Recent posts have mentioned a "co-variance." I have never heard this
term and couldn't find it either in the glossary or the FAQ section.
Can someone please explain what it is -- and it's relevance to VP? If
you could explain it so that a "non-math" person like me could
understand, it would be great.
Thanks,
Lainie
Jazbo covers this quite well. He points out that the variance of 4
hands of single play is just 4 times the variance of a single hand.
But if you play a 4-play machine, in some ways things seem more
volitile, and in others they are not as volitile.
The idea here is that in single play, each new hand is independent of
the last. If your first hand is good, you still don't know anything
about the next three. But with 4-play, if you are dealt a good hand
(like 2, 3, or 4 deuces) you know that all four hand are going to give
you a good payout. If you are dealt a grabage hand, you are likely to
lose all four hands. The results tend to be related. You can treat
one of the hands the way you normally would, and have the expected
variance. But the outcome of the other three will tend to go the same
direction as the outcome of the first. They are correlated.
Covariance takes this correlation into account.
In general the covariance is much lower than the variance (around 1/10
according to Jazbo), so the overal variance of a single 4-play hand is
much lower than the variance of 4 single-play hands. However, ther
variance is still higher than for 1 single-play hand, so you can still
go through your bankroll much more quickly (or win more quickly)
playing a multiplay machine compared to a similar denomination single
play machine.
- John
--- In vpFREE@yahoogroups.com, "lainiewolf702" <lainiewolf702@...> wrote:
Recent posts have mentioned a "co-variance." I have never heard this
term and couldn't find it either in the glossary or the FAQ section.
Can someone please explain what it is -- and it's relevance to VP? If
you could explain it so that a "non-math" person like me could
understand, it would be great.Thanks,
Lainie
Thanks John, I think I'm understanding what you're saying. Would it be correct to say that you should subtract the co-variance of x-play game from the variance of the single line version of that same game to assess the overall variance for the x-play game?
That is, let's say you're playing 8/5 Bonus (where Variance = 20.90). Based on your comments, is it correct for me to assume that the co-variance would be around 2.09, making x-play (if x-play were 10 hands or more) have an approximate Variance of 18.81?
Am I getting this correctly?
Thanks,
Lainie
Jazbo covers this quite well. He points out that the variance of 4
hands of single play is just 4 times the variance of a single hand.
But if you play a 4-play machine, in some ways things seem more
volitile, and in others they are not as volitile.
The idea here is that in single play, each new hand is independent of
the last. If your first hand is good, you still don't know anything
about the next three. But with 4-play, if you are dealt a good hand
(like 2, 3, or 4 deuces) you know that all four hand are going to give
you a good payout. If you are dealt a grabage hand, you are likely to
lose all four hands. The results tend to be related. You can treat
one of the hands the way you normally would, and have the expected
variance. But the outcome of the other three will tend to go the same
direction as the outcome of the first. They are correlated.
Covariance takes this correlation into account.
In general the covariance is much lower than the variance (around 1/10
according to Jazbo), so the overal variance of a single 4-play hand is
much lower than the variance of 4 single-play hands. However, ther
variance is still higher than for 1 single-play hand, so you can still
go through your bankroll much more quickly (or win more quickly)
playing a multiplay machine compared to a similar denomination single
play machine.
- John
murphyfields <jkludge@juno.com> wrote:
--- In vpFREE@yahoogroups.com, "lainiewolf702" <lainiewolf702@...> wrote:
Recent posts have mentioned a "co-variance." I have never heard this
term and couldn't find it either in the glossary or the FAQ section.
Can someone please explain what it is -- and it's relevance to VP? If
you could explain it so that a "non-math" person like me could
understand, it would be great.Thanks,
Lainie
__________________________________________________
Do You Yahoo!?
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[Non-text portions of this message have been removed]
<<But if you play a 4-play machine, in some ways things seem more
volatile, and in others they are not as volatile. >>
I have a whole chapter on multi-line in my upcoming VP book, explaining a lot of this in non-math terms. I say you get to the long-term faster, but you need a bigger session bankroll. Be prepared for a more volatile roller coaster ride in the short term; you can go more deeply into your total bankroll than with single-line.
________________________________________
Jean $¢ott
New book coming this summer
"FRUGAL VIDEO POKER"
http://www.FrugalGambler.biz
[Non-text portions of this message have been removed]
Thanks Jean, I can't wait to read it!
Jean Scott <QueenofComps@frugalgambler.biz> wrote: <<But if you play a 4-play machine, in some ways things seem more
volatile, and in others they are not as volatile. >>
I have a whole chapter on multi-line in my upcoming VP book, explaining a lot of this in non-math terms. I say you get to the long-term faster, but you need a bigger session bankroll. Be prepared for a more volatile roller coaster ride in the short term; you can go more deeply into your total bankroll than with single-line.
