vpFREE2 Forums

Need Calculation Help

In a message dated 07/09/2006 9:52:33 A.M. Eastern Daylight Time,
correna2@yahoo.com writes:

I tried to plug this into both WinPoker and FVP...
without success. Can either of these programs handle this
scenario? If so, how?

The way I would check this on WinPoker is to change (temporarily) ALL Royal
Flushes to 5000 pay and then put in the hand for analysis.

Karen
From Toronto

.

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

Yes, once you have the paytable changed and the hand plugged in, you should
be able to see a list of all possible draws with EV for each.

Chandler

···

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com]On Behalf Of
krallison416@aol.com
Sent: Thursday, September 07, 2006 9:02 AM
To: vpFREE@yahoogroups.com
Subject: Re: [vpFREE] Need Calculation Help

In a message dated 07/09/2006 9:52:33 A.M. Eastern Daylight Time,
correna2@yahoo.com writes:

I tried to plug this into both WinPoker and FVP...
without success. Can either of these programs handle this
scenario? If so, how?

The way I would check this on WinPoker is to change (temporarily) ALL Royal
Flushes to 5000 pay and then put in the hand for analysis.

Karen
From Toronto

.

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

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

Yahoo! Groups Links

Thanks Karen, I should have thought of that myself. I did as you
suggested and it worked. The correct play did not change (hold
KQJ9).
Does anyone know what the added EV is for the 1000 coin bonus?

···

******************************************

The way I would check this on WinPoker is to change (temporarily)

ALL Royal Flushes to 5000 pay and then put in the hand for analysis.
  
Karen
From Toronto

I'm on the road and don't have reference material so this is off the top
of my head. I will not be held responsible for any mistakes.

Go to "Analyze Game" for 10/7. Take a look at the percentage payback
for the Royal. It should say something like 1.67%. Write that down.
Then change the 10/7 payscale to show the 5000 coin royal. Analyze
the game and take a look at the percentage payback the Royal then
represents. Subtract the normal payback (100.17) from that number.
Whatever the difference is divide it by four then add 100.17 to it and
voila! You have the payback of the game.

But now that I think about it, I'm just starting on my morning coffee, just
change the Royal to 4250 and analyze and you should get the same
number.

···

--- In vpFREE@yahoogroups.com, "correna2" <correna2@...> wrote:

Thanks Karen, I should have thought of that myself. I did as you
suggested and it worked. The correct play did not change (hold
KQJ9).
Does anyone know what the added EV is for the 1000 coin bonus?
******************************************

> The way I would check this on WinPoker is to change (temporarily)
ALL Royal Flushes to 5000 pay and then put in the hand for analysis.
  
Karen
From Toronto

I think it should be a 16th of whatever contribution the royal is to game
return. I don't play much DB and that figure isn't on the top of my head,
but in JB royal contribution to ER is about 2% making the total game return
an additional .125. Approximately. I'm using seat of the pants figures and
math.

Chandler

···

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com]On Behalf Of
correna2
Sent: Thursday, September 07, 2006 9:49 AM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] Re: Need Calculation Help

Thanks Karen, I should have thought of that myself. I did as you
suggested and it worked. The correct play did not change (hold
KQJ9).
Does anyone know what the added EV is for the 1000 coin bonus?
******************************************

The way I would check this on WinPoker is to change (temporarily)

ALL Royal Flushes to 5000 pay and then put in the hand for analysis.

Karen
From Toronto

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

Yahoo! Groups Links

Why would you put all Royal Flushes to 5000 paay, when only one of the
four pays 5000, and the rest only 4000?

Wouldn't putting a value of 4250 (for all RF's) be more appropriate?

···

--- In vpFREE@yahoogroups.com, krallison416@... wrote:

The way I would check this on WinPoker is to change (temporarily)

ALL Royal Flushes to 5000 pay and then put in the hand for analysis.

Not if you were looking for the proper hold on a heart RF draw.

Chandler

···

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com]On Behalf Of
Adams Myth
Sent: Thursday, September 07, 2006 10:42 AM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] Re: Need Calculation Help

Why would you put all Royal Flushes to 5000 paay, when only one of the
four pays 5000, and the rest only 4000?

