vpFREE2 Forums

Rob Singer

#1

Greetings from Las Vegas, Home of the Monthly vpFREE Lunches:

Rob Singer has decided to discontinue posting on vpFREE and has
unsubscribed as a member. I've revised the vpFREE Rob Singer Policy,
which is now located in the FAQ, as follows:

···

***************
       
53. Who is Rob Singer? - Rob Singer says that "Rob Singer is a
professional gambler from Scottsdale, Arizona, and top expert in
winning at video poker". He also is the author of "The Undeniable
Truth About Video Poker" and writes a weekly video poker column for
GAMING TODAY.

Traditional Video Poker Experts, who have examined Rob Singer's methods
and strategies, contend that they are mathematically unsound, and they
question the accuracy of his reported results. Discussion of his
system(s) on the old vp_heaven internet forum was very disruptive and
led to the demise of that group.

Discussion of the Singer system(s) on vpFREE is discouraged, but is
appropriate on FREEvpFREE
<http://www.smartgroups.com/groups/freevpfree> or on his VPTRUTH web
site <http://www.vptruth.com/index2.cfm>.

             ***************
       
Every member who unsubscribes from vpFREE is asked why they
unsubscribed in an automated exit survey. Here are Rob Singer's
comments, which I'm posting at his request:

From: "Rob Singer" <rsinger1111@Cox.net>
To: "vpFREE Moderator" <vpFREE-owner@yahoogroups.com>
Subject: Re: File - UnSub
Date sent: Thu, 16 Oct 2003 23:32:15 -0700

I live in a world of truth and common sense -- something seriously
lacking in most gambling circles. By that definition, I am not
comfortable being moderated by a single person with views vastly
different than mine. In fact, I see no sense in moderation as long as
the posting is not an attack. But again, I'm being moderated by someone
who not only cannot understand the rationale behind my short-term style
of Play Strategies, but cannot accept or believe I win more often and
more money than any other known player by using my methods. Thus, I'm
at the moderator's personal mercy - something I'm clearly not used to
and do not believe in.

Although I support the concept behind vpfree, the majority of the posts
are sadly inept, terribly monotonous, and are laced with the
commercialization of products that, as I've said millions of times, are
mainly available to sustain the compulsive gambling of the famous names
who do really struggle with the game - as well as with their incessant
habit. And it may be interesting to a few to discuss where the best
penny or nickel games are, how many points are needed to get a 2-for-1
buffet at road-kill buffets like Az. Charlies or Fiesta Rancho, and the
endless mathematical postings of those who lives are controlled by
blinders; but I've seen enough rambling to last 'throughout infinity'.
I have over 100 messages a week to reply to, and there's over 3400
members who subscribe to my free newsletter that I send out weekly or
so in the form of short bursts of information - and many belong to vpfree.
In my opinion, vpfree should open up a bit - or stagnate in time. It's a
plethora of vp information, but is anything but 'free'. There are no fees,
but people pay with the forum's extreme position against free speech. And
in the end, they'll still come to me for the truth about the game.

#2

Well, Tom, you were far more lenient than I could ever imagine a sane
person to be, and bent over backwords to give the guy a safe place to
post his complete dreck. If your "moderation" was too much for him,
it should give him a clue that he can't accept even a modicum of peer
review.

By the way, I have waited to post this, but I have it on athority
that Rob Singer has "claimed" not to even believe what he himself
says. That is, he has claimed in the past that people should "not
assume that he (the person) believes what Rob Singer (the pen name)
says."

If that is true, it means that Rob Singer actually knows better, but
has properly surmised that the only way to be a "famous name" in the
field of VP these days is to say something that hasn't been said
before. And since, for the most part, VP has only one correct
answer, the only way to be a new name is to say things that
contradict with what is actually true.

If it is true, I have more respect for his intelligence, but far less
respect for his character.

Rob Singer has decided to discontinue posting on vpFREE and has
unsubscribed as a member. >
Every member who unsubscribes from vpFREE is asked why they
unsubscribed in an automated exit survey. Here are Rob Singer's
comments, which I'm posting at his request:

From: "Rob Singer" <rsinger1111@C...>
To: "vpFREE Moderator" <vpFREE-

owner@yahoogroups.com>

Subject: Re: File - UnSub
Date sent: Thu, 16 Oct 2003 23:32:15 -0700

I live in a world of truth and common sense -- something seriously
lacking in most gambling circles. By that definition, I am not
comfortable being moderated by a single person with views vastly
different than mine. In fact, I see no sense in moderation as long

as

the posting is not an attack. But again, I'm being moderated by

someone

who not only cannot understand the rationale behind my short-term

style

of Play Strategies, but cannot accept or believe I win more often

and

more money than any other known player by using my methods. Thus,

I'm

at the moderator's personal mercy - something I'm clearly not used

to

and do not believe in.

Although I support the concept behind vpfree, the majority of the

posts

are sadly inept, terribly monotonous, and are laced with the
commercialization of products that, as I've said millions of times,

are

mainly available to sustain the compulsive gambling of the famous

names

who do really struggle with the game - as well as with their

incessant

habit. And it may be interesting to a few to discuss where the best
penny or nickel games are, how many points are needed to get a 2-

for-1

buffet at road-kill buffets like Az. Charlies or Fiesta Rancho, and

the

endless mathematical postings of those who lives are controlled by
blinders; but I've seen enough rambling to last 'throughout

infinity'.

I have over 100 messages a week to reply to, and there's over 3400
members who subscribe to my free newsletter that I send out weekly

or

so in the form of short bursts of information - and many belong to

vpfree.

In my opinion, vpfree should open up a bit - or stagnate in time.

It's a

plethora of vp information, but is anything but 'free'. There are

no fees,

but people pay with the forum's extreme position against free

speech. And

···

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

in the end, they'll still come to me for the truth about the game.

#3

Since joining this group, I have tried to glean sense from everything
that is written and incorporate bits and pieces into my own VP play.
I haven't learned anything for many months...

There is much that Rob writes (in his book and his columns) that
makes practical sense, for instance:
  * Don't get caught up in the comp game
  * Move UP in Coin-level when you are losing, (to re-coup losses)
  * stay at LOW Coin-level when you are ahead (to stay ahead)
  * Set profit goals
  * Have a plan before entering casino
  * Do not deviate from Plan (recognize hypnotic gambling fever
environment)

Unfortunately, this great money management is mixed in with Rob's
sometimes vicious attacks on most of the other VP authors
("experts?"). Part of Rob's agenda is to undo what he sees as endemic
damage done by many authors of the game. This is where the friction
occurs and most folks lose interest, as we don't come here for ad
nauseum confrontation and flame war arguments.