________________________________________
Jean $¢ott
New book coming this summer
"FRUGAL VIDEO POKER"
http://www.FrugalGambler.biz
[Non-text portions of this message have been removed]
---------------------------------
Do you Yahoo!?
Next-gen email? Have it all with the all-new Yahoo! Mail Beta.
[Non-text portions of this message have been removed]
Thanks John, I think I'm understanding what you're saying. Would it
be correct to say that you should subtract the co-variance of x-play
game from the variance of the single line version of that same game to
assess the overall variance for the x-play game?
That is, let's say you're playing 8/5 Bonus (where Variance =
20.90). Based on your comments, is it correct for me to assume that
the co-variance would be around 2.09, making x-play (if x-play were 10
hands or more) have an approximate Variance of 18.81?
Am I getting this correctly?
Thanks,
Lainie
Lainie:
Wow, there is nothing like trying to explain something to somebody
else to help you learn. After trying to come up with a better answer,
I realized that I really did not know what I was talking about myself,
so had to go learn quite a bit. I am afraid a few of the things I said
before were incorrect.
If you don't mind, I'll switch games to 9/6 JoB so I can use some of
Jazbo's numbers.
For 9/6 JoB, the variance is 19.51, and the covariance is 1.966, so
the 1/10 rule works pretty well (it actually ranges from around 7% to
12% depending on the game, according to Jazbo).
So (very roughly speaking), for multi-play, you have to start with the
variance of a single hand, and boost it by 10% for each additional
hand. For triple play, the variance increases by a factor of 1.2.
For 5-play, it increases by a factor of 1.4, and for 10-play it
increases by a factor of 1.9.
By comparison, going from 25c to 50c denomination will increase the
variance by a factor of 4. So if you can switch from 1-play quarters
to 5 play nickels, you can be wagering the same amount of money each
time you hit the deal button (5*25c = 5*5*5c) but significantly reduce
your variance.
I rocemmend looking at Jazbo's explanation
and look under video poker, N-play, as well as the explanations given
by "The wizard of odds":
http://wizardofodds.com/videopoker/appendix3.html
- John
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
Thanks John, this really helps (as did Jazbo's site). I really appreciate all your effort.
Reading through this -- and thinking about the implications, I was wondering what you (and everyone else) think about whether players could use this to calculate the variance for the variety of multiplay that they want to play and then use that variance (and the denomination they're going to play) to estimate the session bankroll requirement.
Put differently, I'm confident that I could put this data into a spreadsheet and come up with the variances that I would have playing 10-play, 25-play, etc. Then, I wonder if I could use each variance to estimate the associated session bankroll.
Thoughts?
Thanks,
Lainie
Thanks John, I think I'm understanding what you're saying. Would it
be correct to say that you should subtract the co-variance of x-play
game from the variance of the single line version of that same game to
assess the overall variance for the x-play game?
That is, let's say you're playing 8/5 Bonus (where Variance =
20.90). Based on your comments, is it correct for me to assume that
the co-variance would be around 2.09, making x-play (if x-play were 10
hands or more) have an approximate Variance of 18.81?
Am I getting this correctly?
Thanks,
Lainie
Lainie:
Wow, there is nothing like trying to explain something to somebody
else to help you learn. After trying to come up with a better answer,
I realized that I really did not know what I was talking about myself,
so had to go learn quite a bit. I am afraid a few of the things I said
before were incorrect.
If you don't mind, I'll switch games to 9/6 JoB so I can use some of
Jazbo's numbers.
For 9/6 JoB, the variance is 19.51, and the covariance is 1.966, so
the 1/10 rule works pretty well (it actually ranges from around 7% to
12% depending on the game, according to Jazbo).
So (very roughly speaking), for multi-play, you have to start with the
variance of a single hand, and boost it by 10% for each additional
hand. For triple play, the variance increases by a factor of 1.2.
For 5-play, it increases by a factor of 1.4, and for 10-play it
increases by a factor of 1.9.
By comparison, going from 25c to 50c denomination will increase the
variance by a factor of 4. So if you can switch from 1-play quarters
to 5 play nickels, you can be wagering the same amount of money each
time you hit the deal button (5*25c = 5*5*5c) but significantly reduce
your variance.
I rocemmend looking at Jazbo's explanation
and look under video poker, N-play, as well as the explanations given
by "The wizard of odds":
http://wizardofodds.com/videopoker/appendix3.html
- John
murphyfields <jkludge@juno.com> wrote:
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
---------------------------------
How low will we go? Check out Yahoo! Messengers low PC-to-Phone call rates.
[Non-text portions of this message have been removed]
Lainie Wolf wrote:
Reading through this -- and thinking about the implications, I was
wondering what you (and everyone else) think about whether players
could use this to calculate the variance for the variety of multiplay
that they want to play and then use that variance (and the
denomination they're going to play) to estimate the session bankroll
requirement.