Wouldn't putting a value of 4250 (for all RF's) be more appropriate?

--- In vpFREE@yahoogroups.com, krallison416@... wrote:

The way I would check this on WinPoker is to change (temporarily)

ALL Royal Flushes to 5000 pay and then put in the hand for analysis.

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

Yahoo! Groups Links

I get it. For strategy derivation, you need to put RF at 5000. For EV
calculation, at 4250.

But it looks like the premium necessary to switch the hold from KQJ9 to
KQJ, i snot as much as an additional 1000, but just around 175. This is
based on the chance of 1-SF and 8-Flush possibilities when you hold
KQJ9, compared to 1-RF and 56 Flush chances when you hold KQJ. I did
not count th evalue of other Straight and HighPair occurrences.

I'd like confirmation from someone.

···

--- In vpFREE@yahoogroups.com, "Chandler" <omnibibulous1@...> wrote:

Not if you were looking for the proper hold on a heart RF draw.

Using FVP and iteration I get a crossover around 11000 for a heart RF.

- John

···

--- In vpFREE@yahoogroups.com, "Adams Myth" <Adams_Myth@...> wrote:

I get it. For strategy derivation, you need to put RF at 5000. For EV
calculation, at 4250.

But it looks like the premium necessary to switch the hold from KQJ9 to
KQJ, i snot as much as an additional 1000, but just around 175. This is
based on the chance of 1-SF and 8-Flush possibilities when you hold
KQJ9, compared to 1-RF and 56 Flush chances when you hold KQJ. I did
not count th evalue of other Straight and HighPair occurrences.

I'd like confirmation from someone.

--- In vpFREE@yahoogroups.com, "Chandler" <omnibibulous1@> wrote:
> Not if you were looking for the proper hold on a heart RF draw.

That would mean I have to think through things more clearly.

This is what I did. Someone tell me where the flaw in the logic is.

If you hold KQJ9 of hearts, if you get the Ten on Draw, you have a
Straight Flush. If you get any other heart, and there are 8 of them,
you would have a Flush. The chance of a getting a Ten is 1/47, and the
chance of getting any of the other hearts is a combined 8/47. So the EV
of the SF or Flush events is 250*1/47 plus 30*8/47 = 10.4255

If you hold KQJ, the chance of getting the Ace and the Ten is a 2*(1/47)
*1/46) = 0.000925. Then if you get any other combination of two hearts,
you would have a Flush. And there are 70 (nine hearts remaining, giving
rise to 72 permutations of two each, minus the two instances of AT and
TA) of such possibilities. The chance of the two heart combination is
again 1/(47*46). So, the EV of holding KQJ is, assuming the RF payoff
to be X, 2*X*(1/47)*(1/46) plus 70*250*(1/47)*(1/46).

If I equate both, I get a value for X to be 10220

Apart from counting the number of Flushes wrong, the big mistake I did
in my previous calculation was using the 1-coin value for Flush and
Straight Flush, and the 5-coin value for the Royal Flush. With those
corrected, I am getting 10220 now.

And the fact that I am not taking into account the Straights and High
pairs could account for the discrepancy between 10220, and what you
have ~ 11000

Suffering through the calculations does indeed sharpen your
understanding of the mechanics. This is a fact Bob Dancer pounds
through in his columns, whenever he can find an excuse for doing so.

···

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

Using FVP and iteration I get a crossover around 11000 for a heart RF.

I am simplifying the logic in the complicated calculation in my prior
mail.

The whole thing is rather simple, really.

The chance of getting two particular cards (the Ace and the Ten of
Hearts) on the draw is 1/46th of the chance of getting one particular
card, say the Ten of Hearts.

Thus, unless the Royal Flush pays about 46 times the value of a
Straight Flush (250), holding for the Straight Flush is the preferred
option.

And voilà, 46 times 250 is 11500. Not the exact value one would get by
plugging in numbers into some software, but a pretty good back of the
envelope calculation.

But then, holding for the Royal Flush is always, glamorous, chivalrous!

I would recommend firing up WP or FVP, entering in a hand, and
observing the possible outcomes.

For my test, the extra card was a 3 of diamonds.

According to FVP, keeping the 9, there are 47 possible outcomes. 26
are garbage, 1 SF, 8 F, 3 ST, and 9 JoB.