Free thinking people, like I like to think of myself, can take the
best of both worlds: the more higher the EV of the Play and the
Higher the Pay Table return, the more likely I'll make that play and
the more likely I'll play that machine. That's the cold math, no
reward to the messenger. No one will know but me, and I certainly
am not going to argue with YOU about how to spend my or your money!

It seems to me that each VP hand has 4 phases:
luck on the deal,
skill on the hold (math),
pure luck again on the draw,
and one more step of skill: the decision to play again or cash out.

The math skill on the hold phase is something that is relatively
easily learned with strategy charts and practice. This discussion
about if it is ever "proper" to deviate from perfect strategy is
LUDICROUS. It is 100% personal choice and I don't understand why any
of us WASTE TIME ARGUING about it!! The numbers, the Odds, say HOLD
THIS. I am going to HOLD whatever the hell I want and why should I
try to influence anyone else's decision??

The other Skilled phase is when to cash out: Rob says when you hit
your session profit goal, quit. Most everyone else here on vpfree
says: Play machines that return over 100% and play as long as you can
stay alert! Again, Figure it out for yourself!! Truth is, most are
so addicted to VP, that they quit when they run out of money.
This is where Rob has tried to argue for his position in this group
and is effectively pounding his head against the wall. It's the
Theory vs. the Practical Application. May as well argue about non-
Euclidian geometry or the existence of the afterlife. The argument
will never end, and the writers get to practice their debating and
writing skills. Blah Blah Blah. Like watching worms mate.

So many people like to be TOLD what to do and to get PERMISSION
from "Experts", those are the people that benefit from this group:
Bosses and Sheep.

Oh yeah: for those caught up in the Comps, this forum is another
great place to swap current events.

And to Rob- (who isn't reading this:) your high % of profittable
sessions/trips proves you know when to quit. It also proves that you
enjoy a large enough bankroll that you can "double-up" your coin
level when you lose, until a given jackpot recoups your losses. Wish
we all had that bankroll, and wish we could all get in and get out
like you.

It will likely get a little slow here without Rob to kick around.
Maybe we'll escalate the debate on petty things to make up for it.
Watch out! homogeneity often results in boredom.

  my 2 cents:
  ~~ MARK P.

"not selling anything either"

--- "vp_FREE" wrote:

Rob Singer has decided to discontinue posting on vpFREE and has
unsubscribed as a member.

  <snip>

#4

I disagree. There are many different strategies for VP that are
mathematically optimal in different ways. Max-EV is not the only
correct way to play, and is only optimal for those who are totally
indifferent to risk.

···

On Monday 20 October 2003 10:07 am, tooncesthecatwhocoulddriveacar wrote:

And since, for the most part, VP has only one correct
answer, the only way to be a new name is to say things that
contradict with what is actually true.

#5

tooncesthecatwhocoulddriveacar wrote:

And since, for the most part, VP has only one correct answer, the
only way to be a new name is to say things that contradict with
what is actually true.

On 20 Oct 2003 at 20:16, Steve Jacobs replied:

I disagree.

I would have been disappointed if you hadn't.

There are many different strategies for VP that are mathematically
optimal in different ways.

No argument from me. However, these other strategies have limited
applicability to adequately bankrolled advantage video poker players.

Max-EV is not the only correct way to play,

I agree again.

and is only optimal for those who are totally indifferent to risk.

Well, yes.

Another, and less mis-leading way, to have said that would have been
"and is only optimal for video poker players who have an adequate bankroll
for the game and denomination they are playing".

In the real video poker world, max-EV is the benchmark standard for
the play of a video poker hand by advantage players who are adequately
bankrolled for the game and denomination they are playing, and who want
to maximize profits.

Video poker situations can be concocted where strategies other than
max-EV are preferable, but these are few and far between for adequately
bankrolled, advantage video poker players. To my knowledge, these alternate
strategies are mainly applicable to under-bankrolled video poker players
whose primary goal is survival.

vpFREE Administrator

#6

Since joining this group, I have tried to glean sense from

everything

that is written and incorporate bits and pieces into my own VP

play.

I haven't learned anything for many months...

I'm confident of that.

#7

Since joining this group, I have tried to glean sense from everything
that is written and incorporate bits and pieces into my own VP play. > I haven't learned anything for many months...

Me neither. I guess that you're like me and already know everything
there is to know? <G>

The other Skilled phase is when to cash out: Rob says when you hit
your session profit goal, quit. Most everyone else here on vpfree
says: Play machines that return over 100% and play as long as you can
stay alert! Again, Figure it out for yourself!!

Rob's recent position on quitting isn't that much different than what
you say most people on vpfree say. Rob recently said on FREEvpFREE
that there isn't any elapsed time requirement between sessions for
using his system.

Truth is, most are so addicted to VP, that they quit when they run
out of money.

Are you still referring to "Most everyone else here on vpfree"?
In any event, how did you arrive at this "truth"?

This is where Rob has tried to argue for his position in this group
and is effectively pounding his head against the wall.

Rob has never been allowed to argue his positions "in this group".

And to Rob- (who isn't reading this:)

If there was some way of proving this, I'd make a bet that
you're wrong.

It will likely get a little slow here without Rob to kick around.

I haven't noticed much kicking around of Rob on vpFREE ever,
especially during his posting tenure.

vpFREE Administrator

···

On 20 Oct 2003 at 19:53, Mark wrote:

#8

Hey Tom:
  Rob made it sound like he got censored here a lot, only you and he know
how much. The free-for-all that is possible on FREEvpFREE hasn't really
happened. Maybe the debate grew old with no new INFO being put forth.

Thanks for "keeping me honest" with your comments- I tried to ANSWER
them below. So! I took a few wild swings and missed!
  ~MARK

---"vp_FREE" wrote in questions:
> Since joining this group, I have tried to glean sense from everything
> that is written and incorporate bits and pieces into my own VP play.
> I haven't learned anything for many months...

Me neither. I guess that you're like me and already know everything
there is to know? <G>

     I hope the impression was more like we've been lacking in content for a
while- Sorry: this is a hackneyed complaint/cheap shot that I should do my
part to fix. ~MARK

> The other Skilled phase is when to cash out: Rob says when you hit
> your session profit goal, quit. Most everyone else here on vpfree
> says: Play machines that return over 100% and play as long as you can
> stay alert! Again, Figure it out for yourself!!

