Videopoker:How reliable is the Math?

[Dave_Breslin]

In Blackjack counting over the years what was important to your play had to
be re-arrainged.Despite decades of math testing by Professors and others
complicated systems were later "found" to yield no more return than simple Hi
-low.
People (not me to scared to bet big) invested $$ in higher level systems,
learned to count on their toes, twisted their ring around to count aces, learn
arcane memory word systems to keep indices in your head (this idiot guilty).To
find after wasting a good chunk of their time that side counts got you
nadda.etc.
       I know this was back in the old days when a 100 million hands run
seemed like a big number to us math impaired but Videopoker is a much more
complicated game what are the changes that if you rely on some of the finer math
pointsof the game in 10 years they going to say oophs we really should have run a
100 trillion hands to be in tolerance and actually prove results?
              PS I like math people because I flunked out.(No one told us
there would
be anything interesting (gambling, computer graphics, etc.)) to do with this
stuff.WHEN I was a kid you had to take on faith that anything you had to slap
yourself in the face to stay awake for was good for you.

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

[rgmustain]

There is a lot of math involved with VP. What math are you
questioning? If it's the payback of the games, this is 100% accurate
because it is based on analyzing every hand. If it's the strategy,
then again it's 100% accurate since the strategy is also determined
by analyzing every hand. If it's something else, please be more
specific.

Dick

  In Blackjack counting over the years what was important to your

play had to

be re-arrainged.Despite decades of math testing by Professors and

others

complicated systems were later "found" to yield no more return than

simple Hi

-low.
People (not me to scared to bet big) invested $$ in higher level

systems,

learned to count on their toes, twisted their ring around to count

aces, learn

arcane memory word systems to keep indices in your head (this idiot

guilty).To

find after wasting a good chunk of their time that side counts got

you

nadda.etc.
       I know this was back in the old days when a 100 million

hands run

seemed like a big number to us math impaired but Videopoker is a

much more

complicated game what are the changes that if you rely on some of

the finer math

pointsof the game in 10 years they going to say oophs we really

should have run a

100 trillion hands to be in tolerance and actually prove results?
              PS I like math people because I flunked out.(No one

told us

there would
be anything interesting (gambling, computer graphics, etc.)) to do

with this

stuff.WHEN I was a kid you had to take on faith that anything you

had to slap

···

--- In vpFREE@yahoogroups.com, cbres77376@a... wrote:

yourself in the face to stay awake for was good for you.

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

[Steve_Jacobs]

  In Blackjack counting over the years what was important to your play had
to be re-arrainged.Despite decades of math testing by Professors and others
complicated systems were later "found" to yield no more return than simple
Hi -low.
People (not me to scared to bet big) invested $$ in higher level systems,
learned to count on their toes, twisted their ring around to count aces,
learn arcane memory word systems to keep indices in your head (this idiot
guilty).To find after wasting a good chunk of their time that side counts
got you nadda.etc.

Side counts for card counting are a lot like penalty cards in VP -- they
have the potential to improve your outcome, but they may not be worth
the additional effort.

       I know this was back in the old days when a 100 million hands run
seemed like a big number to us math impaired but Videopoker is a much more
complicated game what are the changes that if you rely on some of the finer
math pointsof the game in 10 years they going to say oophs we really should
have run a 100 trillion hands to be in tolerance and actually prove
results?

The commercial VP programs are not based on simulating a large number
of hands. Instead, they use combinatorial analysis to calculate the results.
This means that the results are completely accurate, and all of the different
programs end up with identical numbers for how often each payoff is hit,
when playing max-EV strategy.

However, these numbers are "reliable" only if you understand that they
are designed for one very specific (narrow) purpose -- to maximize EV.
The VP "experts" teach that EV is the cat's meow, the one true golden
standard that should be sought above all else. In my (not so humble)
opinion, that is quite misguided.

The idea that there is a single playing strategy which is always best
is a myth, but it is a myth that is likely to continue to be treated as "fact"
for a long time to come. The brutal truth is that the best way to play
depends on what the player wants to accomplish. A recent thread on
vpFREE is a good example to illustrate my point. I've presented a
formula for computing RoRBR, which is "Risk of Ruin Before Royal",
and showed that a bankoll of 731 units gives the player a 50/50 shot
at hitting a royal, when playing 9/6 JoB. However, the thing that hasn't
been discussed recently is the fact that this number of 731 units applies
only to a player who is using the max-EV strategy, and it is possible to
do better by using a different strategy. If a player says "I don't care about
EV, I care about stretching my bankroll to get the best shot at hitting
a royal flush," then the player should adopt a best-shot(royal) strategy.

For 9/6 JoB, the best-shot(royal) strategy reduces the 50/50 bankroll
from 731 units to 720 units. To put that another way, if two players
start with 731 units each, the player who uses a max-EV strategy will
have a 50.02% chance of surviving to hit a royal, while the player
who uses a best-shot(royal) strategy will have a 50.54% chance of
hitting the royal. This is a lot like comparing two coin-toss games,
where one uses a coin that is almost exactly fair, while the other
uses a coin that is biased to come up heads 50.54% of the time
and tails 49.46% of the time. Which coin do you want to use?

