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Lenny Frome Article

#1

Elliot Frome wrote:

As I have countless examples of my dad's work in calculating Game
EV, I know how he calculated it. Coins returned/coins wagered. I'm
not even sure if the two of US are agreeing on that as the
definition of the game EV, yet alone we are clearly disagreeing on
Coins returned and coins wagered.

If you mean EXPECTED coins returned, divided by coins wagered (aka "action"), then we're in agreement that this is the definition of the game's EV. This is also informally referred to as "payback" by Lenny Frome and others, but most serious analysts today use the term Game EV since EV is formally defined in statistics.

I'm not asking you to keep true to my methodology on the whole. I
simply meant if you're going to cite an example where my methodology
falls thru USING my methodology to make sure you stay True to it. Otherwise, we'll really get confused.

I thought I did that, and showed where your methodology failed to be an accurate model of reality.

> Nothing wrong with it except that it's even more twisted than my
> example, which was intentionally wrong just to show numbers can be

thrown around to "prove" just about anything.

I suggest you read Peter Griffin's "Extra Stuff" book. On page 115

he

describes a betting system for craps with a 56% win rate. It's
achieved in a way similar to the way you're twisting things

around.

Of course, he ends up showing just how ridiculous it is.

I haven't read the book (doesn't mean I won't search it out), but I
don't see where the logic is twisted. I'm still waiting for it.

I guess I'm just not talented enough at showing examples of erroneous methodology to make it clear to you. Peter Griffin's book does not deal with video poker but with gambling in general, and he is very accurate mathematically.

As I suggested to someone else here, check it with a statistician who is familiar with game theory. (That's the mathematics field called game theory, not the theory of video poker.)

> On this SESSION, your return happened to be 100%, but that's
entirely

unrelated to EV no matter how you figure it. It's more likely that
I'll get no payoff, then the session return is 0%. The EV is the
weighted average (mean) of all possible outcomes.

Yes...a weighted average of ALL possible outcomes. Why would
throwing in some extra 100% possible outcomes not affect the
weighted average?

Simply because it's a dependent event. AFTER achieving a payoff on the VP game, you have a 50% probability of either doubling your payoff or losing it. I showed this very clearly in my articles in Video Poker Times.

> >In my eyes, I wagered 6 coins and won back 10 (5 each time). 10/6

>is 166.67%. I may have 5 times the amount of money I started

with,

>but that is not EV or payback.

Sorry, Elliot, but what your eyes see and reality are two entirely
different things.

Sorry, but I respectfully disagree.

I'm glad it's respectfully. ;- )

> >A computer simulation will not solve our 'dispute'. We are

>disagreeing on the calculation, not the result. In your example,
>unless we both agree that coin in was 35 and returned was 60, no
>computer simulation will do us any good.

There is no "dispute." Just bad math. I'm sorry that you put down

the

idea of a computer simulation. Are you afraid to do it?

Afraid..not at all. I'm a professional computer programmer. It
would take no more than an hour or two to set it up. But until we
agree on the calculation, there is no point. You say it's one
event, I say it's two events. I say if you put in 5 coins and get a
High Pair, and Double Up and win, that you've wagered 10 coins and
won 15. you're saying you wagered 5 coins and won 10. Until we
agree on a method for calculating what the program says, nothing
will be accomplished. If you'd like though, I'll write it and let
it sit there until we agree on how to use the numbers it will
produce.

You're right about our difference of opinion of whether five or ten coins were wagered, and that's exactly where you go wrong. You never bet any more coins or credits to double up. Only the original five were the bet.

> >It would appear that you are looking at the end result. I started

>with 1 coin, I ended with 6 coins, thus a 600% return. This is a
>correct calculation of the 'return of your money'.

If in a single event you start with one coin and end up with six,
then 600% is a correct calculation of "return of your money" on

that

single event. Again, this has nothing to do with expectation of

the

game as a whole.

And isn't the end result what is most important?