Rob's recent position on quitting isn't that much different than what
you say most people on vpfree say. Rob recently said on FREEvpFREE
that there isn't any elapsed time requirement between sessions for
using his system.

      TRUE! good point!
Everyone's own measure of success and happiness is quite a personal thing,
no one need share that info, (excepting certain amounts to the IRS! ) ~MARK

> Truth is, most are so addicted to VP, that they quit when they run
> out of money.

Are you still referring to "Most everyone else here on vpfree"?
In any event, how did you arrive at this "truth"?

     It's another Cheap Shot, sorry! VP players in general. The addiction
comment wasn't necessary, but it is hard to keep playing once you run out of
money, so maybe I got that part correct. ~MARK

> This is where Rob has tried to argue for his position in this group
> and is effectively pounding his head against the wall.

Rob has never been allowed to argue his positions "in this group".

      TRUE again (but he tries I'll bet!) ~MARK

> And to Rob- (who isn't reading this:)

If there was some way of proving this, I'd make a bet that
you're wrong.

     Gotcha here: I was being 100% facetious. ~MARK

> It will likely get a little slow here without Rob to kick around.

I haven't noticed much kicking around of Rob on vpFREE ever,
especially during his posting tenure.

     Oh, there have been a few blistering posts, maybe not so much lately with
the shift to FREEvpFREE of the posts on this subject. ~MARK

···

> On 20 Oct 2003 at 19:53, Mark originally wrote:

vpFREE Admin

#9

Another, and less mis-leading way, to have said that would have

been

"and is only optimal for video poker players who have an adequate

bankroll

for the game and denomination they are playing".

In the real video poker world, max-EV is the benchmark standard

for

the play of a video poker hand by advantage players who are

adequately

bankrolled for the game and denomination they are playing, and who

want

to maximize profits.

Video poker situations can be concocted where strategies other

than

max-EV are preferable, but these are few and far between for

adequately

bankrolled, advantage video poker players. To my knowledge, these

alternate

strategies are mainly applicable to under-bankrolled video poker

players

whose primary goal is survival.

vpFREE Administrator

Very well said, Tom.
Linda in Biloxi

#10

tooncesthecatwhocoulddriveacar wrote:

>and is only optimal for those who are totally indifferent to risk.

Well, yes.

Another, and less mis-leading way, to have said that would have been
"and is only optimal for video poker players who have an adequate bankroll
for the game and denomination they are playing".

I disagree (but you would have been disappointed if I didn't). First, there
is nothing misleading about my statement. Max-EV is only optimal for
those who don't care about risk. This is true for blackjack, VP, and any
other game, and that statement is mathematically precise.

Second, having an "adequate bankroll" does not magically make
max-EV optimal for players who are risk averse, nor does wishful
thinking. This too is true for blackjack, VP, or any other game.
Optimal betting and optimal play are both impacted by risk, and for
any mathematically specific objective which balances risk and EV,
the optimal strategy is very likely to require *some* departures from
the max-EV strategy. It is misleading to suggest otherwise.

This does NOT mean that a risk averse strategy will necessarily
be vastly different than a max-EV strategy, but it is important to
understand that "optimal" isn't a vague concept, it has a specific
meaning that can be verified mathematically.

In the real video poker world, max-EV is the benchmark standard for
the play of a video poker hand by advantage players who are adequately
bankrolled for the game and denomination they are playing, and who want
to maximize profits.

For many non-VP games, the difference between max-EV strategy and
alternate strategies is almost immeasureable. However, the high variance
of VP makes the playing strategy more sensitive to risk. This implies that
max-EV and min-risk strategies for the same VP game will rarely be identical,
and can differ in ways that significantly impact the player's results. IMO,
implying that "real world" VP players should ignore this is to suggest that
they bury their heads in the sand.

Video poker situations can be concocted where strategies other than
max-EV are preferable, but these are few and far between for adequately
bankrolled, advantage video poker players.

Nonsense. For players who care about risk, the mathematically optimal
strategy will *rarely* be identical to max-EV strategy. The only time the
min-risk and max-EV strategies will be identical is when the game is
very close to breakeven. You may call that "few and far between" if
you wish, but "most of the time" would be less misleading.

To my knowledge, these alternate
strategies are mainly applicable to under-bankrolled video poker players
whose primary goal is survival.

They are applicable to any players who care about risk. Those who
are completely risk neutral can certainly be content with max-EV.

···

On Monday 20 October 2003 10:15 pm, vp_FREE wrote:

#11

I'd like to amend my judgement of "misleading" to "very misleading",
but I won't because it might not be mathematically precise. <G>

Steve, I don't have any problem with your facts in this post or in all
the many others I've read over the years. I do however think you could
have identified "adequately bankrolled, advantage players who aren't risk averse" in some better way than "those who are totally indifferent to risk".

I have corrected the "adverse" for "averse" typo that was in the Dogma
revision.

vpFREE Administrator

···

On 21 Oct 2003 at 21:08, Steve Jacobs wrote:

> >and is only optimal for those who are totally indifferent to risk.

I disagree (but you would have been disappointed if I didn't). First,
there is nothing misleading about my statement.

#12

Please tell me the difference between "not risk averse" and "totally
indifferent to risk". Also explain what "adequately bankrolled" means
for a player who is not risk averse. The very concept of an "adequate
bankroll" is rooted in concerns about risk. A player who is not risk
averse and whose bankroll has been reduced to a single wager is
still adequately bankrolled.

I'm still at a loss as to what you find misleading about my post. I'm not
posting anything here that I consider to be an opinion, but only
conclusions that I've reached based on mathematical considerations.
So, if you don't have any problem with my facts, yet find my posts
misleading, then we must be using different definitions of the word
"fact."

Or is this one of those "don't confuse me with facts" things? :wink:

···

On Tuesday 21 October 2003 09:29 pm, vp_FREE wrote:

On 21 Oct 2003 at 21:08, Steve Jacobs wrote:
> > >and is only optimal for those who are totally indifferent to risk.
>
> I disagree (but you would have been disappointed if I didn't). First,
> there is nothing misleading about my statement.

I'd like to amend my judgement of "misleading" to "very misleading",
but I won't because it might not be mathematically precise. <G>

Steve, I don't have any problem with your facts in this post or in all
the many others I've read over the years. I do however think you could
have identified "adequately bankrolled, advantage players who aren't risk
averse" in some better way than "those who are totally indifferent to
risk".

