vpFREE2 Forums

Digest Number 6910

Re: Variance for STP-JoB

First, I want to applogize for my previous post. I have spent way more time
playing video poker in the last few years than I have studying statistics.
Cogno is quite correct when he states that standard deviation is the square
root of variance, not the other way around. I should have caught this error
as well as the procedural one.
Second, I want to point out that the calculations I made were based on the
two assumptions of the original poster: A)That variance is the square root
of standard deviation and B)That STP adds 51% to the standard deviation.
Since assumption A is false, the results of my computations were of no value
even though the computations were correct.
Third, I would like to offer the correct procedure with the correct
assumptions. For 9/6 Job the variance is 19.51, so the SD is the square root
of this or 4.417. The SD for Job-STP then is 151% of 4.417 =6.670. The new
variance then is the square of 6.670 or 44.48. This value is close to the
44.50 given in the original post on the topic, but he could not have arrived
there from his stated assumptions.
Fourth, math teachers are often accused of only caring about getting the
correct answer. In fact, the correct answer arrived at by faulty
assumptions/procedures/logic can have disastrous effects on the learning
process. Example: playing 9/6 JoB and drawing a royal flush while holding a
single 10. While there is ( in a rational world) no market for the wrong
answer, the main goal in the math class is logic and procedure.
Fifth, while Cogno made a correct observation regarding my error, he made no
attempt to explain the correct method for obtaining the desired result.
While sarcasm is often amusing ( I often resort to it myself ) it is seldom
constructive.
Sixth, I respect and appreciate the other contributers on this board,
especially the regular ones, like Cogno, who take their time to share with
us.
Thank you, Joel P.

···

On Sun, Jun 20, 2010 at 12:38 AM, <vpFREE@yahoogroups.com> wrote:

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Messages In This Digest (9 Messages)
1a. Re: Variance for STP-JoB<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_1a>From: kiwiboy4921 2a.
Re: Caesars Windsor, Canada?<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_2a>From:
wipiliti@aol.com 2b. Re: Caesars Windsor, Canada?<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_2b>From: Albert Pearson 3a.
Re: FW: Governors of 35 states filed suit against Fed Government...<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_3a>From: kellypkjoe 3b.
Re: FW: Governors of 35 states filed suit against Fed Government...<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_3b>From: Sellers Phil 3c.
Re: FW: Governors of 35 states filed suit against Fed Government...<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_3c>From: Richard Long 4a.
Do You Trust Indian Casinos?<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_4a>From: mikeymic 4b.
Re: Do You Trust Indian Casinos?<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_4b>From: James Thompson 4c.
Re: Do You Trust Indian Casinos?<http://mail.google.com/mail/?ui=2&view=js&name=main_init,tlist&ver=aZxD9j7SvLo.en.&am=!ogafcFI2wOKxxX0e0fc-Mi7GVQpC9CC2e8bqXvkkz9pyE2ntaA&fri#129544b115126455_4c>From: Charles Galle
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Messages
1a. Re: Variance for STP-JoB
<http://groups.yahoo.com/group/vpFREE/message/107670;_ylc=X3oDMTJzaWhiN2FhBF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3MARzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "kiwiboy4921" waynes@kiwiplan.com
<waynes@kiwiplan.com?Subject=+Re%3A%20Variance%20for%20STP-JoB> kiwiboy4921
<http://profiles.yahoo.com/kiwiboy4921> Sat Jun 19, 2010 6:45 am (PDT)

Cogno is right (if a little sarcastic!). SD is the square root of Variance.