Bottom line: EV isn't everything.

···

On Thursday 24 November 2005 07:56 am, cbres77376@aol.com wrote:

[Cogno_Scienti]

<<I know this was back in the old days when a 100 million hands run seemed
like a big number to us math impaired but Videopoker is a much more
complicated game what are the changes that if you rely on some of the finer
math pointsof the game in 10 years they going to say oophs we really should
have run a 100 trillion hands to be in tolerance and actually prove
results?>>

The math of video poker is nowadays calculated exactly so there is no issue
of not running enough hands. I think people still misunderstand Bob Dancer's
statement that STUDYING the penalty cards is worth much more than 0.002%.
He's saying that the STUDY is valuable in itself. The penalty cards in most
games are, as everyone agrees, not worth much and I in fact don't bother
with them in most games (especially that Ace-Jack situation in SDB). But
studying why some holds are worth more than others lets me learn new games
more easily and remember correct holds in situations where I do not have or
do not wish to bring out a strategy card.

Cogno

[rgmustain]

Steve,

Perhaps the best example of a goal-oriented strategy is multistrike.
The goals at each level are different and so are the strategies.
While the ultimate goal is to maximize EV for all hands, the goals at
lower levels are influenced by the goal of reaching the next level
and not maximizing EV at that level.

Have you looked at multistrike in your efforts to understand
different goals? If I missed a previous post on this subject a
pointer would be appreciated.

Thanks,
Dick

> In Blackjack counting over the years what was important to your

play had

> to be re-arrainged.Despite decades of math testing by Professors

and others

> complicated systems were later "found" to yield no more return

than simple

> Hi -low.
> People (not me to scared to bet big) invested $$ in higher level

systems,

> learned to count on their toes, twisted their ring around to

count aces,

> learn arcane memory word systems to keep indices in your head

(this idiot

> guilty).To find after wasting a good chunk of their time that

side counts

> got you nadda.etc.

Side counts for card counting are a lot like penalty cards in VP --

they

have the potential to improve your outcome, but they may not be

worth

the additional effort.

> I know this was back in the old days when a 100 million

hands run

> seemed like a big number to us math impaired but Videopoker is a

much more

> complicated game what are the changes that if you rely on some of

the finer

> math pointsof the game in 10 years they going to say oophs we

really should

> have run a 100 trillion hands to be in tolerance and actually

prove

> results?

The commercial VP programs are not based on simulating a large

number

of hands. Instead, they use combinatorial analysis to calculate

the results.

This means that the results are completely accurate, and all of the

different

programs end up with identical numbers for how often each payoff is

hit,

when playing max-EV strategy.

However, these numbers are "reliable" only if you understand that

they

are designed for one very specific (narrow) purpose -- to maximize

EV.

The VP "experts" teach that EV is the cat's meow, the one true

golden

standard that should be sought above all else. In my (not so

humble)

opinion, that is quite misguided.

The idea that there is a single playing strategy which is always

best

is a myth, but it is a myth that is likely to continue to be

treated as "fact"

for a long time to come. The brutal truth is that the best way to

play

depends on what the player wants to accomplish. A recent thread on
vpFREE is a good example to illustrate my point. I've presented a
formula for computing RoRBR, which is "Risk of Ruin Before Royal",
and showed that a bankoll of 731 units gives the player a 50/50 shot
at hitting a royal, when playing 9/6 JoB. However, the thing that

hasn't

been discussed recently is the fact that this number of 731 units

applies

only to a player who is using the max-EV strategy, and it is

possible to

do better by using a different strategy. If a player says "I don't

care about

EV, I care about stretching my bankroll to get the best shot at

hitting

a royal flush," then the player should adopt a best-shot(royal)

strategy.

For 9/6 JoB, the best-shot(royal) strategy reduces the 50/50

bankroll

from 731 units to 720 units. To put that another way, if two

players

start with 731 units each, the player who uses a max-EV strategy

will

have a 50.02% chance of surviving to hit a royal, while the player
who uses a best-shot(royal) strategy will have a 50.54% chance of
hitting the royal. This is a lot like comparing two coin-toss

games,

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:

On Thursday 24 November 2005 07:56 am, cbres77376@a... wrote:
where one uses a coin that is almost exactly fair, while the other
uses a coin that is biased to come up heads 50.54% of the time
and tails 49.46% of the time. Which coin do you want to use?

Bottom line: EV isn't everything.

[Steve_Jacobs]

Steve,

Perhaps the best example of a goal-oriented strategy is multistrike.
The goals at each level are different and so are the strategies.
While the ultimate goal is to maximize EV for all hands, the goals at
lower levels are influenced by the goal of reaching the next level
and not maximizing EV at that level.

Part of what I'm saying is that I don't believe in "ultimate" goals. The
game isn't what decides what is "best" but rather it is the player
making a conscious decision about what he/she wants to achieve.

Have you looked at multistrike in your efforts to understand
different goals? If I missed a previous post on this subject a
pointer would be appreciated.