#13

Steve, please excuse me, as I have never seen arguments for a min-
risk strategy for VP written about seriously, except in the context
of "beginners who are trying to make their money last as long as
possible."

First of all, I am most aware of risk-averse strategies applying to
BJ. As far as I could tell, the point of playing a risk-averse
playing strategy is so that you can afford to make higher wagers with
the same size bankroll, paradoxically increasing your overall EV.
The point being, is that the goal of the risk-averse strategy is to
maximize EV for the same bankroll, without increasing risk.

For the analogous situation to occur in VP, you need to be able to
lower risk so much so that you can now justify an increase in
denomination. But, if you increase denomination, you often have to
give up even more return, since the higher the denomination, the less
lucrative the game. Thus, the opportunities to use a risk-averse
strategy to ultimatelty increase EV without increasing risk are far
less.

If this is true, the main point of a risk-averse VP strategy is to
decrease Risk of Ruin. But if you have a sufficient bankroll, the
argument to decrease EV for even less RoR doesn't seem compelling,
even if the player is risk-averse by nature. I don't think that
means that they are indifferent to risk, but that at a certain point,
decreasing risk even further doesn't add to overall utility. Of
course the catch is that players with an insufficient bankroll that
would need to lower RoR tend to be "risk-seekers" by nature. That
is, they look for excuses to go for a jackpot hand, if it doesn't
cost too much extra in EV. Thus, this would argue that there
wouldn't be much interest in risk-averse VP strategies.

But, perhaps, this is an area of VP that I just wasn't aware of.

Scott

> tooncesthecatwhocoulddriveacar wrote:
>
> >and is only optimal for those who are totally indifferent to

risk.

>
> Well, yes.
>
> Another, and less mis-leading way, to have said that would have

been

> "and is only optimal for video poker players who have an adequate

bankroll

> for the game and denomination they are playing".

I disagree (but you would have been disappointed if I didn't).

First, there

is nothing misleading about my statement. Max-EV is only optimal

for

those who don't care about risk. This is true for blackjack, VP,

and any

other game, and that statement is mathematically precise.

Second, having an "adequate bankroll" does not magically make
max-EV optimal for players who are risk averse, nor does wishful
thinking. This too is true for blackjack, VP, or any other game.
Optimal betting and optimal play are both impacted by risk, and for
any mathematically specific objective which balances risk and EV,
the optimal strategy is very likely to require *some* departures

from

the max-EV strategy. It is misleading to suggest otherwise.

This does NOT mean that a risk averse strategy will necessarily
be vastly different than a max-EV strategy, but it is important to
understand that "optimal" isn't a vague concept, it has a specific
meaning that can be verified mathematically.

> In the real video poker world, max-EV is the benchmark standard

for

> the play of a video poker hand by advantage players who are

adequately

> bankrolled for the game and denomination they are playing, and

who want

> to maximize profits.

For many non-VP games, the difference between max-EV strategy and
alternate strategies is almost immeasureable. However, the high

variance

of VP makes the playing strategy more sensitive to risk. This

implies that

max-EV and min-risk strategies for the same VP game will rarely be

identical,

and can differ in ways that significantly impact the player's

results. IMO,

implying that "real world" VP players should ignore this is to

suggest that

they bury their heads in the sand.

> Video poker situations can be concocted where strategies other

than

> max-EV are preferable, but these are few and far between for

adequately

> bankrolled, advantage video poker players.

Nonsense. For players who care about risk, the mathematically

optimal

strategy will *rarely* be identical to max-EV strategy. The only

time the

min-risk and max-EV strategies will be identical is when the game is
very close to breakeven. You may call that "few and far between" if
you wish, but "most of the time" would be less misleading.

> To my knowledge, these alternate
> strategies are mainly applicable to under-bankrolled video poker

players

···

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

On Monday 20 October 2003 10:15 pm, vp_FREE wrote:
> whose primary goal is survival.

They are applicable to any players who care about risk. Those who
are completely risk neutral can certainly be content with max-EV.

#14

and is only optimal for those who are totally indifferent to risk

Please tell me the difference between "not risk averse" and "totally
indifferent to risk".

Well the first difference is that I used "not risk averse" in context,
as a modifier for advantage players, while you used your phrase in a
vacuum, leaving some question as to who you were referring to.

The second difference is that "risk averse" IMO isn't "totally indifferent
to risk" but allows for the consideration, evaluation and assumption of
risk if deemed desireable.

Also explain what "adequately bankrolled"
means for a player who is not risk averse. The very concept of an
"adequate bankroll" is rooted in concerns about risk. A player who
is not risk averse and whose bankroll has been reduced to a single
wager is still adequately bankrolled.

I'll pass on this for now since I think this is mostly semantics. I'll
revisit it later if you wish.

I'm still at a loss as to what you find misleading about my post.
I'm not posting anything here that I consider to be an opinion, but
only conclusions that I've reached based on mathematical
considerations. So, if you don't have any problem with my facts, yet
find my posts misleading, then we must be using different definitions
of the word "fact."

I don't have any problem with your "facts". I do have a problem with
your "totally indifferent to risk" phrasing, because it is misleading.

My first thought when I read "and is only optimal for those who are
totally indifferent to risk" was that you were referring to some group
of foolhardy, financially irresponsible people, and it took a while
before I realized you had to be talking about me and advantage video
poker players.

BUT, "totally indifferent to risk" doesn't apply to me nor to any
advantage video poker players that I know. We aren't indifferent to risk.
We carefully consider and analyze risk, and then decide if we want to
deal with that risk, or not. If we decide to handle the risk, and if we
are adequately bankrolled, then we can properly use max-EV strategy rather
than some more conservative strategy, and we can be unconcerned with the
risk - but never indifferent.

You may have intended for "totally indifferent to risk" to describe a state
of mind, after the risk has been considered and accepted, but IMO it's a
huge stretch to say that "totally indifferent" allows for such consideration.

SO, IMO your statement was misleading because you said that max-EV is
"only optimal for those who are totally indifferent to risk", since
max-EV is optimal for some advantage video poker players, and they aren't
indifferent to risk.

This hair splitting discussion is probably of limited interest to many,
so any future responses by me on whether or not your statement was
misleading will be done on FREEvpFREE.

vpFREE Administrator

···

On 22 Oct 2003 at 5:49, Steve Jacobs wrote:

#15

First of all, I am most aware of risk-averse strategies applying to
BJ. As far as I could tell, the point of playing a risk-averse
playing strategy is so that you can afford to make higher wagers with
the same size bankroll, paradoxically increasing your overall EV.
The point being, is that the goal of the risk-averse strategy is to
maximize EV for the same bankroll, without increasing risk.