Lainie,
I'll emphasize very simply that variance is very unsatisfactory when
it comes to predicting short term video poker results (those for under
anything less than 1 mllion to 10 million hands, where the greater the
variance, the greater number of hands required for significant
meaningfulness).
Session to session, the statistic is near worthless by itself, other
than to say that the higher the variance the larger the bankroll you
need. It's impossible to quantify that relationship into any
practical amounts.
I pretty much put variance to one practical use -- the basic economic
reality that to preserve a bankroll one should look for an
appropriately higher expected return if you assume greater risk in the
form of playing a higher variance game.
- Harry
My $0.02.
Although, quantitatively, the variance gives almost nothing in financial "advice", as to
bankroll, when you are in a "short session" situation, I feel that it presents you with
qualitative information, in a realtive sense, when one compares the variance of one game
with respect to the variances of other games.
That is, with similar ER's, in the short term, with respect to "bankroll", it is usually "safer"
to choose that game with the lowest variance.
Now, it is true, making such a choice, might result is a more "boring" session (whatever
that means), you may (note MAY, not WILL) find that your money lasts a bit longer.
.....bl
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:
Lainie Wolf wrote:
> Reading through this -- and thinking about the implications, I was
> wondering what you (and everyone else) think about whether players
> could use this to calculate the variance for the variety of multiplay
> that they want to play and then use that variance (and the
> denomination they're going to play) to estimate the session bankroll
> requirement.Lainie,
I'll emphasize very simply that variance is very unsatisfactory when
it comes to predicting short term video poker results (those for under
anything less than 1 mllion to 10 million hands, where the greater the
variance, the greater number of hands required for significant
meaningfulness).Session to session, the statistic is near worthless by itself, other
than to say that the higher the variance the larger the bankroll you
need. It's impossible to quantify that relationship into any
practical amounts.I pretty much put variance to one practical use -- the basic economic
reality that to preserve a bankroll one should look for an
appropriately higher expected return if you assume greater risk in the
form of playing a higher variance game.- Harry
Lainie, to expand a bit on what Harry and bl wrote...
You can use variance to get an estimate of where you might end up
after a session. The shorter the session, the rougher the estimate
will be.
Even so, you cannot use variance to estimate a session bankroll
requirement. That is because the endpoint "picture" does not
reflect what may have happened during a session. If you start with
a $500 "bankroll", there will be many instances where you lose $500,
but if you keep playing you end up in positive territory. Using
variance misses those instances.
Another way of saying this is re-writing my first sentence to: "You
can use variance to get an estimate of where you might end up after
a session, if you have an unlimited bankroll."
--Dunbar
Thanks John, this really helps (as did Jazbo's site). I really
appreciate all your effort.
Reading through this -- and thinking about the implications, I
was wondering what you (and everyone else) think about whether
players could use this to calculate the variance for the variety of
multiplay that they want to play and then use that variance (and the
denomination they're going to play) to estimate the session bankroll
requirement.
Put differently, I'm confident that I could put this data into a
spreadsheet and come up with the variances that I would have playing
10-play, 25-play, etc. Then, I wonder if I could use each variance
to estimate the associated session bankroll.
Thoughts?
Thanks,
Lainie
murphyfields <jkludge@...> wrote:
--- In vpFREE@yahoogroups.com, Lainie Wolf
<lainiewolf702@> wrote:
>
> Thanks John, I think I'm understanding what you're saying. Would
it
be correct to say that you should subtract the co-variance of x-
play
game from the variance of the single line version of that same
game to
assess the overall variance for the x-play game?
>
> That is, let's say you're playing 8/5 Bonus (where Variance =
20.90). Based on your comments, is it correct for me to assume that
the co-variance would be around 2.09, making x-play (if x-play
were 10
hands or more) have an approximate Variance of 18.81?
>
> Am I getting this correctly?
>
> Thanks,
> Lainie
>Lainie:
Wow, there is nothing like trying to explain something to somebody
else to help you learn. After trying to come up with a better
answer,
I realized that I really did not know what I was talking about
myself,
so had to go learn quite a bit. I am afraid a few of the things I
said
before were incorrect.
If you don't mind, I'll switch games to 9/6 JoB so I can use some
of
Jazbo's numbers.
For 9/6 JoB, the variance is 19.51, and the covariance is 1.966, so
the 1/10 rule works pretty well (it actually ranges from around 7%
to
12% depending on the game, according to Jazbo).
So (very roughly speaking), for multi-play, you have to start with
the
variance of a single hand, and boost it by 10% for each additional
hand. For triple play, the variance increases by a factor of 1.2.