I have not (yet) studied multistrike at all, but I suspect that it may
lead to interesting new insights in alternate strategies.

···

On Thursday 24 November 2005 06:17 pm, mroejacks wrote:

[Michael_Boutot]

If people would spend the time studying they waste in repeatedly
declaring it is not worth their time to do so there would be enough
time to learn all penalty cards & memorize the encyclopedia as well.
BTW: Side count of aces in black jack quite critical.

> Steve,
>
> Perhaps the best example of a goal-oriented strategy is

multistrike.

> The goals at each level are different and so are the strategies.
> While the ultimate goal is to maximize EV for all hands, the

goals at

> lower levels are influenced by the goal of reaching the next level
> and not maximizing EV at that level.

Part of what I'm saying is that I don't believe in "ultimate"

goals. The

game isn't what decides what is "best" but rather it is the player
making a conscious decision about what he/she wants to achieve.

> Have you looked at multistrike in your efforts to understand
> different goals? If I missed a previous post on this subject a
> pointer would be appreciated.

I have not (yet) studied multistrike at all, but I suspect that it

may

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:

On Thursday 24 November 2005 06:17 pm, mroejacks wrote:
lead to interesting new insights in alternate strategies.

[John9]

Dick, I appreciate what you meant but Multistrike strategy is still EV-based on each level. The value of the later levels is built in to the lower ones.
   
  Steve, I greatly appreciate you pointing out that EV is just one of many possible values on which to base a strategy. Let's take a for-instance: in a quickest-royal strategy, an extreme case but possibly useful in certain tournament situations, I presume you would hold only high cards of the same suit, 2-card royal > 1 high card, etc. You would throw away anything else. This would be an extremely simple strategy for which to compute the return.
   
  But in a min-royal strategy, which I assume you mean hitting a royal in the fewest # hands while preserving bankroll, how do you know where to draw the line? For example, in 9/6 JOB, would you keep all 3-card royals over high pairs, or just 4-card flushes, or what? In other words, how do you juxtapose the two criteria, hitting a royal versus preserving bankroll? I'm guessing that it's where the two individual criteria would intersect on a graph. And how would the resulting strategy differ from max-EV strategy, if at all?
   
  John

  Steve,

Perhaps the best example of a goal-oriented strategy is multistrike.
The goals at each level are different and so are the strategies.
While the ultimate goal is to maximize EV for all hands, the goals at
lower levels are influenced by the goal of reaching the next level
and not maximizing EV at that level.

Have you looked at multistrike in your efforts to understand
different goals? If I missed a previous post on this subject a
pointer would be appreciated.

Thanks,
Dick

> In Blackjack counting over the years what was important to your

play had

> to be re-arrainged.Despite decades of math testing by Professors

and others

> complicated systems were later "found" to yield no more return

than simple

> Hi -low.
> People (not me to scared to bet big) invested $$ in higher level

systems,

> learned to count on their toes, twisted their ring around to

count aces,

> learn arcane memory word systems to keep indices in your head

(this idiot

> guilty).To find after wasting a good chunk of their time that

side counts

> got you nadda.etc.

Side counts for card counting are a lot like penalty cards in VP --

they

have the potential to improve your outcome, but they may not be

worth

the additional effort.

> I know this was back in the old days when a 100 million

hands run

> seemed like a big number to us math impaired but Videopoker is a

much more

> complicated game what are the changes that if you rely on some of

the finer

> math pointsof the game in 10 years they going to say oophs we

really should

> have run a 100 trillion hands to be in tolerance and actually

prove

> results?

The commercial VP programs are not based on simulating a large

number

of hands. Instead, they use combinatorial analysis to calculate

the results.

This means that the results are completely accurate, and all of the

different

programs end up with identical numbers for how often each payoff is

hit,

when playing max-EV strategy.

However, these numbers are "reliable" only if you understand that

they

are designed for one very specific (narrow) purpose -- to maximize

EV.

The VP "experts" teach that EV is the cat's meow, the one true

golden

standard that should be sought above all else. In my (not so

humble)

opinion, that is quite misguided.

The idea that there is a single playing strategy which is always

best

is a myth, but it is a myth that is likely to continue to be

treated as "fact"

for a long time to come. The brutal truth is that the best way to

play

depends on what the player wants to accomplish. A recent thread on
vpFREE is a good example to illustrate my point. I've presented a
formula for computing RoRBR, which is "Risk of Ruin Before Royal",
and showed that a bankoll of 731 units gives the player a 50/50 shot
at hitting a royal, when playing 9/6 JoB. However, the thing that

hasn't

been discussed recently is the fact that this number of 731 units

applies

only to a player who is using the max-EV strategy, and it is

possible to

do better by using a different strategy. If a player says "I don't

care about

EV, I care about stretching my bankroll to get the best shot at

hitting

a royal flush," then the player should adopt a best-shot(royal)

strategy.