Part of the problem when discussing risk-averse strategies for
BJ is that Kelly play is sometimes incorrectly described as
risk-averse. Kelly play is log-optimal, meaning that it seeks
to maximize the expected logarithm of the players bankroll. This
is equivalent to choosing a bet size and playing strategy which
combine to multiply the current bankroll by the largest possible
factor, on average. It is also equivalent to maximizing the geometric
mean of the players bankroll. This is not the same as maximizing EV,
but maximizes bankroll growth rate assuming the player will always
wager a fixed fraction of bankroll. Many Kelly players simply
use the Kelly Criterion to choose bet size while using a playing
strategy that is based on card counting. This is technically
sub-optimal, in the same way that choosing VP denomination
to limit risk while playing max-EV strategy is not quite optimal.
However, for blackjack the loss from using a suboptimal playing
strategy is truly miniscule, because the low variance makes
"close call" strategy changes less significant.

Min-risk strategies can be applied to short term objectives, such
as growing a bankroll by some fixed factor, or they can be used
for an endless stream of plays, in the same what the max-EV
strategy is often described.

For the analogous situation to occur in VP, you need to be able to
lower risk so much so that you can now justify an increase in
denomination. But, if you increase denomination, you often have to
give up even more return, since the higher the denomination, the less
lucrative the game. Thus, the opportunities to use a risk-averse
strategy to ultimatelty increase EV without increasing risk are far
less.

Let's suppose for a moment that you are a Kelly player who wishes
to adapt Kelly principles to VP. The correct way to do this is to
just forget about EV and use expected log(bankroll) as the criteria
for choosing betting denomination based on your bankroll, and for
making playing decisions. The main effect of choosing a Kelly
objective is to devalue royal flushes by some amount. The specific
amount depends on your bankroll, but it might be in the range of
10% to 20%. Other high payoffs would be devalues as well, but
by a much smaller factor. The optimal betting denomination,
assuming your chosen game is available in many denominations,
will be whichever denomination gives a higher expected value
for log(bankroll) after averaging over all possible outcomes while
using the log-optimal playing strategy. In practice this is more
difficult to compute than a max-EV strategy, because chaning
bet size causes the optimal wager to change and vice-versa.

Now, armed with the truly optimal betting/playing strategy which
is based on your chosen objective, you are in a position to
determine how much you lose (measured relative to your
objective) by reverting to max-EV strategy. If your real
objective includes some amount of risk aversion, then the
optimal playing strategy for that objective will almost invariably
deviate from max-EV, but it is a mistake to think of this in terms
of "lost EV". The EV is not lost at all, but is spent willingly to
purchase a greater quantity of "utility" in terms of your true
objective.

If this is true, the main point of a risk-averse VP strategy is to
decrease Risk of Ruin.

Yes, and the cost in reduced EV is considered to be worth the
benefit of lowered RoR. It matters not whether this improved risk
comes from a change in bet size or a change in strategy. But,
if you are constrained in some way, such as having to choose
between playing quarters or dollars, then those constraints in
betting strategy imply that your main opportunity to reduce risk
will come from altering your playing strategy. Unless you are just
below the threshold where changing denomination will not
alter risk, you won't really have a choice for betting strategy in
VP.

But if you have a sufficient bankroll, the
argument to decrease EV for even less RoR doesn't seem compelling,
even if the player is risk-averse by nature.

The reason it doesn't seem compelling may be that you are used to
thinking that EV is the most important thing. For a player who is truly
risk average, the optimal VP strategy will almost certainly involves
some deviations from max-EV strategy. But worrying about EV is
misguided, what the risk-averse player should be thinking is that
resorting to max-EV strategy is costing "utility" based on their true
objective, and that utility is what really matters, not EV.

An analogy can be drawn between playing VP and driving a car.
Think of EV as gas mileage and risk as time. If you are in a hurry
to get somewhere, you become willing to sacrifice gas mileage in
order to save time. Time becomes more important to you than the
cost of fuel. If you are not in a hurry, then fuel economy becomes
more important than minimizing travel time. The "best" driving
strategy is thus relative to your objective -- save time, or save
money. It is a tradeoff, and neither is inherently better than the
other, it simply depends on present circumstances.

I don't think that
means that they are indifferent to risk, but that at a certain point,
decreasing risk even further doesn't add to overall utility.

A player who wishes to play optimally for his/her chosen objective
will strive to do so. Deviating from the betting/playing strategy that
is optimal for one's true objective can only reduce utility. So, it
follows logically that using a max-EV strategy when your true
objective is something else is sub-optimal, except in the (very
unusual) case where the optimal strategy happens to be identical
to the max-EV strategy. For VP, I believe this would happen only
for players who have no real concern for risk.

Of course the catch is that players with an insufficient bankroll that
would need to lower RoR tend to be "risk-seekers" by nature. That
is, they look for excuses to go for a jackpot hand, if it doesn't
cost too much extra in EV. Thus, this would argue that there
wouldn't be much interest in risk-averse VP strategies.

All of my comments are based on an assumption that the player is
"rational" in a mathematical sense, preferring more money to less
money when the risk is the same, and preferring less risk to more
risk when the EV is the same. Rational players can have different
objectives, but their choices are mathematically more "confined" than
players who sacrifice utility for no apparent reason.

···

On Wednesday 22 October 2003 09:31 am, tooncesthecatwhocoulddriveacar wrote:

#16

After posting this I received an email from a friend who used to
play on a blackjack team. His recollection was that the team
looked into risk-averse play and found that the resulting
strategy adjustments made a significant difference in overall
performance. Thus, my description above may be off base,
especially in regard to the "truly miniscule" part. I apologize
for any confusion this may have caused.

This does not alter my view on the situation for VP.

···

On Wednesday 22 October 2003 08:55 pm, I wrote:

Many Kelly players simply
use the Kelly Criterion to choose bet size while using a playing
strategy that is based on card counting. �This is technically
sub-optimal, in the same way that choosing VP denomination
to limit risk while playing max-EV strategy is not quite optimal.
However, for blackjack the loss from using a suboptimal playing
strategy is truly miniscule, because the low variance makes
"close call" strategy changes less significant.

#17

>> and is only optimal for those who are totally indifferent to risk
>
> Please tell me the difference between "not risk averse" and "totally
> indifferent to risk".