For 5-play, it increases by a factor of 1.4, and for 10-play it
increases by a factor of 1.9.By comparison, going from 25c to 50c denomination will increase the
variance by a factor of 4. So if you can switch from 1-play
quarters
to 5 play nickels, you can be wagering the same amount of money
each
time you hit the deal button (5*25c = 5*5*5c) but significantly
reduce
your variance.
I rocemmend looking at Jazbo's explanation
and look under video poker, N-play, as well as the explanations
given
by "The wizard of odds":
http://wizardofodds.com/videopoker/appendix3.html
- John
---------------------------------
How low will we go? Check out Yahoo! Messenger's low PC-to-Phone
call rates.
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
[Non-text portions of this message have been removed]
That's a great way to put it. WONDERFUL!
I think that I will ask my wife to make a "Sampler" for my wall.
<smile>
......bl
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:>
"You can use variance to get an estimate of where you might end up after
a session, if you have an unlimited bankroll."--Dunbar
Thanks for your responses Dunbar, BL, John, Dan, Harry and Jean. I've been thinking about your responses, and I think some background would be helpful -- so I'm not asking my questions in a vaccuum.
I typically play quarter 9/6 Jacks (or other games that allow me to use that strategy since I know that I make mistakes when I switch between games that require different strategies). I estimate that with my dedicated VP bankroll and restricting my play to casinos that offer enough CB and BBC to make the plays positive, I have almost no ROR.
That being said, when I go out to play, I have a "coin-in" goal for the session. I use "coin-in" goals because they allow me to maximize slot club program benefits. Because of my approach, it's vital that I reach my "coin-in" goal each time I play, and I have to make sure I have enough of a session bankroll with me to allow me to reach my goal.
When I used to play FPDW, I noticed that I had many sessions where I was under-bankrolled and lost my entire session bankroll before the session was able to turn around. When I started bringing a larger session bankroll, I was usually able to turn things around and not lose more than a few hundred dollars in a session.
I learned that my experiences were due to the game's fluctuation and that by looking at a game's variance, I could gauge fluctuation. I know that the higher the variance, the larger the session bankroll needed to reach a specific "coin-in" goal.
Lately, I've had less time available to play, yet I still want to reach my "coin-in" goals. Also, since just playing single line 9/6 Jacks gets boring, I've been looking for ways to add some excitement. Thus, N-play games are a great solution for me.
Now, I get to the hard part. When I can find fifty or hundred play nickels, I've experienced that my usual quarter session bankroll seems to be sufficient for playing 20-25 lines, even though I'm going from betting $1.25 per pull to $5.00-$6.25 -- and that same bankroll would not be sufficient for playing single line dollars ($5.00 per pull). I've also noticed that double my usual quarter session bankroll seems to be sufficient for fifty play nickels or two cent hundred play, and I assume that that's because the increased number of lines mitigates the fluctuation.
While I'm not a "math person," I am a "logic person," and I've come up with an approach that I think may work to estimate the session banroll needed for N-play games. Unfortunately, I don't have the skill to test my theory. Since many of you possess skills that are far superior to mine, I'm wondering if you could test my theory, see if you think it could work and help me...
Here's the approach:
1. Calculate the session bankroll required for $10k coin-in of single line 9/6 Jacks.
2. Calculate the variance for ten, fifteen, twenty, twenty five, fifty and hundred line 9/6 Jacks (using the co-variance).
3. Using the ratio of session bankroll required for single line play to its variance, extrapolate the session bankrolls required for ten, fifteen, twenty, twenty five, fifty and hundred play (based on the variances calculated in step 2 above).
4. Sanity check the answers by comparing the estimated session bankroll requirements for N-play games with session bankroll requirements for single line games that have similar variances. So, hypothetically, if the variance for fifteen play 9/6 Jacks is 22.153 (and I'm just making that up), logically, the session bankroll required should be very similar to the session bankroll required for single line 9/5 DJ, which has a variance of 22.106.
What do you think of this approach?
Thanks for your help.
Lainie
Lainie, to expand a bit on what Harry and bl wrote...
You can use variance to get an estimate of where you might end up
after a session. The shorter the session, the rougher the estimate
will be.
Even so, you cannot use variance to estimate a session bankroll
requirement. That is because the endpoint "picture" does not
reflect what may have happened during a session. If you start with
a $500 "bankroll", there will be many instances where you lose $500,
but if you keep playing you end up in positive territory. Using
variance misses those instances.
Another way of saying this is re-writing my first sentence to: "You
can use variance to get an estimate of where you might end up after
a session, if you have an unlimited bankroll."
--Dunbar
Thanks John, this really helps (as did Jazbo's site). I really
appreciate all your effort.
Reading through this -- and thinking about the implications, I
was wondering what you (and everyone else) think about whether
players could use this to calculate the variance for the variety of
multiplay that they want to play and then use that variance (and the
denomination they're going to play) to estimate the session bankroll
requirement.