--- In vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>, "Cogno Scienti"
<cognoscienti@...> wrote:
>
> Thank goodness you spoke up. All these years I thought standard deviation
> was the square root of variance!
>
> Cogno
>
>
>
> > -----Original Message-----
> > From: vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com> [mailto:
vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>] On Behalf
> > Of Joel Prickett
> > Sent: Friday, June 18, 2010 5:15 PM
> > To: vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>
> > Subject: [vpFREE] Variance for STP-JoB
> >
> > I don't want to pick nits, but as a math teacher I can't let an error
> > in
> > formulation stand as public knowledge. Given the 19.51 variance of the
> > base
> > game of JoB, the standard deviation would be the square of 19.51 or
> > 380.64.
> > So if the new standard deviation for STP adds 51% to the original, 151%
> > of
> > 380.64 = 574.77. The new variance is the square root of this amount, or
> > 23.97 and not the 44.50 as stated. The simple way to calculate would be
> > to
> > multiply 19.51 by the square root of 1.51 to obtain the same result.I
> > hope
> > not to ruffle any feathers, but had to speak up. Respectfully, Joel P.
> >
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
> > ------------------------------------
> >
> > vpFREE Links: http://members.cox.net/vpfree/Links.htm
> >
> > Yahoo! Groups Links
> >
> >
> >
>

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2a. Re: Caesars Windsor, Canada?
<http://groups.yahoo.com/group/vpFREE/message/107671;_ylc=X3oDMTJzZmY5dnQ4BF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3MQRzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "wipiliti@aol.com" wipiliti@aol.com
<wipiliti@aol.com?Subject=+Re%3A%20Caesars%20Windsor%2C%20Canada%3F> wipiliti
<http://profiles.yahoo.com/wipiliti> Sat Jun 19, 2010 11:10 am (PDT)

I have two comped tickets to see Tony Bennett on Aug. 8, but I don't plan
on staying or playing a lot then. It's a shame what they've done to the VP
inventory.

In a message dated 6/19/2010 3:26:02 A.M. Eastern Daylight Time,
donthughesjr@ameritech.net <donthughesjr%40ameritech.net> writes:

I visited Caesars Windsor last week, and looked everywhere for any VP
machine that paid over 98.5%....there were none....they used to have some,
but
they were all removed...I probably won't go back there....DTH

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

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2b. Re: Caesars Windsor, Canada?
<http://groups.yahoo.com/group/vpFREE/message/107673;_ylc=X3oDMTJzaGs1aTZnBF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3MwRzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "Albert Pearson" ehpee@rogers.com
<ehpee@rogers.com?Subject=+Re%3A%20Caesars%20Windsor%2C%20Canada%3F> ehpee123
<http://profiles.yahoo.com/ehpee123> Sat Jun 19, 2010 4:15 pm (PDT)

I never said that a 99% return is good. I said that a 99% return is
playable. If you throw comps, CB, and BB into the equation you can get good
value for your play while still being a small net loser on your gambling.
Like I said before you have to look at the whole package. At Windsor with
their 98% machines and stingy BB, and CB and even Comps you couldn't drag me
there.

Regards

A.P.

--- On Fri, 6/18/10, Dave <haaljo@yahoo.com <haaljo%40yahoo.com>> wrote:

From: Dave <haaljo@yahoo.com <haaljo%40yahoo.com>>
Subject: [vpFREE] Re: Caesars Windsor, Canada?
To: vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>
Date: Friday, June 18, 2010, 11:51 PM

Wow, I have to express caution on good games defined as less than 100%
TOTAL retrurn. A $1 VP gamber at a liesurely pace is putting through
$3K/hour. You losing $30/hour if E.V. is 99% TOTAL return.
Also, would you believe alchohol reduces E.V. or some other distraction
:-), annonyance, interesting scenery......

Factoid here's the First listed VPFREE policy:
http://members.cox.net/vpfree/POL.htm

"The vpFREE Video Poker Group is a free internet forum for the discussion
and exchange of information about video poker and video poker related
topics. vpFREE is dedicated to sharing, promoting and preserving good video
poker situations that can survive and prosper in an open market
environment."