The end result is of course important. To a professional gambler,
all that really matters at the end of the day is win or loss. Most
people are not professional gamblers. That's why most people in LV
can start with $100 and double it in the first 5 minutes, but won't
stop. They want their entertainment value too. They have in mind
they are going to gamble for 3 hours or 5 hours or 8 hours. What
this really means is that over that period of time they will be able
to wager a certain amount of money (i.e. 600 hands * 5 hours * 5
coins = 15000 coins). Since a hand of Double-Up using a portion of
that time, in turn takes a number of those hands, in turn a portion
of those coins, you must include it's 100% payback in your weighted
average in order to figure out how a player can expect to do over a
period of time or a set number of hands played or coin in.

this is NOT the same calculation as expected NET WIN or NET LOSS. I
think we're simply comparing apples to oranges, both intending to
describe the same thing, but not really.

To figure a game EV, it is the EXPECTED end result that we are trying to calculate, nothing else.

The Double Up does two things: It slows your play, and it increases the variance. (For a very low payback game, slowing your play is a good thing because it reduces your expected loss rate.)

> >I realize the Double-Up option doesn't allow you this choice.

>It 'holds' the money and you decide to play or not. Once you

decide

>to 'play' you start a whole new game with it's own EV and this EV
>must be weighted in the overall payback. Because Double-Up has a
>100% EV, it's easy to 'lose' it.

Yes. That's how it increases the variance.

I'm not saying it doesn't increase the variance. but you are still
playing a portion of your hands at 99.5% and a portion at 100%
requiring the weighted average. IF the machine REQUIRED you to play
Double UP after every winning hand, I agree that THEN it is one
event inseperable and the payback would stay constant.

So long as you insist that the double up is a separate event, you will continue to come to this same conclusion, just as your dad did, and just as I did until I realized that it is a dependent event.

> >I'm glad a 10 year old article can generate such interest!

>
>Elliot

So am I, and I hope we can be on good terms with each other. I'd

like

to meet you.

I consider this to be friendly discussion about a complex topic. I'm sure we will meet at some point. As I work from the East Coast,
I'm not always able to make all the events in LV.

Please let me know when you'll be in LV, and we'll arrange to meet. I hope we keep it friendly.

> If it's any consolation, I fell into this same trap of figuring
that

a 100% return Double Up would shift the game's total payback

closer

to 100%, whether the game's basic payback is below or above 100%,

and

that's what I said in my newsletter and other places for a long

time.

Now I know better. I have come to the realization that playing a
hand, followed by any subsequent double up, must be considered a
single play. True, it is more than one event, but the double up is
dependent on the play of the dealt hand, so they can not be
considered independently.

I agree that if you consider it a single play that the EV will not
change. I have yet to see anything that has convinced me that they
MUST be seen this way.

Elliot, please send me your snailmail address privately, and I'll send you copies of the two issues of my newsletter with the articles on Double Up.

So long as I have the option to not play it,
I consider it two distinct events. At the point the screen pops up
to choose Double Down, the coins I won in VP are mine (mine, mine,
mine...all mine). When I choose to play, I'm starting a new game. The fact that I only have this choice after a winning hand is what
limits the player's ability to play 100% all the time, but it still
makes it (to me) a distinct event. That's not to say I consider how
you view it as wrong, merely different.

You could play the VP game only until you have a payoff, then Double Up as many times as you like. It still would not change the overall game EV.

At this point, I think we may have beaten this one to death for
now. I don't necessarily seeing us convincing the other. But then
again, if all the analysts/writers agreed on everything, there
wouldn't be the need for so many of us! :>

Good point.

Dan

···

--
Dan Paymar, author of "Video Poker - Optimum Play"
Editor and publisher of "Video Poker Times" newsletter
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind"
- Louis Pasteur

#2

See. We're making progress. We're getting closer towards agreeing
to disagree!

Elliot Frome wrote:

If you mean EXPECTED coins returned, divided by coins wagered (aka
"action"), then we're in agreement that this is the definition of

the

game's EV. This is also informally referred to as "payback" by

Lenny

Frome and others, but most serious analysts today use the term

Game

EV since EV is formally defined in statistics.

Of course for Expected Value, I'm talking Expected coins returned
divided by coins wagered. Looking back at a session, I would
calculate what my actual return was in the same manner. I would
calculate net win/loss or return on my investment by counting the
bills in my wallet.