Put differently, I'm confident that I could put this data into a
spreadsheet and come up with the variances that I would have playing
10-play, 25-play, etc. Then, I wonder if I could use each variance
to estimate the associated session bankroll.
Thoughts?
Thanks,
Lainiemurphyfields <jkludge@...> wrote:
--- In vpFREE@yahoogroups.com, Lainie Wolf
<lainiewolf702@> wrote:
>
> Thanks John, I think I'm understanding what you're saying. Would
it
be correct to say that you should subtract the co-variance of x-
play
game from the variance of the single line version of that same
game to
assess the overall variance for the x-play game?
>
> That is, let's say you're playing 8/5 Bonus (where Variance =
20.90). Based on your comments, is it correct for me to assume that
the co-variance would be around 2.09, making x-play (if x-play
were 10
hands or more) have an approximate Variance of 18.81?
>
> Am I getting this correctly?
>
> Thanks,
> Lainie
>Lainie:
Wow, there is nothing like trying to explain something to somebody
else to help you learn. After trying to come up with a better
answer,
I realized that I really did not know what I was talking about
myself,
so had to go learn quite a bit. I am afraid a few of the things I
said
before were incorrect.
If you don't mind, I'll switch games to 9/6 JoB so I can use some
of
Jazbo's numbers.
For 9/6 JoB, the variance is 19.51, and the covariance is 1.966, so
the 1/10 rule works pretty well (it actually ranges from around 7%
to
12% depending on the game, according to Jazbo).
So (very roughly speaking), for multi-play, you have to start with
the
variance of a single hand, and boost it by 10% for each additional
hand. For triple play, the variance increases by a factor of 1.2.
For 5-play, it increases by a factor of 1.4, and for 10-play it
increases by a factor of 1.9.By comparison, going from 25c to 50c denomination will increase the
variance by a factor of 4. So if you can switch from 1-play
quarters
to 5 play nickels, you can be wagering the same amount of money
each
time you hit the deal button (5*25c = 5*5*5c) but significantly
reduce
your variance.
I rocemmend looking at Jazbo's explanation
and look under video poker, N-play, as well as the explanations
given
by "The wizard of odds":
http://wizardofodds.com/videopoker/appendix3.html
- John
---------------------------------
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call rates.
dunbar_dra <h_dunbar@hotmail.com> wrote:
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
[Non-text portions of this message have been removed]
__________________________________________________
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[Non-text portions of this message have been removed]
I typically play quarter 9/6 Jacks (or other games that allow me
to >use that strategy since I know that I make mistakes when I switch
between games that require different strategies). I estimate that
with >my dedicated VP bankroll and restricting my play to casinos that
offer >enough CB and BBC to make the plays positive, I have almost no
ROR.
Are you sure? Even if you're getting 1% CB/BBC and have a bankroll of
5 royals, your ROR on perfect-play 9/6 job is still 8%.
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
Yes I'm sure. I know the EXACT total of my dedicated vp bankroll, and I used the wizard of odds website (http://wizardofodds.com/videopoker/appendix1.html) to make my estimate.
If you haven't used his charts, you might want to check this out. These charts are a great resource for deciding what to play and for evaluating the impact of slot club promos on your ability to play games at various denominations. (Note, since they're based on the number of hands you play, you have to multiply the numbers in the chart by your total bet per hand. That is, if you play nickels, multiply the numbers by $0.25, if you play quarters, multiply the numbers by $1.25, etc.)
I hope this helps.
Lainie
I typically play quarter 9/6 Jacks (or other games that allow me
to >use that strategy since I know that I make mistakes when I switch
between games that require different strategies). I estimate that
with >my dedicated VP bankroll and restricting my play to casinos that
offer >enough CB and BBC to make the plays positive, I have almost no
ROR.
Are you sure? Even if you're getting 1% CB/BBC and have a bankroll of
5 royals, your ROR on perfect-play 9/6 job is still 8%.
nightoftheiguana2000 <nightoftheiguana2000@yahoo.com> wrote:
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
---------------------------------
Yahoo! Messenger with Voice. Make PC-to-Phone Calls to the US (and 30+ countries) for 2¢/min or less.
[Non-text portions of this message have been removed]
While I'm not a "math person," I am a "logic person," and I've
come up with an approach that I think may work to estimate the
session banroll needed for N-play games. Unfortunately, I don't
have the skill to test my theory. Since many of you possess skills
that are far superior to mine, I'm wondering if you could test my
theory, see if you think it could work and help me...
Here's the approach:
1. Calculate the session bankroll required for $10k coin-in of
single line 9/6 Jacks.
How are you calculating single-line session bankroll requirement,
Lainie?
