N the smaller the SD. For a normally
distributed population, 95% of the actual results will fall within
2SDs of the mean, but in probibalistic games of chance like video
poker with highly variable outcomes, this SD is likely to be quite
large, especially if only a small number of trials are conducted
(that's why you can win and lose big in the so-called short-term).In
terms of 'percent return', I would suspect that all VP games have SDs
much greater than 1% unless very large numbers of trials are
conducted.

#6

ADR,

Thanks for bringing this back to the level it warrants. I don't know what I
was thinking! <bg>

lb

..... How much you win or lose is only relevant to the mass intake of

alcohol.

Now, that 50/50 figure can be adjusted by taking the square root of how
many drinks you have, then multiply that by the alcohol percentage less,

of

···

course, the mean average of any free buffets you've had within the last 24
hours......

#7

then multiply that by the alcohol percentage less, of

course, the mean average of any free buffets you've had within the

last 24

hours.

The mean average is an apt expression for many of my free buffets...

···

--- In vpFREE@yahoogroups.com, adr <adr@b...> wrote:

#8

That clarifies things, but correct me on a couple of points: my
understanding is that a higher SD predicts a greater probablity

that the

results will fall within the range of averages, i.e. a SD or 1 is

roughty

66% while a SD or 2 is a virtual certainty (the 95% that you

mention).

Please correct me if that is not right.

What the 66% and 95% numbers that you quote refer to are the
probabilities that the end result of a fixed series of trials (eg
video poker hands) will end up within 1 standard deviation of the
mean of the results of those trials (66%) or 2 standard deviations
(95%). If we take a game with a theoretical mean rate of return of
100% and the standard deviation of that return after 1000 trials is
10%, then 95% of the players playing that game, will, after having
completed 1000 trials have between 80% (2 SD below the mean) and 120%
(2 SD above the mean) of the money they had gambled (this is a highly
theoretical example!!).

Also, assuming a large number of trials, you seem to be saying that

while

the "volitility" effects short term outcomes, the SD goes up as

samples

increase. At the same time you say that as samples increase the SD

goes

down. I'm a little confused.

As the number of trials increases so the fit of the data to a normal
distribution improves. The standard deviation of a bigger dataset
will, therefore, be smaller because the observed data fits better to
the expected data ie the outcome is more predictable. Thus for very
large data sets (eg millions of poker hands) the standard deviation
will be much smaller than for small data sets (eg 1000 poker hands).
95% of the results will still end up within 2SDs of the mean, but the
extent of that spread will be much smaller. Using the same game
example as above, perhaps the standard deviation after 1million hands
is 1%(rather than the 10% for 1000 hands). Thus, after 1 million
hands of play, 95% of the time you would end up with between 98% and
102% of the money you had gambled.

Hope that helps,

CPC

> Standard deviation is the root mean square of deviations from the
> mean for a given frequency distribution, and its 'size' will vary
> depending on the number of observations in that distribution. In
> general, the larger the N the smaller the SD. For a normally
> distributed population, 95% of the actual results will fall within
> 2SDs of the mean, but in probibalistic games of chance like video
> poker with highly variable outcomes, this SD is likely to be quite
> large, especially if only a small number of trials are conducted
> (that's why you can win and lose big in the so-called short-

term).In

> terms of 'percent return', I would suspect that all VP games have

SDs

···

--- In vpFREE@yahoogroups.com, "Lawrence Boxer" <ljboxer@e...> wrote:

> much greater than 1% unless very large numbers of trials are
> conducted.

#9

>..... How much you win or lose is only relevant to the mass intake of
alcohol.
> Now, that 50/50 figure can be adjusted by taking the square root of how
> many drinks you have, then multiply that by the alcohol percentage less,
of
> course, the mean average of any free buffets you've had within the last

24

> hours......

BTW, here is the formula for determining long term, where C=comps (which
would include alcohol):

ER/EV x SD + C = C

Interesting, because as alcohol consumption rises, the coin-in aspects of ER
and EV also increase while other components decrease. Therefore, while SD
remains a constant, C tends to increase.

lb

#10

Thus, after 1 million

hands of play, 95% of the time you would end up with between 98% and
102% of the money you had gambled.

Hope that helps,

CPC<<

Yes, very much. Thanks! I was in the ballpark, just not exactly in
the game. Based on your info and my prior knowledge, I think it
reinforces the fact that over most players' experience, the SD is not
extremely meaningful, particularly given the normal volitility
(deviations) we see. Great info. Thanks again.

lb

#11

...the Standard Deviation, and the overlap you mention is the normal

distribution

inside or outside the SD, although the specific numbers you give are

only

examples. But it does illustrate that long term results can fall

within the

SD and still be negligible, which is pretty much a given I think.

With a SD

of 1, for example, roughly 66% of results fall somewhere within the

SD,

while the remainder (34%) fall outside, either high or low. I don't

know the

specific SDs as applied to various vp games, but I'd be interested

in seeing

them. My guess is that they're below 1.>

I think they're much larger than that, but math is not my profession
so correct me if I'm wrong. I've understood that you can figure a vp
game's SD from the variance figure that WinPoker generates in its
analysis of a game. WP notes that 9/6 JB carries a variance figure of
19.51. Isn't the SD of this game, then, the SQRT of 19.51, which
would be (rounded) 4.42? If so, wouldn't most vp games have even
higher SD figures than that since most games have higher variance
values than JB?

Pete

···

--- In vpFREE@yahoogroups.com, "Lawrence Boxer" <ljboxer@e...> wrote:

#12

--- In vpFREE@yahoogroups.com, "paisonvp <paison@i...>"
<paison@i...> wrote:

--- In vpFREE@yahoogroups.com, "Lawrence Boxer" <ljboxer@e...>

wrote:

>...the Standard Deviation, and the overlap you mention is the

normal

distribution
> inside or outside the SD, although the specific numbers you give

are

only
> examples. But it does illustrate that long term results can fall
within the
> SD and still be negligible, which is pretty much a given I

think.

With a SD
> of 1, for example, roughly 66% of results fall somewhere within

the

SD,
> while the remainder (34%) fall outside, either high or low. I

don't

know the
> specific SDs as applied to various vp games, but I'd be

interested

in seeing
> them. My guess is that they're below 1.>

I think they're much larger than that, but math is not my

profession

so correct me if I'm wrong. I've understood that you can figure a

vp

game's SD from the variance figure that WinPoker generates in its
analysis of a game. WP notes that 9/6 JB carries a variance

figure of

19.51. Isn't the SD of this game, then, the SQRT of 19.51, which
would be (rounded) 4.42? If so, wouldn't most vp games have even
higher SD figures than that since most games have higher variance
values than JB?

Pete

Spot on in your calculation of SD, although the number quoted by
WinPoker is not in '% return' but rather the variance in expected
coin return across each payline when an entire set of possible
hands in the game (2-3 milion)is run through the simulator. To
determine the SD in % return you would need to run the simulation
through a v. large n 1+million hands multiple times (at least 30)
and then compute the statistical parameters, mean, variance, and SD.
All this is a bit futile, however, because all we are trying to do
is sort out which games are more liekly to generate a positive
result, and the simple measures of expected value and expected
return are perfectly adequate.