For 9/6 JoB, the best-shot(royal) strategy reduces the 50/50

bankroll

from 731 units to 720 units. To put that another way, if two

players

start with 731 units each, the player who uses a max-EV strategy

will

have a 50.02% chance of surviving to hit a royal, while the player
who uses a best-shot(royal) strategy will have a 50.54% chance of
hitting the royal. This is a lot like comparing two coin-toss

games,

where one uses a coin that is almost exactly fair, while the other
uses a coin that is biased to come up heads 50.54% of the time
and tails 49.46% of the time. Which coin do you want to use?

Bottom line: EV isn't everything.

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

···

mroejacks <rgmustain@att.net> wrote:
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x...> wrote:

On Thursday 24 November 2005 07:56 am, cbres77376@a... wrote:

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

[rgmustain]

EV-based on each level. The value of the later levels is built in to
the lower ones.

I thought that is what I said. My point was that the correct strategy
at the lower levels, to maximize the overall EV, would not maximize the
return for that level if that level was looked at by itself.

While this is not really very important from a multistrike perspective
it may give some insight as to other situations where maximizing EV
would not be the correct strategy because of other considerations.

Dick

···

--- In vpFREE@yahoogroups.com, John <john_oc_ca@y...> wrote:

Dick, I appreciate what you meant but Multistrike strategy is still

[Steve_Jacobs]

> Dick, I appreciate what you meant but Multistrike strategy is still

EV-based on each level. The value of the later levels is built in to
the lower ones.

I thought that is what I said. My point was that the correct strategy
at the lower levels, to maximize the overall EV, would not maximize the
return for that level if that level was looked at by itself.

One must always look at the overall game in order to maximize EV
for that game. Technically, the outcome isn't known until all the dust
has settled and all levels have been played out. If you look only at
the overall outcome of each play, and maximize overall EV of each
play, then the correct strategy for each level will result.

While this is not really very important from a multistrike perspective
it may give some insight as to other situations where maximizing EV
would not be the correct strategy because of other considerations.

The reason that maximizing something else becomes "correct" is
that the player decides they would prefer to maximize that other
something. There is absolutely nothing inherent in EV that makes
it "superior" to other objectives. EV is generally easier to compute,
and therefore easier to optimize, than other measures of performance,
but it isn't "special" in any mathematically meaningful sense. It is
simply one option among an infinite variety of "optimal" strategies.

A player might choose to minimize RoR in order to have the absolute
best chance at playing a favorable game forever, without ever going
broke. If a player finds that more appealing than getting the most
average dollars per game played, then that is the "right" way to
play, for _that_ player.

A player who really likes to hit royals, and wants to minimize the
number of trips to the ATM between royals, might choose RoRBR
to give them the best shot a stretching the _current_ bankroll until
a royal comes along.

A different player who also likes royals, but wants to pay the least
number of dollars in terms of losses between royals, should choose
a min-cost(royal) strategy.

Each of these alternate strategies is better than max-EV, if the player
wishes to base his/her play on the alternate objective rather than
maximizing dollars returned per game played.

···

On Friday 25 November 2005 04:17 pm, mroejacks wrote:

--- In vpFREE@yahoogroups.com, John <john_oc_ca@y...> wrote:

[Steve_Jacobs]

  Steve, I greatly appreciate you pointing out that EV is just one of many
possible values on which to base a strategy. Let's take a for-instance: in
a quickest-royal strategy, an extreme case but possibly useful in certain
tournament situations, I presume you would hold only high cards of the same
suit, 2-card royal > 1 high card, etc. You would throw away anything else.
This would be an extremely simple strategy for which to compute the return.

Yes, this gives the highest probability of hitting a royal on the very next
play, which is the same as minimizing the average number of plays needed
to hit a royal. For 9/6 JoB, the EV for this strategy is 55.016%, so it is
extremely costly to always try so hard to hit a royal, but this strategy
reduces the royal cycle from 40390.5 to 23164.7, so royals do occur much
more often when this strategy is used.

On average, a player will lose 11220.37 units between royals, by playing
so aggressively. In contrast, the min-cost(royal) strategy reduces the cost
to 976 units per royal.

The bankroll needed to give a 50/50 shot at the royal, when using this
strategy, is 7778 units, as opposed to the 720 unit bankroll needed for
the best-shot(royal) strategy.

  But in a min-royal strategy, which I assume you mean hitting a royal in
the fewest # hands while preserving bankroll, how do you know where to draw
the line? For example, in 9/6 JOB, would you keep all 3-card royals over
high pairs, or just 4-card flushes, or what? In other words, how do you
juxtapose the two criteria, hitting a royal versus preserving bankroll? I'm
guessing that it's where the two individual criteria would intersect on a
graph. And how would the resulting strategy differ from max-EV strategy, if
at all?

I don't recall using the phrase "min-royal strategy" so I'll assume you meant
to say "best-shot(royal) strategy." The idea behind best-shot(royal) isn't to
hit the royal quickly (the max-royal strategy you describe above is best at
that), and it isn't really designed to preserve bankroll (the min-cost(royal)
strategy is best at that). It also doesn't try to balance opposing goals,
but tries to do just one thing: maximize the probability of _eventually_
hitting the royal. This is sort of the opposite of trying to hit a royal as
soon as possible, and the solution it tied directly to my RoRBR formula,
which is used to compute the overall probability of eventually hitting the
royal.