2. Calculate the variance for ten, fifteen, twenty, twenty
five, fifty and hundred line 9/6 Jacks (using the co-variance).
Okay.
3. Using the ratio of session bankroll required for single line
play to its variance, extrapolate the session bankrolls required for
ten, fifteen, twenty, twenty five, fifty and hundred play (based on
the variances calculated in step 2 above).
It's not obvious to me that this step makes sense. However, it
could be checked against one of Dan Paymar's results. If your
extrapolation matches up, it would be much easier, I think, than
simming every possible combo of number-of-lines and cashback.
4. Sanity check the answers by comparing the estimated session
bankroll requirements for N-play games with session bankroll
requirements for single line games that have similar variances. So,
hypothetically, if the variance for fifteen play 9/6 Jacks is 22.153
(and I'm just making that up), logically, the session bankroll
required should be very similar to the session bankroll required for
single line 9/5 DJ, which has a variance of 22.106.
A "sanity check" for internal consistency is always a good idea.
What do you think of this approach?
I think it's worth checking out.
--Dunbar
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
Lainie, I didn't read carefully enough the part of your post that I
quoted! I somehow missed the point that you were calling on other
people to test the idea.
The question "How are you calculating single-line session bankroll
requirement, Lainie?" wasn't appropriate, given that you were asking
someone else to test your theory. (sorry about that!)
The reason I asked you the question was that I'm interested if
people are using something other than Dunbar's Risk Analyzer for
Video Poker to get session bankroll requirements. I wasn't trying
to be coy. I'm ambivalent about dropping plugs for my program.
When I saw "session bankroll requirement" as part of your 4 steps,
I wanted to know how you were going to go about getting that!
Your approach does have a common sense appeal. I just thought of a
simpler test. You could try comparing two (single-line) games with
substantially different variances. That is, you apply your 4-step
method to 2 different single-line games.
1. get the session bankroll of game 1.
2. use the variance of game 1 and game 2.
3. use the ratio from Game 1 to extrapolate a session bankroll value
for game 2.
4. sanity check.
This is easy enough that I'll do it tomorrow, if no one does it
sooner.
This is not a definitive "test" of your method, but it's worth
doing, IMO.
--Dunbar
> While I'm not a "math person," I am a "logic person," and I've
come up with an approach that I think may work to estimate the
session banroll needed for N-play games. Unfortunately, I don't
have the skill to test my theory. Since many of you possess
skills
that are far superior to mine, I'm wondering if you could test my
theory, see if you think it could work and help me...
>
> Here's the approach:
>
> 1. Calculate the session bankroll required for $10k coin-in
of
single line 9/6 Jacks.
How are you calculating single-line session bankroll requirement,
Lainie?> 2. Calculate the variance for ten, fifteen, twenty, twenty
five, fifty and hundred line 9/6 Jacks (using the co-variance).Okay.
> 3. Using the ratio of session bankroll required for single
line
play to its variance, extrapolate the session bankrolls required
for
ten, fifteen, twenty, twenty five, fifty and hundred play (based
on
the variances calculated in step 2 above).
It's not obvious to me that this step makes sense. However, it
could be checked against one of Dan Paymar's results. If your
extrapolation matches up, it would be much easier, I think, than
simming every possible combo of number-of-lines and cashback.> 4. Sanity check the answers by comparing the estimated
session
bankroll requirements for N-play games with session bankroll
requirements for single line games that have similar variances.
So,
hypothetically, if the variance for fifteen play 9/6 Jacks is
22.153
(and I'm just making that up), logically, the session bankroll
required should be very similar to the session bankroll required
for
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@> wrote:
single line 9/5 DJ, which has a variance of 22.106.
>
A "sanity check" for internal consistency is always a good idea.
> What do you think of this approach?I think it's worth checking out.
--Dunbar
Bravo!
What Lanie has done is re-dsicover a well known scaling relationship! The method she
outlines is quite sound and will (should) give quite good results. THe sanity check,
however, is not really needed (or accurate), the vairance alone is not a good predictor of
RoR, etc.
So why does her method work?
Well, the variance and EV are not a complete descrition of even single line VP play. You
need the higher order moments (like kurtosis, etc) OR the complete pay-table with
probabilities (or equivelently the complete PDF). With all the information ou can compute
the RoR for a finite number of hans.
That said, for the sme game, the "shape" of the PDF for 1-line is exactly the same as for
multi-line. If you know the PDF for single-line, you can commpute the RoR for single line.
You can also transform ("scale" is better word) the 1-line PDF into a multiline PDF, and in
theory use that for the RoR computaion. But, since the RoR computation uses a "chopped
off " (truncated) PDF, the results may not be exact, depending upon how (when) the scaling
is done.
So how accurate is L's method?
