vpFREE2 Forums

royal flush stat

#21

I used the formula for the binomial distribution, thus my numbers are
fairly exact, limited only by calculation precision. You used the
BINOMDIST function and I believe found some roundoff errors in that
function. If you google BINOMDIST I believe you will find some
articles about inaccuracies in that function. Just to clarify:
Binomial distribution = COMBIN(n,x)*(p^x)*((1-p)^(n-x))
BINOMDIST = an EXCEL function which isn't always exact

Here's the binomial distribution calculation for 4 royals:

40390.54745193 times 40389.54745193 times 40388.54745193 times
40387.54745193 /24 times
(1/40390.54745193)^4 times
(40389.54745193/40390.54745193)^(40390.54745193-4)
= 1.532736127203% (double precision floating point calculation)

May I humbly suggest that if whatever calculation you are using does
not produce a similar number, there is a problem with your calculation.

···

--- In vpFREE@yahoogroups.com, "Bob Dancer" <bob.dancer@...> wrote:

Night said: By "binomial distribution" Steve is refering to:
COMBIN(n,x)*(p^x)*((1-p)^(n-x))
Which may or may not be the same as EXCEL BINOMDIST(x, n, p, false)
n=sample size, x=number of hits, p=probability of getting a hit

Fair enough. I'm willing to trust Excel on this. Since we know Poisson
is a close approximation, and we saw that the numbers NIGHT came out
with (using Poisson) were indeed close to BINOMDIST. Further, Excel
would have every reason to have their BINOMDIST be appropriate, I'm
content to continue to use it.

Whether or not CDSFRULE is concerned with the number of keystrokes I
"waste" by doing so.

Bob Dancer

For the best in video poker information, visit www.bobdancer.com
or call 1-800-244-2224 M-F 9-5 Pacific Time.

[Non-text portions of this message have been removed]

#22

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@...> wrote:

I used the formula for the binomial distribution, thus my numbers

are

fairly exact, limited only by calculation precision. You used the
BINOMDIST function and I believe found some roundoff errors in that
function. If you google BINOMDIST I believe you will find some
articles about inaccuracies in that function. Just to clarify:
Binomial distribution = COMBIN(n,x)*(p^x)*((1-p)^(n-x))
BINOMDIST = an EXCEL function which isn't always exact

Here's the binomial distribution calculation for 4 royals:

40390.54745193 times 40389.54745193 times 40388.54745193 times

There's nothing wrong with your math except that it doesn't really
make sense to have a noninteger number of trials -- at least if I
follow your ASCII math it looks like you're calculating the
probability of 4 royals in 40390.547... trials.

I checked BINOMDIST in Excel against a tool that I have confidence
maintains numerical precision for very large or small numbers, and
they agreed to the displayed precision. That was the 2002 version of
Excel. Generally I don't trust spreadsheets for anything more
complicated than accounting applications, but it seems to be OK for
this one.

Mike

#23

Bob said his version of BINOMDIST returned 1.577933817% for 4 royals.
The correct answer is 1.532736127203% using wizard's 9/6job royal
cycle of 19933230517200/493512264

···

--- In vpFREE@yahoogroups.com, "Michael Peck" <mpeck1@...> wrote:

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@> wrote:
>
> I used the formula for the binomial distribution, thus my numbers
are
> fairly exact, limited only by calculation precision. You used the
> BINOMDIST function and I believe found some roundoff errors in that
> function. If you google BINOMDIST I believe you will find some
> articles about inaccuracies in that function. Just to clarify:
> Binomial distribution = COMBIN(n,x)*(p^x)*((1-p)^(n-x))
> BINOMDIST = an EXCEL function which isn't always exact
>
> Here's the binomial distribution calculation for 4 royals:
>
> 40390.54745193 times 40389.54745193 times 40388.54745193 times
>

There's nothing wrong with your math except that it doesn't really
make sense to have a noninteger number of trials -- at least if I
follow your ASCII math it looks like you're calculating the
probability of 4 royals in 40390.547... trials.

I checked BINOMDIST in Excel against a tool that I have confidence
maintains numerical precision for very large or small numbers, and
they agreed to the displayed precision. That was the 2002 version of
Excel. Generally I don't trust spreadsheets for anything more
complicated than accounting applications, but it seems to be OK for
this one.

Mike

#24

Using Excel 2002, I get your value to 9 significant digits, which I
hope is close enough for most purposes! ;>)

I used =BINOMDIST(4,40390,1/40390,FALSE) and the value is:
1.532736126%.

Your value was
1.532736127%.

--Dunbar

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@...> wrote:

Bob said his version of BINOMDIST returned 1.577933817% for 4

royals.

···

The correct answer is 1.532736127203% using wizard's 9/6job royal
cycle of 19933230517200/493512264

#25

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@...> wrote:

Bob said his version of BINOMDIST returned 1.577933817% for 4 royals.
The correct answer is 1.532736127203% using wizard's 9/6job royal
cycle of 19933230517200/493512264

I get 1.5328% using both software I trust and Excel 2002. That's for
the probability of exactly 4 royals in 40,391 hands with a probability
per hand of 1/40390.55 per Winpoker.

Perhaps Bob used different inputs than we did, or he's using an
earlier version of Excel.

Do we really need to reproduce these numbers to 13 digits? I guess my
error rate is probably slightly higher than 1 in a trillion hands. And
even if I played perfectly knowing that there's about a 1.5% chance of
getting 4 royals in a royal cycle is all I care about.

I hope a smiley wasn't needed after the second sentence in the last
paragraph.

Mike

#26

I now get 1.53% using Excel 2002. I can't tell you exactly what I had
earlier to get 1.57% as I didn't save that version.

But since I now get the correct number, I suspect the problem lies more
in user error rather than BINOMDIST error. This train has been useful to
me.

Bob Dancer

For the best in video poker information, visit www.bobdancer.com
or call 1-800-244-2224 M-F 9-5 Pacific Time.

[Non-text portions of this message have been removed]

#27

This is a point I was going to make also. Does the 13 digit precision
have a particular use, e.g. in a later calculation that wasn't
discussed? Or is it just a question of knowing which algorythm is most
accurate? Since the calculation is different for every game (because
the average interval between RF's varies from each game), does this
make much difference in the probabilities? Finally, I'm curious how
Bob uses this information (to estimate bankroll risk?).

···

--- In vpFREE@yahoogroups.com, "Michael Peck" <mpeck1@...> wrote:

Do we really need to reproduce these numbers to 13 digits? I guess my
error rate is probably slightly higher than 1 in a trillion hands. And
even if I played perfectly knowing that there's about a 1.5% chance of
getting 4 royals in a royal cycle is all I care about.
Mike