I thought I did that, and showed where your methodology failed to

be an accurate model of reality.

No, actually, I don't think you did. Your example was you bet 5
coins, draw a flush to get back 30 and the attempt to double-up
where your expectation is 100%. You stated that according to my
methodology the payback would be 80+%. IN reality according to my
calculation it's 170+%. You wagered 35, you won 60. You consider
it to be you wagered 5 and won 30. We both arrive at the same 'net
win'. We don't agree on how much was wagered. That's the real
difference in our calculations.

I guess I'm just not talented enough at showing examples of

erroneous

methodology to make it clear to you. Peter Griffin's book does not
deal with video poker but with gambling in general, and he is very
accurate mathematically.

As I suggested to someone else here, check it with a statistician

who

is familiar with game theory. (That's the mathematics field called
game theory, not the theory of video poker.)

I will gladly search out such books. I had an excellent teacher in
mathematics, who I consider to be amongst the most accurate I've
ever known. My Dad. I won't say he never made a mistake, but most
of the 'mistakes' that people have attributed to him were purposeful
simplifications for the masses. In the end, he was writing for the
millions of average people who go to casinos, not the Professors in
Universities. Sometimes things need to be explained in a way
that 'average Joe' can understand it, even if it's not 100% true to
theory.

Simply because it's a dependent event. AFTER achieving a payoff on
the VP game, you have a 50% probability of either doubling your
payoff or losing it. I showed this very clearly in my articles in
Video Poker Times.

For lack of a better expression, it's optionally dependent on the VP
game (in one direction only in that you can choose not to play it).

You're right about our difference of opinion of whether five or

ten

coins were wagered, and that's exactly where you go wrong. You

never

bet any more coins or credits to double up. Only the original five
were the bet.

I understand why you think that's where I go 'wrong', but so long as
I have the right to pull my money out before Double-Up, I am making
a conscious decision to re-risk the money, starting a new bet. If I
did not have this option, it would be different.

To figure a game EV, it is the EXPECTED end result that we are

trying

to calculate, nothing else.

The Double Up does two things: It slows your play, and it

increases

the variance. (For a very low payback game, slowing your play is

a good thing because it reduces your expected loss rate.)

But, don't you see, we are BOTH calculating the same expected
result. We're representing it differently, but we're arriving at
the same expectation to the player. So long as the player
understands how we've calculated it, it should not be a problem.

I play 10 hands of VP. Get a High Pair on each and play Double-Up
losing 5 and winning 5.

To me, I've wagered 100 coins and I get 100 coins back. To you, you
wagered 50 coins and got 50 coins back. As long as one is
consistent about the calculation, we can both accurately state the
how many coins the person is going to lose over a set period time
(according to the theoretical ev of each seperate game). We choose
different percentage representations because in your estimation I
am 'double counting'. I don't consider it 'double counting' because
I consider double-up a seperate event.

Both of us could accurately determine win/loss rate given the
payback of a VP, and knowing how many hands of VP the person will
play and under what conditions they will play Double-Up (ALL winning
hands? Only High Pairs? High Pairs and 2 Pairs? etc...).

So long as you insist that the double up is a separate event, you
will continue to come to this same conclusion, just as your dad

did,

and just as I did until I realized that it is a dependent event.

And so long as I can pull my money out after the VP hand, I will
continue to consider it a seperate event.

Please let me know when you'll be in LV, and we'll arrange to

meet. I

hope we keep it friendly.

Like I believe my father was, I'm a pretty easy going guy. I
believe the masses benefit by having numerous analysts/writers to
choose from who don't always agree. This is why I also believe that
the theory of the math classroom, while it has its place, cannot be
adhered to 100% when attempting to explain it all to the average
player (VPFree is NOT a representative sampling of the average
player!).

Elliot, please send me your snailmail address privately, and I'll
send you copies of the two issues of my newsletter with the

articles

on Double Up.