Dropping the 9, there are 1081 possible outcomes. 634 are garbage, 1
royal, 35 flushes, 27 ST, 9 3Kd, 27 2-pr, and 348 JoB

I think the problem is your payoff of 250 for a flush.

- John

···

--- In vpFREE@yahoogroups.com, "Adams Myth" <Adams_Myth@...> wrote:

That would mean I have to think through things more clearly.

This is what I did. Someone tell me where the flaw in the logic is.

If you hold KQJ9 of hearts, if you get the Ten on Draw, you have a
Straight Flush. If you get any other heart, and there are 8 of them,
you would have a Flush. The chance of a getting a Ten is 1/47, and the
chance of getting any of the other hearts is a combined 8/47. So the EV
of the SF or Flush events is 250*1/47 plus 30*8/47 = 10.4255

If you hold KQJ, the chance of getting the Ace and the Ten is a 2*(1/47)
*1/46) = 0.000925. Then if you get any other combination of two hearts,
you would have a Flush. And there are 70 (nine hearts remaining, giving
rise to 72 permutations of two each, minus the two instances of AT and
TA) of such possibilities. The chance of the two heart combination is
again 1/(47*46). So, the EV of holding KQJ is, assuming the RF payoff
to be X, 2*X*(1/47)*(1/46) plus 70*250*(1/47)*(1/46).

If I equate both, I get a value for X to be 10220

Apart from counting the number of Flushes wrong, the big mistake I did
in my previous calculation was using the 1-coin value for Flush and
Straight Flush, and the 5-coin value for the Royal Flush. With those
corrected, I am getting 10220 now.

And the fact that I am not taking into account the Straights and High
pairs could account for the discrepancy between 10220, and what you
have ~ 11000

Suffering through the calculations does indeed sharpen your
understanding of the mechanics. This is a fact Bob Dancer pounds
through in his columns, whenever he can find an excuse for doing so.

--- In vpFREE@yahoogroups.com, "murphyfields" <jkludge@> wrote:
> Using FVP and iteration I get a crossover around 11000 for a heart RF.

Just averaging the royal like this won't be accurate, since that
assumes that there are exactly proportionally as many hands that are
royal draws at 4250 that aren't at 4000 and are at 5000 that aren't at
4250. Adding 1/4 times the payback at a royal of 5000 plus 3/4 times
the payback at a royal of 4000 will be more accurate. When there are
hands with royal draws in both hearts and another suit and the bonus
changes the strategy from being a non-heart royal draw to being a
heart royal draw, even that isn't going to perfect, but since, as far
as I know, in 10/7, all such hands are straight draws anyway, even
with the heart royal bonus, this shouldn't affect the calculation, so
it probably is perfect.

···

--- In vpFREE@yahoogroups.com, "correna2" <correna2@...> wrote:

Thanks Karen, I should have thought of that myself. I did as you
suggested and it worked. The correct play did not change (hold
KQJ9).
Does anyone know what the added EV is for the 1000 coin bonus?
******************************************

> The way I would check this on WinPoker is to change (temporarily)
ALL Royal Flushes to 5000 pay and then put in the hand for analysis.
  
Karen
From Toronto

I'm on the road and don't have reference material so this is off the top
of my head. I will not be held responsible for any mistakes.

Go to "Analyze Game" for 10/7. Take a look at the percentage payback
for the Royal. It should say something like 1.67%. Write that down.
Then change the 10/7 payscale to show the 5000 coin royal. Analyze
the game and take a look at the percentage payback the Royal then
represents. Subtract the normal payback (100.17) from that number.
Whatever the difference is divide it by four then add 100.17 to it and
voila! You have the payback of the game.

But now that I think about it, I'm just starting on my morning coffee, just
change the Royal to 4250 and analyze and you should get the same
number.

Look at it this way.

A hand is dealt - KQJ9 of hearts, plus an irrelevant card. The
question is whether to hold KQJ and hope for a Royal Flush or hold
KQJ9 and hope for a Straight Flush. One may hane to settle for just a
Flush, with no guarantee of evan an even paying hand.