Just sayin,
Dave in Boston

--- In vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>, "deuceswild1000"
<deuceswild1000@...> wrote:
>
>
>
> --- In vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>, Albert Pearson
<ehpee@> wrote:
> >
> > I must be going blind or our understanding of the term playable is
vastly different.
> > To me a playable machine must be at least very close to 99% i.e. 9/7 DB
or airport deuces or 9/6 DDB or better.
>
> ----------------------------------------------------------
>
> Albert,
>
> I totally agree with you. However, what is playable is differenet to
different people. That is why I am constantly chiding posters on here to
quantify their statements that "the machines are totally unplayable"
>
> I see people criticized for playing less than 100% machines. Some claim
that anyone who plays less than 100% should save their money and go to
Vegas, totally disregarding the cost of travel , which has the effect of
making the effective return negative.
>
> So, I urge all posters to quantify the term "playabel" like Albert did in
his posting. And if they are "unplayable" quantitfy those also and let the
reader decide.
>

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

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3a. Re: FW: Governors of 35 states filed suit against Fed Government...
<http://groups.yahoo.com/group/vpFREE/message/107672;_ylc=X3oDMTJzMGZyOWdhBF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3MgRzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "kellypkjoe" kellypkjoe@yahoo.com
<kellypkjoe@yahoo.com?Subject=+Re%3A%20FW%3A%20Governors%20of%2035%20states%20filed%20suit%20against%20Fed%20Government%2E%2E%2E>
kellypkjoe <http://profiles.yahoo.com/kellypkjoe> Sat Jun 19, 2010 2:59 pm
(PDT)

It is worse than inappropriate. It is Offense and the poster deserves to
be banned. The rule is not to get into religious oe political. in
discussing a subject. This was Far Far worst than anything I have ever seen
posted.

--- On Fri, 6/18/10, vpFREE Administrator <vpfreeadmin@cox.net<vpfreeadmin%40cox.net>> > wrote:

From: vpFREE Administrator <vpfreeadmin@cox.net <vpfreeadmin%40cox.net>>
Subject: [vpFREE] Re: FW: Governors of 35 states filed suit against Fed
Government...
To: vpFREE@Yahoogroups.com <vpFREE%40Yahoogroups.com>
Cc: "David Kathary" <dwk33@hotmail.com <dwk33%40hotmail.com>>
Date: Friday, June 18, 2010, 11:12 PM

The chain letter email advocating a constitutional convention that was

just posted on vpFREE is very inappropriate and has been deleted.

Please don't post these types of messages on vpFREE.

vpFREE Administrator

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

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3b. Re: FW: Governors of 35 states filed suit against Fed Government...
<http://groups.yahoo.com/group/vpFREE/message/107674;_ylc=X3oDMTJzb3F0YXBlBF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3NARzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "Sellers Phil" pwsellers01@yahoo.com
<pwsellers01@yahoo.com?Subject=+Re%3A%20FW%3A%20Governors%20of%2035%20states%20filed%20suit%20against%20Fed%20Government%2E%2E%2E>
pwsellers01 <http://profiles.yahoo.com/pwsellers01> Sat Jun 19, 2010
4:29 pm (PDT)

Oh get over yourself. While the topic may not have anything to do with VP
it is also not worthy of being banned from the group. Then you have to
comment on it to keep the thread alive. Well I, as one of MANY, support the
idea of a 28th amendment!

>It is worse than inappropriate. It is Offense and the poster deserves to
be banned. The rule is not to get into religious oe political. in
discussing a subject. This was Far >Far worst than anything I have ever
seen posted.

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

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3c. Re: FW: Governors of 35 states filed suit against Fed Government...
<http://groups.yahoo.com/group/vpFREE/message/107675;_ylc=X3oDMTJzbmJjdjhsBF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3NQRzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "Richard Long" carlboy101@yahoo.com
<carlboy101@yahoo.com?Subject=+Re%3A%20FW%3A%20Governors%20of%2035%20states%20filed%20suit%20against%20Fed%20Government%2E%2E%2E>
carlboy101 <http://profiles.yahoo.com/carlboy101> Sat Jun 19, 2010 6:03 pm
(PDT)

Actually, in the big picture it does have a bearing on video poker, and
everything else we do.