To save me further typing (of another e-mail), I'll just use my
business P.O. Box (it's on our website, so I don't mind posting
here);

Compu-Flyers
P.O. Box 132
Bogota, NJ 07603

#3

Elliot Frome wrote:
>As I have countless examples of my dad's work in calculating Game
>EV, I know how he calculated it. Coins returned/coins wagered. I'm
>not even sure if the two of US are agreeing on that as the
>definition of the game EV, yet alone we are clearly disagreeing on
>Coins returned and coins wagered.

If you mean EXPECTED coins returned, divided by coins wagered (aka
"action"), then we're in agreement that this is the definition of the
game's EV. This is also informally referred to as "payback" by Lenny
Frome and others, but most serious analysts today use the term Game
EV since EV is formally defined in statistics.

Griffin was very much opposed to defining EV on the basis of _total_
coins wagered. In fact, doing so leads to the conclusion that odds
bets at craps will lower EV.

Griffin defined EV as coins returned per _initial_ wager, and his
calculation of basic strategy for blackjack required this definition.
Using (average coins returned) / (average wager) leads to a
different optimal strategy which has some properties that Griffin
felt were "strange." Griffin describes this in the same "Extra Stuff"
book that you cite. See the section "Disagreements on Blackjack
Percentage" starting on page 111.

My position is that either method can be used, but the two
definitions of EV are definitely qualitatively different. When
computing basic strategies for blackjack, I use Griffin's
method of basing the strategy on initial wager.

>> I suggest you read Peter Griffin's "Extra Stuff" book. On page 115
>>he describes a betting system for craps with a 56% win rate. It's
>> achieved in a way similar to the way you're twisting things
>>around.

I'm looking at page 115 of "Extra Stuff". I don't think his method of
getting a 56% win rate is at all similar to what Elliot is describing.

···

On Wednesday 31 March 2004 09:11 pm, Dan Paymar wrote:

#4

Steve Jacobs wrote:

Griffin was very much opposed to defining EV on the basis of _total_
coins wagered. In fact, doing so leads to the conclusion that odds
bets at craps will lower EV.

<snip>

My position is that either method can be used, but the two
definitions of EV are definitely qualitatively different.

I've been disappointed that this discussion has had only limited
practical focus. Mention of the loosely parallel situation of a craps
odds bet, while not fully analogous, brings things home to what I
think is the most salient point of the discussion:

Doubling doesn't improve the long-term prospects for a vp player
(positive or negative game). It increases variance and consequently
bankroll requirement -- or, for a negative game, increases risk (as
defined by the probability of losing a given amount, assuming that a
player has no lifetime preset profit "stop" point).

(Steve, have I covered myself in defining "risk", yet?? If so, maybe
you have a short-hand reference for me :wink:

It's a play that should be avoided.

- Harry

#5

Define it however you want. It seems to me that your intent is to define
it in such a way that doubling is wrong. Whatever.

Doubling can help the player, depending on the personal objectives
that the player is striving for. It makes no difference whether I use
the term "risk" or "jello pudding" to label the mathematical property
which leads to that conclusion. The fact remains that there are
some situations and players who would be mathematically justified
to take the double up wager. If you don't think you fit into that
category, then don't use it, but to flat out claim that it should always
be avoided is mathematically misleading.

···

On Thursday 01 April 2004 10:50 am, Harry Porter wrote:

Doubling doesn't improve the long-term prospects for a vp player
(positive or negative game). It increases variance and consequently
bankroll requirement -- or, for a negative game, increases risk (as
defined by the probability of losing a given amount, assuming that a
player has no lifetime preset profit "stop" point).

(Steve, have I covered myself in defining "risk", yet?? If so, maybe
you have a short-hand reference for me :wink:

#6

Harry Porter wrote:
> (Steve, have I covered myself in defining "risk", yet??

Steve Jacobs replied:

Define it however you want. It seems to me that your intent is to
define it in such a way that doubling is wrong.

The definition wasn't selected with a prejudice against doubling.
Rather, it was driven by what I perceive the greater body of players
hold as their goal - via observation, posts, and discussions.

You've defined the negative player's goal to achieve a certain profit
objective and then quit play permanently.

While that is perhaps the most rational approach for a negative
player, I see the greater concern of most players to be the risk of
large losses and their primary goal is a sustained bankroll. There's
no intent to quit when a certain profit is attained. To the contrary,
profits induce greater play intensity (and frequently unwise increase
in play denomination).