Suppose you ignored the covariance completey. Then you would assume that the PDF 1-
play = PDF multiply. In this case, your approximation of the PDF would be within about
5%. Not bad. [Where did I get this number? It's the square root of the correlation
coeffcient (=covariance/variance) scaled by the number of hands]. In other words, when
the correlation coeffcicient is small (the normalized covariance), this approximation is
good-- and the effect of multplay on the PDF are small. So what is the effect on the ROR?
For very small (0% or so) and very large ROR (100% or so), the ROR doesn't change much
with the number of hands. Hence, for small or large RoR, ignoring the effects of mulitplay
is a good bet. In between, there will be some error, though probably not much (I can't say
that it will be 5%-- that's the error for the PDF not the RoR)
One can then imporve on this 'do nothing approach'-- using scaling. It isn't that hard to
show mathematically how it works and Lanie's approach is excellent. I'd preffer to look at
it this way: Playing multi-play reduces the varaince relative to single play. Hence the RoR
is always lower (in betting units). One can compute the multiplay variance for Hm-hands
and then find the corresponding number of hands (H1) of single-play that had the same
variance. This effective number of hands (H1) will be smaller (than Hm) Then, you can use
the single-play RoR for H1 hands for the mulit-play RoR for Hm hands. This is a bit
different than Lannie's scaling method (and probably a tab more accurate)-- but both
should give good enough results. Then again, for small RoR, ignoring the covariance
completely (since the correlation coeff is small, say 0.1 for JoB) isn't a bad choice either. I
We'll see if Dan's simulations agree.
Here's the approach:
1. Calculate the session bankroll required for $10k coin-in of single line 9/6 Jacks.
2. Calculate the variance for ten, fifteen, twenty, twenty five, fifty and hundred line 9/6
Jacks (using the co-variance).
3. Using the ratio of session bankroll required for single line play to its variance,
extrapolate the session bankrolls required for ten, fifteen, twenty, twenty five, fifty and
hundred play (based on the variances calculated in step 2 above).
4. Sanity check the answers by comparing the estimated session bankroll
requirements for N-play games with session bankroll requirements for single line games
that have similar variances. So, hypothetically, if the variance for fifteen play 9/6 Jacks is
22.153 (and I'm just making that up), logically, the session bankroll required should be
very similar to the session bankroll required for single line 9/5 DJ, which has a variance of
22.106.
--- In vpFREE@yahoogroups.com, Lainie Wolf <lainiewolf702@...> wrote:
What do you think of this approach?
I did the "simpler" test that I described below. Here is what I did.
1. I found the session bankroll that you would need in order to have
a 2% RoR after 8000 hands of single-line 25c 9/6 JOB.
2. I used the ratio of variance to estimate what session bankroll
would be needed to play NSUD and Pick'em with the same 2% RoR as JOB.
3. I then calculated the actual RoR for those bankroll estimates and
compared the result to 2%.
Here's what I found:
1. It takes $700 to have a 2% RoR for 8000 hands of single-line 25c
9/6 JOB. (according to Dunbar's Risk Analyzer for Video Poker)
2. JOB variance is 19.51; NSUD variance is 25.78; Pick'em variance
is 15.01.
The variance ratio of NSUD to JOB is 25.78/19.51 = 1.32, and the
predicted session bankroll for a 2% RoR would be $700 * 1.32 =
$924.96.
The variance ratio of Pick'em to JOB is 15.01/19.51 = 0.77, and the
predicted session bankroll for a 2% RoR would be $700 * 0.77 =
$538.54.
3.
NSUD: Using a $924.96 bankroll for 8000 single-line hands, there
is a 2% RoR, same as for JOB. That was encouragingly. But...
Pick'em: Using a $538.54 bankroll for 8000 single-line hands, there
is a 13% RoR. That's too far from 2% to be useful.
In fact, even a $700 session bankroll in 25c Pick'em has a 4.5%
RoR. The game with the smaller variance has the bigger RoR! After
thinking about it, I decided it made sense. Pick'em has 5% of its
EV tied up in quads or better, and quads occur about once every 2000
hands. It's easy to have a significant shortage of quads in just
8000 hands. JOB, on the other hand, has just 2.5% of its EV tied
up in rare hands.
If you looked at a longer "session", Pick'em would have the lower
RoR for the same bankroll.
None of this proves or disproves Lainie's suggestion. It only shows
that the suggestion cannot be generalized to comparing different
games. We probably already knew that, but I thought I'd check it
anyway.
Dan Paymar's new data will be a good test for Lainie's suggestion.
--Dunbar
I just thought of a
simpler test. You could try comparing two (single-line) games
with
substantially different variances. That is, you apply your 4-step
method to 2 different single-line games.
1. get the session bankroll of game 1.
2. use the variance of game 1 and game 2.
3. use the ratio from Game 1 to extrapolate a session bankroll
value
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
for game 2.