I've developed a method called "virtual payoffs" that I use to compute
optimal strategies. The math behind it is a bit complicated, but the idea
is really quite simple. What I do is pretend that we're playing a game that
is slightly different than the actual game. This is done by pretending that
the payoffs are different than their actual values, so that "virtual" values
are used in place of each real payoff. Then, I use a VP program to find
the best strategy for a game that uses these virtual payoffs, by maximizing
"virtual EV" instead of maximizing "actual EV." The big trick here is to
find a formula that turns real payoffs into virtual values that correctly
represent the desired objective.

It would require a lot of highly technical posts to give a detailed
description of how this works, so I won't try to do that right now, but I can
give several examples of virtual payoff tables that I've used to find some
optimal strategies. For these examples, I'll use a 9/6 JoB game with a
royal jackpot of 1300 units. This gives the game a healthy EV for the
player so that RoR can be used for one of the examples.

The following table shows virtual payoffs that apply to the 9/6 JoB game.
For the Max-EV strategy, the actual payoffs for the game are used. I've
rounded the virtual payoffs for this table, but when I compute optimal
strategies the virtual payoffs are specified to 14 digit accuracy. These
numbers are all very precisely defined.

<pre>
    Max Min Min Max
Hand EV RoR bs_RF mc_RF Cost Royal

···

On Friday 25 November 2005 01:07 pm, John wrote:
-------------------------------------------------------------------------------------
Royal 1300 1003.5 1038.7 975.99 1277.9 1
Str-flush 50 49.492 48.839 50 49.166 0
4/kind 25 24.875 24.713 25 24.591 0
Full House 9 8.9850 8.9654 9 8.8638 0
Flush 6 5.9937 5.9856 6 5.9149 0
Straight 4 3.9975 3.9942 4 3.9489 0
3/kind 3 2.9987 2.9971 3 2.9660 0
Two Pair 2 1.9996 1.9990 2 1.9830 0
High Pair 1 1 1 1 1 0
-------------------------------------------------------------------------------------
</pre>

The optimal strategy for each of these cases is found by plugging the
virtual payoffs into any VP program that computes a max-EV strategy.
I don't know if any commercial VP programs will allow non-integer
payoffs to be entered, but my own program supports this, and it is
very useful for studying alternate strategies. If the commercial programs
don't allow this, you might try multiplying all payoffs by 100 or 1000
and rounding to approximate the virtual payoffs.

For 9/6 JoB there is a simpler trick for finding the best-shot(royal)
strategy. Changing the royal payoff to 1038, while leaving all other
payoffs at the actual values, just happens to give the correct RoRBR
strategy. The same strategy results from any royal payoff between
1022 and 1043. However, this kind of trick doesn't work for 8/5 JoB
or for 10/7 DB, and I haven't tried it for other games.

Here a quick summary of what each of these strategies is trying to do:

Min-RoR minimizes overall risk-of-ruin, which is equivalent to maximizing
the probability that the player will play forever without ever going broke.
The 50/50 bankroll for this strategy is 1661 units, which gives the player
a 50% chance of playing forever without going broke. The max-EV strategy
gives a 50/50 bankroll of 1670 units.

The bs_RF column is best-shot(royal) strategy, which maximizes the
probability of hitting a royal before going broke. This strategy has a
50/50 bankroll of 720 units, which gives the player a 50% chance of
hitting a royal before going broke. This bankroll is smaller than the
50/50 bankroll for Min-RoR strategy, because the task of hitting a royal
is easier than the task of playing forever. The max-EV strategy gives
a 50/50 bankroll 731 units when trying to hit a royal before going broke.

The mc_RF column is min-cost(royal) strategy, which minimizes the
average loss that occurs between royal flushes. When the royal payoff
if 975.99 units, royals occur just often enough to pay their own cost,
making the game exactly breakeven. By comparison, the average loss
between royals when playing the Max-EV strategy is 984.299 units.

The Min-cost column is the strategy that maximizes the average number
of units returned per unit consumed by losses. This views the game as
if you were playing at a casino on the border between two countries and
using the VP game to exchange currency. If the VP machine accepted
only U.S. dollars but made all payoffs in Canadian dollars, then this strategy
would give the player the best possible exchange rate. For this game,
each dollar paid back to the player costs only 98.297651 dollars that are
paid to the machine in lost wagers, on average. This strategy can also
be viewed as a "best winning streak" strategy. If you start with one unit
and collect your net winnings, but re-play only the original unit and keep
playing until you eventually lose, then this strategy maximizes your average
payoff from these winning streaks. By comparison, the Max-EV strategy
has an average cost of 98.297656 units lost per unit returned to the player.
This strategy is almost identical to Max-EV for this game, and this tends
to hold true for most games.

The Max-Royal strategy tries to hit royals at all costs. This strategy would
discard a dealt straight-flush in order to try for a royal instead. This
would be the right play to make on the last few hands of a tournament,
if your only hope for winning a prize is to hit a royal flush. Otherwise,
this strategy is a great way to burn through a bankroll in a hurry.