Well the first difference is that I used "not risk averse" in context,
as a modifier for advantage players, while you used your phrase in a
vacuum, leaving some question as to who you were referring to.

The second difference is that "risk averse" IMO isn't "totally indifferent
to risk" but allows for the consideration, evaluation and assumption of
risk if deemed desireable.

The phrase "risk averse" implies more that a mere awareness that risk
exists, it implies a desire to limit or constrain risk in actual practice.

My first thought when I read "and is only optimal for those who are
totally indifferent to risk" was that you were referring to some group
of foolhardy, financially irresponsible people,

No, I would save "foolhardy, financially irresponsible" as a description
of people who are risk-seeking, or who gamble with no particular
objective whatsoever, not caring about risk or EV. Thrill seekers.

and it took a while
before I realized you had to be talking about me and advantage video
poker players.

This falls partly under the "if the shoe fits...." category. I now see
why you characterize my posts as misleading, but the "fix" for this
is not for me to change what I'm saying. Be assured that I'm not
trying to equate max-EV with "foolhardy and financially irresponsible."
However, part of what I'm saying is that the concepts "I care about
risk" and "I use max-EV strategy because it is optimal" are not entirely
compatible, especially for VP players.

Based on our extensive discussion in email, I think you view max-EV
strategy as truly optimal for you and VP players who approach the
game in the same way that you personally approach the game. I'm
afraid this is a mistaken notion, but I haven't been able to convince
you. The view that risk is important is mathematically incompatible
with the view that max-EV strategy is optimal, because adding risk
into the equation changes the very meaning of "optimal." This doesn't
mean that the optimal strategy is radically different than max-EV, only
that factoring in risk will "bend" the strategy a bit in order to make it
optimal for EV+risk rather than EV alone. Optimal is relative to your
objective, not an absolute thing that applies only to EV.

The max-EV strategy remains truly optimal only for those players who
care so little about risk that no strategy adjustments come into play.
Adjusting the denomination does have the largest impact on risk, but
to achieve "truly optimal" requires alterations in the playing strategy,
and this remains true even if you could adjust unit size in increments
that are arbitrarily small.

BUT, "totally indifferent to risk" doesn't apply to me nor to any
advantage video poker players that I know. We aren't indifferent to risk.

Good, glad to hear it. For you and all the advantage video poker players
you know, max-EV strategy is less than optimal. You may have believed
you were playing exactly correctly for your objectives, but if you tell me
that risk is truly important to you, then you can't have it both ways.

I've said it before and I'll say it again now. If the things I'm saying have
never caused you to stop and say "that can't be right," then you probably
haven't understood what I'm saying. You probably won't accept this,
and will continue to believe that I'm being misleading. Some of what
you believe to be true is in fact not true at all, and so my words seem
contradictory to you, thus misleading. You need to carefully consider
the possibility that what you believe to be true may in fact be wrong.
This is hard (impossible?) if you still profess "zero doubt."

We carefully consider and analyze risk, and then decide if we want to
deal with that risk, or not. If we decide to handle the risk, and if we
are adequately bankrolled, then we can properly use max-EV strategy rather
than some more conservative strategy, and we can be unconcerned with the
risk - but never indifferent.

That depends very much on exactly what you mean by "properly use
max-EV strategy." If you wish to be achieve 100% absolutely without any
qualification optimal results and you do indeed care about risk, then in
order to reach that ultimate level of performance, you MUST abandon the
flawed notion that max-EV strategy is part of THAT process.

If, on the other hand, you are content with "pretty good" rather than
"abolutely optimal," then using the max-EV strategy probably won't hurt
very much. You just shouldn't refer to this as "optimal" because once
you give up any utility, your play is no longer optimal.

You may have intended for "totally indifferent to risk" to describe a state
of mind, after the risk has been considered and accepted, but IMO it's a
huge stretch to say that "totally indifferent" allows for such
consideration.

I'm not talking about state of mind, I am talking only about mathematical
truth. But, through all of our discussion, I don't think you've really
understood the implications of what I'm saying.

SO, IMO your statement was misleading because you said that max-EV is
"only optimal for those who are totally indifferent to risk", since
max-EV is optimal for some advantage video poker players, and they aren't
indifferent to risk.

Nope. You THOUGHT my statement was misleading, because you believed
that your own use of max-EV strategy was optimal and mathematically
consistent with your own objectives. What I'm telling you now, and what
I've been trying very hard to explain to you for quite some time now, is that
your beliefs are not in harmony with mathematics. The statements "max-EV
is optimal" and "risk matters" are mathematically incompatible. They cannot
be reconciled.

Or maybe you do understand but you are using the word "optimal"
incorrectly. Optimal means "best possible" and does not allow for ANY
sacrifice in measured performance.

This hair splitting discussion is probably of limited interest to many,
so any future responses by me on whether or not your statement was
misleading will be done on FREEvpFREE.

Tom, I'm not trying to split hairs here, I promise you. I'm trying very hard
to explain a concept that may be extremely difficult to accept. Most people,
possibly yourself included, have a view of EV that is just not quite right.

···

On Wednesday 22 October 2003 08:24 pm, vp_FREE wrote:

On 22 Oct 2003 at 5:49, Steve Jacobs wrote:

#18

First of all, I would recommend not taking this discussion to
FREEVpFREE. I would argue that it's one of the more interesting
concepts I've seen on these groups in years.

I think the issue is that the two of you are talking in two different
contexts. Steve is referring to the concepts of utility and
microeconomics, while Tom is referring to risk in a commonsense way.
Let me give you an example:

Two video machines are available at Scott's casino. Both generate a
random number from 0 to 99, and both require a $5 wager and are only
available in that amount. Both games can be played at the rate of
1000 hands/hour.

Game #1 -- "Big Bucks": If the random number is 99, player wins $505.
Game #2 -- "Slow and Steady": If the random number is odd, player
wins $10.08.

Tom says: "The EV of BB is 5 cents per hand or $50/hour. The EV of
S&S is 4 cents per hand or $40/hour. BB is clearly riskier, though
more exciting. Luckily, I have $10,000 in my gambling bankroll, so
according to my RoR calculations, I am adequately bankrolled to play
BB, despite the extra risk. Therefore, I will take on extra risk and
play BB"

Steve says: "Playing S&S will cost me $10/hour versus BB. However,
there is an inherent value in knowing that I will never find myself
down the thousands of dollars in this game that BB could cost me.
Even though I am adequately bankrolled, being down $2000 is more
painful than being up $2000 would cause happiness (the definition of
a risk-averse person is that each additional dollar has less utility
than the last). So I will play the less lucrative S&S, and bask in
the knowledge that I will surely be ahead at the end of the night."