4. sanity check.This is easy enough that I'll do it tomorrow, if no one does it
sooner.This is not a definitive "test" of your method, but it's worth
doing, IMO.--Dunbar
I've pretty much put out what I have to say on this topic already.
But I'll emphasize that Lainie's search for a bankroll relationship
has always stressed short-term session play.
It should be self-evident that what may be true with respect to a
relationship between variance and long-term bankroll/ROR won't hold
session to session. The majority of sessions won't include the very
infrequent hands that tremendously skew the variance statistic.
There's some room for exploration of a relationship between session
bankroll and a variance number based upon a paytable in which that
infrequent hand pays are zeroed out (since a downside session will
most likely exclude such hits). But, bottom line, any attempt to draw
a correlation between a session bankroll requirement and standard
variance is futile.
------------
With respect to longer term contemplation of a relationship between
variance and game bankroll, I expect it would be evident to Dunbar
that variance and bankroll don't scale particularly well in either the
short term or long term, as might be suggested by anecdotal runs using
his own calculator. As cdfsrule essentially notes, that would only be
the case when the PDF's of two games are of very similar shape. It
should be clear that the PDF's of games with strikingly different
paytable configurations (say, PE, JB, and DDB) will have unique
characteristics.
The case of a comparison of long term bankroll requirement of single
line play vs. n-play is somewhat unique. In this case, there's reason
to expect that the contribution of covariance to game variance
"normalizes" fairly quickly, so that as cdfsrule again notes, the two
have similar long-term PDF's. There's cause to expect that relative
variance might yield a rule-of-thumb guidance to n-play bankroll.
However, in the short run, the contribution of covariance to session
variance is particularly skewed relative to base game variance. Once
again, any comparison of variance numbers between single line and
n-play won't yield any viable expectation of n-play session bankroll
requirement.
- Harry
Shouldn't there be a correlation for ROR to variance in games that
are both close in total payback? By your own analysis, the higher
ROR for Pick em comes from so much of the EV being tied up in the
quads, well isn't that where variance usually comes from?, which is
why a 10/7 DB has a higher variance than 9/6 JOB though it has a
higher total payback.
I did the "simpler" test that I described below. Here is what I
did.
1. I found the session bankroll that you would need in order to
have
a 2% RoR after 8000 hands of single-line 25c 9/6 JOB.
2. I used the ratio of variance to estimate what session bankroll
would be needed to play NSUD and Pick'em with the same 2% RoR as
JOB.
3. I then calculated the actual RoR for those bankroll estimates
and
compared the result to 2%.
Here's what I found:
1. It takes $700 to have a 2% RoR for 8000 hands of single-line
25c
9/6 JOB. (according to Dunbar's Risk Analyzer for Video Poker)
2. JOB variance is 19.51; NSUD variance is 25.78; Pick'em variance
is 15.01.The variance ratio of NSUD to JOB is 25.78/19.51 = 1.32, and the
predicted session bankroll for a 2% RoR would be $700 * 1.32 =
$924.96.The variance ratio of Pick'em to JOB is 15.01/19.51 = 0.77, and
the
predicted session bankroll for a 2% RoR would be $700 * 0.77 =
$538.54.3.
NSUD: Using a $924.96 bankroll for 8000 single-line hands, there
is a 2% RoR, same as for JOB. That was encouragingly. But...Pick'em: Using a $538.54 bankroll for 8000 single-line hands,
there
is a 13% RoR. That's too far from 2% to be useful.
In fact, even a $700 session bankroll in 25c Pick'em has a 4.5%
RoR. The game with the smaller variance has the bigger RoR!
After
thinking about it, I decided it made sense. Pick'em has 5% of its
EV tied up in quads or better, and quads occur about once every
2000
hands. It's easy to have a significant shortage of quads in just
8000 hands. JOB, on the other hand, has just 2.5% of its EV tied
up in rare hands.If you looked at a longer "session", Pick'em would have the lower
RoR for the same bankroll.None of this proves or disproves Lainie's suggestion. It only
shows
that the suggestion cannot be generalized to comparing different
games. We probably already knew that, but I thought I'd check it
anyway.Dan Paymar's new data will be a good test for Lainie's suggestion.
--Dunbar
> I just thought of a
> simpler test. You could try comparing two (single-line) games
with
> substantially different variances. That is, you apply your 4-
step
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@> wrote:
> method to 2 different single-line games.
> 1. get the session bankroll of game 1.
> 2. use the variance of game 1 and game 2.
> 3. use the ratio from Game 1 to extrapolate a session bankroll
value
> for game 2.
> 4. sanity check.
>
> This is easy enough that I'll do it tomorrow, if no one does it
> sooner.
>
> This is not a definitive "test" of your method, but it's worth
> doing, IMO.
>
> --Dunbar
>