The strategy shown below is best-shot(royal) strategy. It tries for royals
a little more often than max-EV strategy.

  Jacks or Better 9/6 best-shot(royal)
  Distribution of Final Hands
----------------------------------------------------------------
Final Hand Payoff % Hit Cycle % Return
----------------------------------------------------------------
Royal Flush 5190 0.0028460595763 35136.29891406983 2.95420984020
Straight Flush 250 0.0111604568767 8960.20665686290 0.55802284383
4/Kind 125 0.2353418470304 424.91380628578 5.88354617576
Full House 45 1.1479534453312 87.11154655854 10.33158100798
Flush 30 1.1150247530435 89.68410766402 6.69014851826
Straight 20 1.1268006944393 88.74683916463 4.50720277776
3/Kind 15 7.4107982065493 13.49382309609 22.23239461965
Two Pair 10 12.8859149191077 7.76041131947 25.77182983822
High Pair 5 21.2456549993828 4.70684476440 21.24565499938
----------------------------------------------------------------
                         45.1814953813371 2.21329549091 100.17459062103

            Recommended Strategy
              High cards: AKQJ
------------------------------------------------------------
Rank Return Cards to keep
------------------------------------------------------------
    1 1038.0000 Royal Flush
    2 50.0000 Straight Flush
    3 25.0000 4/Kind
    4 23.7680 4/royal
    5 9.0000 Full House
    6 6.0000 Flush
    7 4.3025 trips
    8 4.0000 Straight
    9 3.5551 4/str-flush (0 holes)
   10 2.5957 two pair
   11 2.3825 4/str-flush (1 hole)
   12 1.7155 suited KQJ
   13 1.7119 suited QJT
   14 1.6221 suited AQJ/AKJ/AKQ
   15 1.6185 suited KJT/KQT
   16 1.5365 pair (AKQJ)
   17 1.5334 suited AJT/AQT/AKT
   18 1.2170 4/flush
   19 0.8723 unsuited KQJT
   20 0.8237 pair (T98765432)
   21 0.8085 unsuited QJT9
   22 0.7447 unsuited JT98
   23 0.7313 3/str-flush (1 hole, 2 high)
   24 0.7266 3/str-flush (0 holes, 1 high)
   25 0.6809 4/straight (0 holes, 0 high)
   26 0.6366 3/str-flush (2 holes, 2 high)
   27 0.6312 3/str-flush (1 hole, 1 high)
   28 0.6255 3/str-flush (0 holes, 0 high)
   29 0.6224 suited QJ
   30 0.6064 suited KJ/KQ
   31 0.5957 unsuited AKQJ
   32 0.5902 suited AJ/AQ/AK
   33 0.5362 3/str-flush (2 holes, 1 high)
   34 0.5319 4/straight (1 hole, 3 high)
   35 0.5304 3/str-flush (1 hole, 0 high)
   36 0.5153 unsuited KQJ
   37 0.5117 suited JT
   38 0.5024 unsuited QJ
   39 0.4976 suited QT
   40 0.4893 unsuited KJ/KQ
   41 0.4838 suited KT
   42 0.4813 Jack
   43 0.4774 Queen
   44 0.4771 unsuited AJ/AQ/AK
   45 0.4752 suited AT
   46 0.4731 King
   47 0.4715 Ace
   48 0.4349 3/str-flush (2 holes, 0 high)
   49 0.3603 (draw 5 cards)
------------------------------------------------------------

[John9]

Great stuff, Steve! That's "thinking outside the box", or maybe it's just thinking things through a bit more to show that there are different ways of looking at a game's return.
   
  Here's another example: let's say you're playing 9/6 JOB where the cashback and promotions come to .55%, making the total return 100.09%. What if you thought of the extra return as being part of the royal payout, rather than paid per hand? This in essence makes the game the same as a progressive paying about 5050 coins for the royal. The strategy then changes from the normally espoused "perfect" EV-based strategy to a completely different one, close to what Steve listed. Imagine these holds: most 3-card royals over a high pair; KT-suited over AK-unsuited, TA-suited over the A alone....
   
  John

···

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

[Michael_Boutot]

That is not a logical notion at all. Changing the holds based on cash
back & other items that do not actually add to the royal? Does not
change the likelihood of any hands coming about. Folks have to stop
recreating the wheel as thier vehicles don't roll right. Better off
listening to RS than this current line of "thought" & that's scary.
The whole subject line was unfortunate & harkens again to a attempt
to avoid doing the work.

Great stuff, Steve! That's "thinking outside the box", or maybe

it's just thinking things through a bit more to show that there are
different ways of looking at a game's return.

   
  Here's another example: let's say you're playing 9/6 JOB where

the cashback and promotions come to .55%, making the total return
100.09%. What if you thought of the extra return as being part of the
royal payout, rather than paid per hand? This in essence makes the
game the same as a progressive paying about 5050 coins for the royal.
The strategy then changes from the normally espoused "perfect" EV-
based strategy to a completely different one, close to what Steve
listed. Imagine these holds: most 3-card royals over a high pair; KT-
suited over AK-unsuited, TA-suited over the A alone....