Now, you may say that you are risk-averse, but there's now way that
You will pay $10/hour for the privledge of lower risk. OK, are you
willing to give up $1/hour? 25 cents/hour? Lots of max-EV plays are
only worth fractions of a penny, but are increasing your risk
profile. Isn't it worth a fraction of a penny 20 times an hour to
lower your risk?

The realistic answer for most VP players, even most advantage players
is no. The plays that we are talking about are things like holding
high pairs instead of 3-card royals (in cases where the royal is the
higher EV) or keeping a full house in 10/7 DB instead of holding 3
aces. Since the "fun" for most VP players is hitting one of these
jackpot hands instead of eeking out a smaller loss, it will be an
uphill battle convincing a VP player that it is in his best financial
interest to give up the EV and take the less-risky hand. Despite the
rational nature of the advice, most of us are in the casino for some
degree of "fun". After all, if we were just pushing buttons for
$10/hour with no variance, they would just call it work.

>> and is only optimal for those who are totally indifferent to

risk

> Please tell me the difference between "not risk averse"

and "totally

> indifferent to risk".

Well the first difference is that I used "not risk averse" in

context,

as a modifier for advantage players, while you used your phrase in

a

vacuum, leaving some question as to who you were referring to.

The second difference is that "risk averse" IMO isn't "totally

indifferent

to risk" but allows for the consideration, evaluation and

assumption of

risk if deemed desireable.

> Also explain what "adequately bankrolled"
> means for a player who is not risk averse. The very concept of an
> "adequate bankroll" is rooted in concerns about risk. A player

who

> is not risk averse and whose bankroll has been reduced to a single
> wager is still adequately bankrolled.

I'll pass on this for now since I think this is mostly semantics.

I'll

revisit it later if you wish.

> I'm still at a loss as to what you find misleading about my post.
> I'm not posting anything here that I consider to be an opinion,

but

> only conclusions that I've reached based on mathematical
> considerations. So, if you don't have any problem with my facts,

yet

> find my posts misleading, then we must be using different

definitions

> of the word "fact."

I don't have any problem with your "facts". I do have a problem

with

your "totally indifferent to risk" phrasing, because it is

misleading.

My first thought when I read "and is only optimal for those who

are

totally indifferent to risk" was that you were referring to some

group

of foolhardy, financially irresponsible people, and it took a while
before I realized you had to be talking about me and advantage

video

poker players.

BUT, "totally indifferent to risk" doesn't apply to me nor to any
advantage video poker players that I know. We aren't indifferent to

risk.

We carefully consider and analyze risk, and then decide if we want

to

deal with that risk, or not. If we decide to handle the risk, and

if we

are adequately bankrolled, then we can properly use max-EV strategy

rather

than some more conservative strategy, and we can be unconcerned

with the

risk - but never indifferent.

You may have intended for "totally indifferent to risk" to describe

a state

of mind, after the risk has been considered and accepted, but IMO

it's a

huge stretch to say that "totally indifferent" allows for such

consideration.

SO, IMO your statement was misleading because you said that max-EV

is

"only optimal for those who are totally indifferent to risk",

since

max-EV is optimal for some advantage video poker players, and they

aren't

indifferent to risk.

This hair splitting discussion is probably of limited interest to

many,

···

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

On 22 Oct 2003 at 5:49, Steve Jacobs wrote:
so any future responses by me on whether or not your statement was
misleading will be done on FREEvpFREE.

vpFREE Administrator

#19

I agree that the discussion has value, and I think your example is an
excellent illustration of the key issue: If we stipulate that an
optimal VP strategy needs to include a risk "consideration," how do
we compute the actual value a lower risk strategy? In other words, if
we know that expert play and .25 cash back at DB produces an expected
yield of .42, how much of that .42 do we need to give up to cut risk
by a third or a half or whatever? And, oh, by the way, what strategy
variances from MAX EV do we need to employ at each level of risk
reduction?

JW

--- In vpFREE@yahoogroups.com, "tooncesthecatwhocoulddriveacar"
<tooncessnl@h...> wrote:

First of all, I would recommend not taking this discussion to
FREEVpFREE. I would argue that it's one of the more interesting
concepts I've seen on these groups in years.

I think the issue is that the two of you are talking in two

different

contexts. Steve is referring to the concepts of utility and
microeconomics, while Tom is referring to risk in a commonsense

way.

Let me give you an example:

Two video machines are available at Scott's casino. Both generate

a

random number from 0 to 99, and both require a $5 wager and are

only

available in that amount. Both games can be played at the rate of
1000 hands/hour.

Game #1 -- "Big Bucks": If the random number is 99, player wins

$505.

Game #2 -- "Slow and Steady": If the random number is odd, player
wins $10.08.

Tom says: "The EV of BB is 5 cents per hand or $50/hour. The EV of
S&S is 4 cents per hand or $40/hour. BB is clearly riskier, though
more exciting. Luckily, I have $10,000 in my gambling bankroll, so
according to my RoR calculations, I am adequately bankrolled to

play

BB, despite the extra risk. Therefore, I will take on extra risk

and

play BB"

Steve says: "Playing S&S will cost me $10/hour versus BB. However,
there is an inherent value in knowing that I will never find myself
down the thousands of dollars in this game that BB could cost me.
Even though I am adequately bankrolled, being down $2000 is more
painful than being up $2000 would cause happiness (the definition

of

a risk-averse person is that each additional dollar has less

utility

than the last). So I will play the less lucrative S&S, and bask in
the knowledge that I will surely be ahead at the end of the night."

Now, you may say that you are risk-averse, but there's now way that
You will pay $10/hour for the privledge of lower risk. OK, are you
willing to give up $1/hour? 25 cents/hour? Lots of max-EV plays

are

only worth fractions of a penny, but are increasing your risk
profile. Isn't it worth a fraction of a penny 20 times an hour to
lower your risk?

The realistic answer for most VP players, even most advantage

players

is no. The plays that we are talking about are things like holding
high pairs instead of 3-card royals (in cases where the royal is

the

higher EV) or keeping a full house in 10/7 DB instead of holding 3
aces. Since the "fun" for most VP players is hitting one of these
jackpot hands instead of eeking out a smaller loss, it will be an
uphill battle convincing a VP player that it is in his best

financial

interest to give up the EV and take the less-risky hand. Despite

the

rational nature of the advice, most of us are in the casino for

some

degree of "fun". After all, if we were just pushing buttons for
$10/hour with no variance, they would just call it work.