Okay, the Straight Flush pays 250. Usually the Royal Flush pays 4000.
Usually the recommended hold is KQJ9.

The question is - what would the Royal Flush have to pay, for the
decision to swing to holding KQJ.

This is a small subset of all the questions that could be asked.

For this particular question, the following approach seems to be
logical. Consider all the paying hands in both the altenatives, and
their probabilities, assign an unknown value for the RF payoff, and
solve for its value, by equating the EV of KQJ hold to that of KQJ9
hold. Any RF payoff less than X would tilt te decision in favour of
holding KQJ9.

The payoffs for RF and SF are quite a bit mmore, compared to any other
potential paying hands in these two situations. So, as a first
approximation, ignore them. The probability of getting two specific
cards (Ace and Ten of Hearts for the RF) out of a 47 card deck is
about 46 times less than the probability of getting one specific card
(Ten of hearts for the SF). This is basic probability. Thus the Royal
Flush would have to pay about 46 times more for one to opt for holding
KQJ instead of KQJ9.

Which gives X a value of 11500. When I pre-defined cards KQJ9x in
WinPoker and FVP, they both gave me a value for the RF to be 9950 for
the breakeven where the decision shift. While the discrepancy has to
be explained, it is in the general ballpark.

I think I won't comment on this anymore.

···

--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@...> wrote:

Just averaging the royal like this won't be accurate, since that

assumes that there are exactly proportionally as many hands that are
royal draws at 4250 that aren't at 4000 and are at 5000 that aren't at
4250.

Strange...using FVP I get a breakpoint of 11040. What did you use for
a 5th card, and what paytable did you use?

- John

···

--- In vpFREE@yahoogroups.com, "Adams Myth" <Adams_Myth@...> wrote:

Look at it this way.

A hand is dealt - KQJ9 of hearts, plus an irrelevant card. The
question is whether to hold KQJ and hope for a Royal Flush or hold
KQJ9 and hope for a Straight Flush. One may hane to settle for just a
Flush, with no guarantee of evan an even paying hand.

Okay, the Straight Flush pays 250. Usually the Royal Flush pays 4000.
Usually the recommended hold is KQJ9.

The question is - what would the Royal Flush have to pay, for the
decision to swing to holding KQJ.

This is a small subset of all the questions that could be asked.

For this particular question, the following approach seems to be
logical. Consider all the paying hands in both the altenatives, and
their probabilities, assign an unknown value for the RF payoff, and
solve for its value, by equating the EV of KQJ hold to that of KQJ9
hold. Any RF payoff less than X would tilt te decision in favour of
holding KQJ9.

The payoffs for RF and SF are quite a bit mmore, compared to any other
potential paying hands in these two situations. So, as a first
approximation, ignore them. The probability of getting two specific
cards (Ace and Ten of Hearts for the RF) out of a 47 card deck is
about 46 times less than the probability of getting one specific card
(Ten of hearts for the SF). This is basic probability. Thus the Royal
Flush would have to pay about 46 times more for one to opt for holding
KQJ instead of KQJ9.

Which gives X a value of 11500. When I pre-defined cards KQJ9x in
WinPoker and FVP, they both gave me a value for the RF to be 9950 for
the breakeven where the decision shift. While the discrepancy has to
be explained, it is in the general ballpark.

I think I won't comment on this anymore.

--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@> wrote:
> Just averaging the royal like this won't be accurate, since that
assumes that there are exactly proportionally as many hands that are
royal draws at 4250 that aren't at 4000 and are at 5000 that aren't at
4250.

I (confidently) get $11,040, also. As a practical matter, though,
there are at least 2 reasons to wait until much higher than that to
draw to the royal.

···

Strange...using FVP I get a breakpoint of 11040. What did you use for
a 5th card, and what paytable did you use?

- John

--- In vpFREE@yahoogroups.com, "Adams Myth" <Adams_Myth@...> wrote:

Look at it this way.

A hand is dealt - KQJ9 of hearts, plus an irrelevant card. The
question is whether to hold KQJ and hope for a Royal Flush or hold
KQJ9 and hope for a Straight Flush. One may hane to settle for just a
Flush, with no guarantee of evan an even paying hand.

Okay, the Straight Flush pays 250. Usually the Royal Flush pays 4000.
Usually the recommended hold is KQJ9.