"Congress shall make no law that applies to the citizens of the United
States that does not apply equally to the Senators and Representatives; and,
Congress shall make no law that applies to the Senators and Representatives
that does not apply equally to the citizens of the United States."
Apparently the latest attempt of those in Congress to exempt themselves
from the provisions of the pending Healthcare Reform is, for many, the last
straw after years of hearing about congressional members retiring, even
after one term, at the same pay they were making, and exempting themselves
from having to pay Social Security, etc.

If WE continue to keep allowing the Congress to act like a Politburo,
everything we do will be at will of them.

________________________________
From: Sellers Phil <pwsellers01@yahoo.com <pwsellers01%40yahoo.com>>
To: vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>
Sent: Sat, June 19, 2010 4:29:51 PM
Subject: Re: [vpFREE] Re: FW: Governors of 35 states filed suit against Fed
Government...

Oh get over yourself. While the topic may not have anything to do with VP
it is also not worthy of being banned from the group. Then you have to
comment on it to keep the thread alive. Well I, as one of MANY, support the
idea of a 28th amendment!

>It is worse than inappropriate. It is Offense and the poster deserves to
be banned. The rule is not to get into religious oe political. in
discussing a subject. This was Far >Far worst than anything I have ever
seen posted.

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

------------------------------------

vpFREE Links: http://members.cox.net/vpfree/Links.htm

Yahoo! Groups Links

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

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4a. Do You Trust Indian Casinos?
<http://groups.yahoo.com/group/vpFREE/message/107676;_ylc=X3oDMTJzMGx2NDQ5BF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3NgRzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "mikeymic" mikeymic@yahoo.com
<mikeymic@yahoo.com?Subject=+Re%3ADo%20You%20Trust%20Indian%20Casinos%3F>
mikeymic <http://profiles.yahoo.com/mikeymic> Sat Jun 19, 2010 10:59 pm
(PDT)

I have had MANY private email discussions about VP play at various Indian
casinos. I would now like to open up the discussion to the entire group.

In general, there is a suspicion that machines are not as regulated on
private Indian land as in, for example, major Las Vegas casinos.

My opinion is that there are undoubtedly unfair VP games being played every
day. In this economy the temptation to squeeze out every dime of profit is
too great to resist.

In terms of my particular post today, I can inform you that there are
indeed some Indian casinos where I will not play. I base my choices not only
by personal experience but also by the many vpFREE members who email me.
Regardless of whether I and others are actually being "cheated", if you feel
unlucky or negative in a casino, then perhaps you should be playing
elsewhere anyway.

But I would like to get a sense, in general, of how the group feels about
this issue. Any of your comments and reasoning would be appreciated.

Mikey

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4b. Re: Do You Trust Indian Casinos?
<http://groups.yahoo.com/group/vpFREE/message/107677;_ylc=X3oDMTJzbzJ0ZHZoBF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3NwRzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "James Thompson" jamesgthompson@hotmail.com
<jamesgthompson@hotmail.com?Subject=+Re%3A%20Do%20You%20Trust%20Indian%20Casinos%3F>
jgtusc <http://profiles.yahoo.com/jgtusc> Sat Jun 19, 2010 11:46 pm (PDT)

I won't play at any casino other than casino's in Nevada. I don't trust
anybody other than Nevada gaming controlled casinos

To: vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>
From: mikeymic@yahoo.com <mikeymic%40yahoo.com>
Date: Sun, 20 Jun 2010 05:54:47 +0000
Subject: [vpFREE] Do You Trust Indian Casinos?

I have had MANY private email discussions about VP play at various Indian
casinos. I would now like to open up the discussion to the entire group.

In general, there is a suspicion that machines are not as regulated on
private Indian land as in, for example, major Las Vegas casinos.

My opinion is that there are undoubtedly unfair VP games being played every
day. In this economy the temptation to squeeze out every dime of profit is
too great to resist.