···

--- In vpFREE@yahoogroups.com, John <john_oc_ca@y...> wrote:

   
  John

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

[Steve_Jacobs]

I think that would only make sense if the bonuses were actually tied to
the royal payoff. The "virtual payoffs" concept doesn't mean that you
can treat payoffs in a completely arbitrary manner. The virtual payoffs
are a result of a specific mathematical analysis that is designed for
a specific outcome.

In particular, cashback that is based on coin-out should probably be
treated as an increase in each of the payoffs.

···

On Saturday 26 November 2005 02:44 pm, John wrote:

Great stuff, Steve! That's "thinking outside the box", or maybe it's just
thinking things through a bit more to show that there are different ways of
looking at a game's return.

  Here's another example: let's say you're playing 9/6 JOB where the
cashback and promotions come to .55%, making the total return 100.09%. What
if you thought of the extra return as being part of the royal payout,
rather than paid per hand?

[John9]

Tell me what the difference is in net return between a game that returns 100.09% with no cashback and another that returns 99.54% plus .55% cashback on coin-in? I say there isn't any. They will have different strategies and variances, but the end result is that both return 100.09% of coin-in.
   
  Since in this case the cashback is based on coin-in, you'd have to calculate the number of times each paying hand occurs between royal flushes and divide the cashback up accordingly, resulting in fractional payouts. As a simpler route, I suggest simply adding the casback to the royal payout in whole units. Slightly different, but the same end result in terms of dollar return... isn't it?
   
  For coin-out cashback systems like Coast and Casino Royale, I'm glad that you agree that the cashback should be factored into the paytables. I suggest that it's no different for coin-in based systems. If someone actually wants the cashback during play rather than to re-invest it in the game, then that's a different animal, analogous to an investment that pays a little each period along with a lump sum at the end (i.e. the royal), versus only the lump sum payment at the end.
   
  John

  > Here's another example: let's say you're playing 9/6 JOB where the

cashback and promotions come to .55%, making the total return 100.09%. What
if you thought of the extra return as being part of the royal payout,
rather than paid per hand?

I think that would only make sense if the bonuses were actually tied to
the royal payoff. The "virtual payoffs" concept doesn't mean that you
can treat payoffs in a completely arbitrary manner. The virtual payoffs
are a result of a specific mathematical analysis that is designed for
a specific outcome.

In particular, cashback that is based on coin-out should probably be
treated as an increase in each of the payoffs.

···

Steve Jacobs <jacobs@xmission.com> wrote:

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

[John9]

So Michael, in FPDW you would only hold 5-of-a-kinds of Ten or higher with 3 deuces? Many have argued that the time to do a hand-pay should be factored into the strategy; this is exactly the kind of thing we're talking about here. If you want to play by the "book", you're welcome to, but most have acknowledged that other factors indeed *do* come into play when talking about a strategy.
   
  I believe tips, cashback, hand pays, and many other things should be factored in; Steve is saying that max-EV is not the only factor by which one can create a strategy, but min-risk, min-time-to-royal, etc etc.

  That is not a logical notion at all. Changing the holds based on cash
back & other items that do not actually add to the royal? Does not
change the likelihood of any hands coming about. Folks have to stop
recreating the wheel as thier vehicles don't roll right. Better off
listening to RS than this current line of "thought" & that's scary.
The whole subject line was unfortunate & harkens again to a attempt
to avoid doing the work.

Great stuff, Steve! That's "thinking outside the box", or maybe

it's just thinking things through a bit more to show that there are
different ways of looking at a game's return.

   
  Here's another example: let's say you're playing 9/6 JOB where

the cashback and promotions come to .55%, making the total return
100.09%. What if you thought of the extra return as being part of the
royal payout, rather than paid per hand? This in essence makes the
game the same as a progressive paying about 5050 coins for the royal.
The strategy then changes from the normally espoused "perfect" EV-
based strategy to a completely different one, close to what Steve
listed. Imagine these holds: most 3-card royals over a high pair; KT-
suited over AK-unsuited, TA-suited over the A alone....

   
  John

---------------------------------
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Michael Boutot <vegas_iwish@yahoo.com> wrote:
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[Tom_Robertson1]

John wrote:

Tell me what the difference is in net return between a game that returns 100.09% with no cashback and another that returns 99.54% plus .55% cashback on coin-in? I say there isn't any. They will have different strategies and variances, but the end result is that both return 100.09% of coin-in.
  
Since in this case the cashback is based on coin-in, you'd have to calculate the number of times each paying hand occurs between royal flushes and divide the cashback up accordingly, resulting in fractional payouts. As a simpler route, I suggest simply adding the casback to the royal payout in whole units. Slightly different, but the same end result in terms of dollar return... isn't it?

It's simpler and more straightforward to treat cash back that's based
on coin in as a reduction of coin in rather than allocating it to each
payout. The net return is identical, but the variance will be lower,
which theoretically can alter optimal strategy. How many times each
hand occurs per royal is irrelevant to the effect that cash back
that's based on coin in has. The loss when a hand results in no pay
is less when cash back is based on coin in than when it is based on
coin out. To do it your way consistently, you'd have to also allocate
cash back to non-paying hands, which ends up treating cash back as a
reduction in coin in.