The question is - what would the Royal Flush have to pay, for the
decision to swing to holding KQJ.

This is a small subset of all the questions that could be asked.

For this particular question, the following approach seems to be
logical. Consider all the paying hands in both the altenatives, and
their probabilities, assign an unknown value for the RF payoff, and
solve for its value, by equating the EV of KQJ hold to that of KQJ9
hold. Any RF payoff less than X would tilt te decision in favour of
holding KQJ9.

The payoffs for RF and SF are quite a bit mmore, compared to any other
potential paying hands in these two situations. So, as a first
approximation, ignore them. The probability of getting two specific
cards (Ace and Ten of Hearts for the RF) out of a 47 card deck is
about 46 times less than the probability of getting one specific card
(Ten of hearts for the SF). This is basic probability. Thus the Royal
Flush would have to pay about 46 times more for one to opt for holding
KQJ instead of KQJ9.

Which gives X a value of 11500. When I pre-defined cards KQJ9x in
WinPoker and FVP, they both gave me a value for the RF to be 9950 for
the breakeven where the decision shift. While the discrepancy has to
be explained, it is in the general ballpark.

I think I won't comment on this anymore.

--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@> wrote:
> Just averaging the royal like this won't be accurate, since that
assumes that there are exactly proportionally as many hands that are
royal draws at 4250 that aren't at 4000 and are at 5000 that aren't at
4250.

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

Yahoo! Groups Links

Don't leave me hanging...what are your 2 reasons?

I (confidently) get $11,040, also. As a practical matter, though,
there are at least 2 reasons to wait until much higher than that to
draw to the royal.

>Strange...using FVP I get a breakpoint of 11040. What did you use for
>a 5th card, and what paytable did you use?
>
>- John
>
>>
>> Look at it this way.
>>
>> A hand is dealt - KQJ9 of hearts, plus an irrelevant card. The
>> question is whether to hold KQJ and hope for a Royal Flush or hold
>> KQJ9 and hope for a Straight Flush. One may hane to settle for just a
>> Flush, with no guarantee of evan an even paying hand.
>>
>> Okay, the Straight Flush pays 250. Usually the Royal Flush pays 4000.
>> Usually the recommended hold is KQJ9.
>>
>> The question is - what would the Royal Flush have to pay, for the
>> decision to swing to holding KQJ.
>>
>> This is a small subset of all the questions that could be asked.
>>
>> For this particular question, the following approach seems to be
>> logical. Consider all the paying hands in both the altenatives, and
>> their probabilities, assign an unknown value for the RF payoff, and
>> solve for its value, by equating the EV of KQJ hold to that of KQJ9
>> hold. Any RF payoff less than X would tilt te decision in favour of
>> holding KQJ9.
>>
>> The payoffs for RF and SF are quite a bit mmore, compared to any

other

>> potential paying hands in these two situations. So, as a first
>> approximation, ignore them. The probability of getting two specific
>> cards (Ace and Ten of Hearts for the RF) out of a 47 card deck is
>> about 46 times less than the probability of getting one specific card
>> (Ten of hearts for the SF). This is basic probability. Thus the Royal
>> Flush would have to pay about 46 times more for one to opt for

holding

>> KQJ instead of KQJ9.
>>
>> Which gives X a value of 11500. When I pre-defined cards KQJ9x in
>> WinPoker and FVP, they both gave me a value for the RF to be 9950 for
>> the breakeven where the decision shift. While the discrepancy has to
>> be explained, it is in the general ballpark.
>>
>> I think I won't comment on this anymore.
>>
>> --- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@>

wrote:

>> > Just averaging the royal like this won't be accurate, since that
>> assumes that there are exactly proportionally as many hands that are
>> royal draws at 4250 that aren't at 4000 and are at 5000 that

aren't at

···

--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@...> wrote:

>--- In vpFREE@yahoogroups.com, "Adams Myth" <Adams_Myth@> wrote:
>> 4250.
>>
>
>
>
>
>
>
>
>vpFREE Links: http://members.cox.net/vpfree/Links.htm
>
>
>Yahoo! Groups Links
>
>
>
>
>
>
>

Each time I did this with a different approach, I got a different
number; but they were all in the same range, around 10000.