In terms of my particular post today, I can inform you that there are
indeed some Indian casinos where I will not play. I base my choices not only
by personal experience but also by the many vpFREE members who email me.
Regardless of whether I and others are actually being "cheated", if you feel
unlucky or negative in a casino, then perhaps you should be playing
elsewhere anyway.

But I would like to get a sense, in general, of how the group feels about
this issue. Any of your comments and reasoning would be appreciated.

Mikey

__________________________________________________________
The New Busy think 9 to 5 is a cute idea. Combine multiple calendars with
Hotmail.

http://www.windowslive.com/campaign/thenewbusy?tile=multicalendar&ocid=PID28326::T:WLMTAGL:ON:WL:en-US:WM_HMP:042010_5

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

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4c. Re: Do You Trust Indian Casinos?
<http://groups.yahoo.com/group/vpFREE/message/107678;_ylc=X3oDMTJzNTFjaTczBF9TAzk3MzU5NzE1BGdycElkAzQ2NDEwMTcEZ3Jwc3BJZAMxNzA1MDY1NzMyBG1zZ0lkAzEwNzY3OARzZWMDZG1zZwRzbGsDdm1zZwRzdGltZQMxMjc3MDE5NDg5> Posted
by: "Charles Galle" galle2u2@yahoo.com
<galle2u2@yahoo.com?Subject=+Re%3A%20Do%20You%20Trust%20Indian%20Casinos%3F>
galle2u2 <http://profiles.yahoo.com/galle2u2> Sat Jun 19, 2010 11:59 pm
(PDT)

That is my same opinion... I feel more comfortable
gambling in Las Vegas,etc. Nevada

Richard from Ca.
--- On Sat, 6/19/10, James Thompson <jamesgthompson@hotmail.com<jamesgthompson%40hotmail.com>> > wrote:

> From: James Thompson <jamesgthompson@hotmail.com<jamesgthompson%40hotmail.com>
>
> Subject: RE: [vpFREE] Do You Trust Indian Casinos?
> To: vpfree@yahoogroups.com <vpfree%40yahoogroups.com>
> Date: Saturday, June 19, 2010, 11:46 PM
>
> I won't play at any casino other than casino's in
> Nevada. I don't trust anybody other than Nevada gaming
> controlled casinos
>
> To: vpFREE@yahoogroups.com <vpFREE%40yahoogroups.com>
> From: mikeymic@yahoo.com <mikeymic%40yahoo.com>
> Date: Sun, 20 Jun 2010 05:54:47 +0000
> Subject: [vpFREE] Do You Trust Indian Casinos?
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> I have had MANY private email
> discussions about VP play at various Indian casinos. I would
> now like to open up the discussion to the entire group.
>
>
>
> In general, there is a suspicion that machines are not as
> regulated on private Indian land as in, for example, major
> Las Vegas casinos.
>
>
>
> My opinion is that there are undoubtedly unfair VP games
> being played every day. In this economy the temptation to
> squeeze out every dime of profit is too great to resist.
>
>
>
> In terms of my particular post today, I can inform you that
> there are indeed some Indian casinos where I will not play.
> I base my choices not only by personal experience but also
> by the many vpFREE members who email me. Regardless of
> whether I and others are actually being "cheated", if you
> feel unlucky or negative in a casino, then perhaps you
> should be playing elsewhere anyway.
>
>
>
> But I would like to get a sense, in general, of how the
> group feels about this issue. Any of your comments and
> reasoning would be appreciated.
>
>
>
> Mikey
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> __________________________________________________________
> The New Busy think 9 to 5 is a cute idea. Combine multiple
> calendars with Hotmail.
>
http://www.windowslive.com/campaign/thenewbusy?tile=multicalendar&ocid=PID28326::T:WLMTAGL:ON:WL:en-US:WM_HMP:042010_5
>
> [Non-text portions of this message have been removed]
>
>
>
> ------------------------------------
>
> vpFREE Links: http://members.cox.net/vpfree/Links.htm
>
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>
>
> vpFREE-fullfeatured@yahoogroups.com<vpFREE-fullfeatured%40yahoogroups.com>
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>

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