>
>
>
> >> and is only optimal for those who are totally indifferent to
risk
>
> > Please tell me the difference between "not risk averse"
and "totally
> > indifferent to risk".
>
> Well the first difference is that I used "not risk averse" in
context,
> as a modifier for advantage players, while you used your phrase

in

a
> vacuum, leaving some question as to who you were referring to.
>
> The second difference is that "risk averse" IMO isn't "totally
indifferent
> to risk" but allows for the consideration, evaluation and
assumption of
> risk if deemed desireable.
>
>
> > Also explain what "adequately bankrolled"
> > means for a player who is not risk averse. The very concept of

an

> > "adequate bankroll" is rooted in concerns about risk. A player
who
> > is not risk averse and whose bankroll has been reduced to a

single

> > wager is still adequately bankrolled.
>
> I'll pass on this for now since I think this is mostly semantics.
I'll
> revisit it later if you wish.
>
>
> > I'm still at a loss as to what you find misleading about my

post.

> > I'm not posting anything here that I consider to be an opinion,
but
> > only conclusions that I've reached based on mathematical
> > considerations. So, if you don't have any problem with my

facts,

yet
> > find my posts misleading, then we must be using different
definitions
> > of the word "fact."
>
> I don't have any problem with your "facts". I do have a problem
with
> your "totally indifferent to risk" phrasing, because it is
misleading.
>
> My first thought when I read "and is only optimal for those who
are
> totally indifferent to risk" was that you were referring to some
group
> of foolhardy, financially irresponsible people, and it took a

while

> before I realized you had to be talking about me and advantage
video
> poker players.
>
> BUT, "totally indifferent to risk" doesn't apply to me nor to any
> advantage video poker players that I know. We aren't indifferent

to

risk.
> We carefully consider and analyze risk, and then decide if we

want

to
> deal with that risk, or not. If we decide to handle the risk, and
if we
> are adequately bankrolled, then we can properly use max-EV

strategy

rather
> than some more conservative strategy, and we can be unconcerned
with the
> risk - but never indifferent.
>
> You may have intended for "totally indifferent to risk" to

describe

a state
> of mind, after the risk has been considered and accepted, but IMO
it's a
> huge stretch to say that "totally indifferent" allows for such
consideration.
>
> SO, IMO your statement was misleading because you said that max-

EV

is
> "only optimal for those who are totally indifferent to risk",
since
> max-EV is optimal for some advantage video poker players, and

they

aren't
> indifferent to risk.
>
> This hair splitting discussion is probably of limited interest to
many,
> so any future responses by me on whether or not your statement

was

···

--- In vpFREE@yahoogroups.com, "vp_FREE" <vpFREE@C...> wrote:
> On 22 Oct 2003 at 5:49, Steve Jacobs wrote:
> misleading will be done on FREEvpFREE.
>
>
> vpFREE Administrator

#20

I tried to promise myself that I wouldn't respond to too many of
these discussions on this board. Its so easy to get 'sucked' in.
However, this particular thread, I have found to be so intriguing.

I've sat on the sidelines trying very hard to ignore any semantics
and trying to get to the heart of the issue.

From a purely mathematical perspective, Steve would appear to be
correct. In theory, it should be possible to lower 'risk' (i.e.
volatiliy) at the expense of some amount of expected value 'EV',
where its understood the EV is the long term average payout of the
machine.

I am trying to get a handle on the practical application of this
theory. It would appear that for most games the only real way to
accomplish this would be to 'devalue' the higher paying (thus less
frequently occurring hands) when building a strategy table, but of
course, giving full weight to these hands when determining the
payback of the machine. This should be relatively easy to do for
most analysis programs. To what extend the hands should be devalued
will be determined by how much risk you want to reduce the paytable
by.

I would think that for a JoB machine, the only hand this could be
accomplished for is the Royal Flush. So presumably, a strategy
table could be made that would 'devalue' the Royal and lower the
relative rankings of 2 & 3 Card Royal Flushes (I can't imagine any
strategy suggesting to do much with a 4-Card Royal. Would anyone
want to go so far as to keep a Flush that includes a 4-Card Royal
instead of going for the Royal...perhaps, but I would really think
the player might want to look for something other than VP to play!).

So, assuming we lower the relative rankings of 2 & 3 card royals by
assuming a Royal only pays 400 per coin (or maybe just 250, creating
a strategy for less than max coin play). So, how many plays are
really impacted and by how much? Perhaps a 2 Card Royal will get
instead be played as a 4-card inside straight? How much will this
lower the EV? How much will this lower the risk/volatlity? I'd
like to say I have the absolute answer to these questions, but at
this time, I don't. I'm wondering if some of those people who are
advocating this style of play have any absolute numbers to share
with us.

For other forms of VP, (such as Double Double et al), would the
application of this theory include devaluing the value of the Four
Aces? Someone suggested perhaps under this plan you keep the Full
House instead of the Three Aces. Again, this might reduce
risk/volatility but at what overall cost in terms of EV? If someone
really is willing to throw three aces to save the full house and
forgo a shot at getting the `big' payout, why are they playing
Double Bonus in the first place!? If you want to reduce risk,
wouldn't it make more sense to just play Bonus or JoB?

This, of course, brings me to the most interesting part. My Dad had
often written articles in response to people who wanted to hit MORE
Royals...in essence INCREASING volatility at the expense of overall
Payback (EV). The mathematical process was pretty similar.
Artificially INCREASE the value of the Royal when determining
strategy but using the REAL value to determine overall payback.
Each increase in the Royal payback would increase the risk and
reduce the EV, all while increasing the chance of hitting a Royal
within a specified period of time. It thus makes sense that it is
possible to REDUCE risk and reduce EV, all while decreasing the
chance of hitting a Royal within a specified period of time.

  Have we gone full circle? Instead of increasing risk and
reducing EV in order to increase one's chances of hitting the
adrenaline pumping Royal, it is being discussed whether one is
willing to REDUCE risk and REDUCE EV and REDUCE one's chances of
hitting a Royal.

Clearly, there is some merit in attempting to reduce risk at the
expense of EV. How much EV for how much risk is essentially a
personal decision. Personally, I'm a bit skeptical that sufficient
risk can be removed relative to the reduction of EV in the game of
Video Poker. If someone has some empirical data, I'd love to look
it over. If no one does, I'll put it on my long list of analysis to
perform and happily report back when I get to it.

JMO

Elliot