I used the 9/6 JoB paytable and changed the Royal Flush pay to 8000;
predefined the cards KQJ9 and went through a few hands before I had a
KQJ9,4. Then went to the "Details" (on WinPoker) or "Perfect Hand
Statistics" on FVP. The two programs work differently in this situation
(on how you get there), but both showed identical (has to be expected)
tables for the possible outcomes with KQJ9 or KQJ hold.

Seeing the ExpReturn to be higher for KQJ9, I kept increasing the RF
payout, and at 10000, things reversed. Then I started backing off a bit
to find the perfect transition point. It was 9950. This was a laborious
process.

But I already had 9950 with a different, simple, straight forward
method.

If you look at the possible paying hands for the two holds (independent
of the RF payout), it is as follows:

Hold Hands Junk JoB 2-Pair 3Kind Straight Flush StFlush RF
KQJ9 47 26 9 0 0 3 8 1 0
KQJ 1081 634 348 27 9 27 35 0 1

Plugging this information in Excel, along with the 9/6 payoffs for each
outcome, it was very simple to come out with the magic number 9950.

I thank you for asking the question. I saved the screenshot with all
these calculations, showing the numbers from WinPoker, FVP, and Excel.
I am going to try post it in the files section (I am not sure if I need
the temporary permission to do that, as per a recent post from the
administrator), I'll leave it for a week and then delete it.

Take a look at the details provided there, and tell me if I am doing
something wrong. At this point it is purely academic, but I'd like to
know the reason for the different answers.

If I need permission to post the file, it might take a little bit of
time. Otherwise, you should see it there now.

···

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

Strange...using FVP I get a breakpoint of 11040. What did you use for
a 5th card, and what paytable did you use?

--- In vpFREE@yahoogroups.com, Tom Robertson <thomasrrobertson@...>
wrote:

I (confidently) get $11,040, also. As a practical matter, though,
there are at least 2 reasons to wait until much higher than that to
draw to the royal.

Such as what?

Does one of them has to do with tipping?

I too did get a 11040 or so yesterday; I forget how I got that.

I think that explains it. I was using 10/7 DB which I believe was
mentioned in the original post.

- John

···

--- In vpFREE@yahoogroups.com, "Adams Myth" <Adams_Myth@...> wrote:

Each time I did this with a different approach, I got a different
number; but they were all in the same range, around 10000.

I used the 9/6 JoB paytable and changed the Royal Flush pay to 8000;
predefined the cards KQJ9 and went through a few hands before I had a
KQJ9,4. Then went to the "Details" (on WinPoker) or "Perfect Hand
Statistics" on FVP. The two programs work differently in this situation
(on how you get there), but both showed identical (has to be expected)
tables for the possible outcomes with KQJ9 or KQJ hold.

Seeing the ExpReturn to be higher for KQJ9, I kept increasing the RF
payout, and at 10000, things reversed. Then I started backing off a bit
to find the perfect transition point. It was 9950. This was a laborious
process.

But I already had 9950 with a different, simple, straight forward
method.

If you look at the possible paying hands for the two holds (independent
of the RF payout), it is as follows:

Hold Hands Junk JoB 2-Pair 3Kind Straight Flush StFlush RF
KQJ9 47 26 9 0 0 3 8 1 0
KQJ 1081 634 348 27 9 27 35 0 1

Plugging this information in Excel, along with the 9/6 payoffs for each
outcome, it was very simple to come out with the magic number 9950.

I thank you for asking the question. I saved the screenshot with all
these calculations, showing the numbers from WinPoker, FVP, and Excel.
I am going to try post it in the files section (I am not sure if I need
the temporary permission to do that, as per a recent post from the
administrator), I'll leave it for a week and then delete it.

Take a look at the details provided there, and tell me if I am doing
something wrong. At this point it is purely academic, but I'd like to
know the reason for the different answers.

If I need permission to post the file, it might take a little bit of
time. Otherwise, you should see it there now.

--- In vpFREE@yahoogroups.com, "murphyfields" <jkludge@> wrote:
>
> Strange...using FVP I get a breakpoint of 11040. What did you use for
> a 5th card, and what paytable did you use?