[John9]

So instead of 5 units coin-in, it would be something like 4.9725? Either that or make all paying and non-paying hands return an extra .0275?

Tom Robertson <thomasrrobertson@earthlink.net> wrote: It's simpler and more straightforward to treat cash back that's based on coin in as a reduction of coin in rather than allocating it to each payout. The net return is identical, but the variance will be lower, which theoretically can alter optimal strategy. How many times each hand occurs per royal is irrelevant to the effect that cash back that's based on coin in has. The loss when a hand results in no pay is less when cash back is based on coin in than when it is based on coin out. To do it your way consistently, you'd have to also allocate
cash back to non-paying hands, which ends up treating cash back as a reduction in coin in.

···

---------------------------------
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[Michael_Boutot]

New is not necessarily better. This board has many people posting who
refuse to learn from history; people unbelievably "proud" to waste
time seeing if 1+1 may equal 3 "for themselves"( RS info for example)
instead of being aware nothing is new under the sun. This discussion
is about an unwillingness to work at details with any excuse not to
do so sounding great. The constant carping against calling
something "perfect play" because one does not feel like learning it
is pointless & unfortunate. You can learn from beyond mere personal
experience or you can never grow. BTW: unless you are playing $2
deuces 4 of them is not a hand pay & there ain't no $2 FPDW. Do the
math!!!!!It does work.

So Michael, in FPDW you would only hold 5-of-a-kinds of Ten or

higher with 3 deuces? Many have argued that the time to do a hand-pay
should be factored into the strategy; this is exactly the kind of
thing we're talking about here. If you want to play by the "book",
you're welcome to, but most have acknowledged that other factors
indeed *do* come into play when talking about a strategy.

   
  I believe tips, cashback, hand pays, and many other things should

be factored in; Steve is saying that max-EV is not the only factor by
which one can create a strategy, but min-risk, min-time-to-royal, etc
etc.

Michael Boutot <vegas_iwish@y...> wrote:
  That is not a logical notion at all. Changing the holds based on

cash

back & other items that do not actually add to the royal? Does not
change the likelihood of any hands coming about. Folks have to stop
recreating the wheel as thier vehicles don't roll right. Better off
listening to RS than this current line of "thought" & that's scary.
The whole subject line was unfortunate & harkens again to a attempt
to avoid doing the work.
>
> Great stuff, Steve! That's "thinking outside the box", or maybe
it's just thinking things through a bit more to show that there are
different ways of looking at a game's return.
>
> Here's another example: let's say you're playing 9/6 JOB where
the cashback and promotions come to .55%, making the total return
100.09%. What if you thought of the extra return as being part of

the

royal payout, rather than paid per hand? This in essence makes the
game the same as a progressive paying about 5050 coins for the

royal.

The strategy then changes from the normally espoused "perfect" EV-
based strategy to a completely different one, close to what Steve
listed. Imagine these holds: most 3-card royals over a high pair;

KT-

suited over AK-unsuited, TA-suited over the A alone....
>
> John
>
>
>
> ---------------------------------
> Yahoo! Music Unlimited - Access over 1 million songs. Try it

free.

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

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Service.

···

--- In vpFREE@yahoogroups.com, John <john_oc_ca@y...> wrote:

--- In vpFREE@yahoogroups.com, John <john_oc_ca@y...> wrote:

---------------------------------
  
---------------------------------
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[Steve_Jacobs]

I'm baffled as to why you think this thread has anything at all to do
with RS. You seem openly hostile toward any idea that strays in
any way from the "EV is everything" philosophy. Perhaps you
misunderstand what I'm saying. I'm not opposed to players using
max-EV strategy, if that is what they they decide is best for them.
However, the idea that maximizing EV is the _only_ meaningful
objective is a flawed concept. It is certainly _one_ reasonable and
mathematically sound measure of performance, but it isn't the only
one.

All of my alternate strategies are based entirely on mathematics, and
each one is optimal in its own (mathematically precise) way. Trying
to cast this as claims that "1 + 1 = 3" simply won't fly.

My claims are absolutely NOT about "unwillingness to work at details,"
in fact quite the opposite. I'm working out details, in terms of precisely
optimal strategies, that in some cases have probably never been
worked out before. For example, my strategy for maximizing the
probability of hitting royals before going broke is something that I don't
believe has been published outside of this forum.

···

On Sunday 27 November 2005 08:25 pm, Michael Boutot wrote:

New is not necessarily better. This board has many people posting who
refuse to learn from history; people unbelievably "proud" to waste
time seeing if 1+1 may equal 3 "for themselves"( RS info for example)
instead of being aware nothing is new under the sun. This discussion
is about an unwillingness to work at details with any excuse not to
do so sounding great. The constant carping against calling
something "perfect play" because one does not feel like learning it
is pointless & unfortunate. You can learn from beyond mere personal
experience or you can never grow. BTW: unless you are playing $2
deuces 4 of them is not a hand pay & there ain't no $2 FPDW. Do the
math!!!!!It does work.