I fully concede that doubling is attractive behavior under your
definition. But I don't think it fits the reality of casino play.

In the context of what I've observed, doubling isn't consistent with
most players' goal. While "caveat emptor" may apply, your statements
mislead less knowledgable players into doubling without realizing the
adverse consequence to their play and immediate goal.

- Harry

#7

While that is perhaps the most rational approach for a negative
player, I see the greater concern of most players to be the risk of
large losses and their primary goal is a sustained bankroll. There's
no intent to quit when a certain profit is attained. To the contrary,
profits induce greater play intensity (and frequently unwise increase
in play denomination).

Playing negative games is simply incompatible with a "primary goal
[of] a sustained bankroll." So, there is no "rational" approach to
sustaining a bankroll and playing negative games indefinitely. Either
the negative game or the sustained bankroll has to give, you just
can't have it both ways. If the entertainment value is worth sacrificing
the sustained bankroll, then a recreational player might enjoy a
negative game. If ongoing losses aren't acceptable, then the only
rational approach to a negative game is a goal which is short term.

A player who chooses a strategy other than "get in, win quick,
and get out" with negative games will _guarantee_ large losses
if they continue to play. Seems to me you are trying to reconcile
objectives that simply cannot be reconciled except in a transient
fashion. With negative games, you can either take a (lucky) shot
at a quick win, or you can die slowly as if pecked to death by
ducks. Yes that really sucks, but that is life on the dark side of the
bell curve. The very attempt to "sustain" the bankroll is what
guarantees its eventual loss.

I fully concede that doubling is attractive behavior under your
definition. But I don't think it fits the reality of casino play.

Then don't use it. But don't try to claim that there are no situations
where it can benefit the player just because you aren't one of the
players who would choose to play in that manner.

In the context of what I've observed, doubling isn't consistent with
most players' goal. While "caveat emptor" may apply, your statements
mislead less knowledgable players into doubling without realizing the
adverse consequence to their play and immediate goal.

It seems as if you want me to flat out lie about what math says. I won't
do it. I'm not going to say "doubling cannot help under any circumstances"
when I know that isn't true, just as I won't say "just play max-EV strategy,
it is always the best thing to do." Both of those statements are things that
I know are false.

Like it or not, the mathematical reality of video poker (and gambling in
general) is not as neat and tidy as most gambling experts claim. I know
that some of these concepts are difficult to grasp, even by very
experienced players, much less those who are relative newcomers.
My main interest is dispelling myths and correcting the mistaken
notions that have been propagating for years. In short, finding out
how things _really_ work without accepting anything as true simply
because "everyone knows it."

People tend to treat their understand of gambling like a religion. They
are comfortable with what they've been taught, and they accept it
virtually as absolute truth. They know that others may have been
taught differently, yet they still feel that their own brand of "truth"
is somehow superior. So you fight me when I say things that violate
your "religion."

It seems rather clear that you feel doubling holds no benefit for
your style of play, and there is nothing wrong with that. Nothing
at all. Now I come along and say "there can be mathematical
justification for doubling" and you accuse me of trying to mislead.
Sorry, but my claim is mathematical fact, and nothing about your
(or anyone else's) personal approach to the game will alter what
math has to say. Doubling is correct for _some_ situations. Not
all. Not most. Some. That is the truth. Sure, people could
misinterpret my words. If someone reads "some" and mentally
subsitutes "most" or "all" then they have much bigger problems
that this discussion can possibly resolve. I don't think that is
happening on a large enough scale to worry about. If anything,
new players will tend to skip my posts, and if they don't they will
hear 15 other "experts" who will say the same thing while I'm
saying something else and conclude that I don't know what I'm
talking about.

In short, you worry to much. You and Bill and about five other
people here are the only ones who read my posts, and half
the time I can't even convince that small group that what I'm
saying makes any sense :wink:

···

On Thursday 01 April 2004 08:10 pm, Harry Porter wrote:

#8

Steve,

I'm replying privately. Beyond what's already been stated I don't
think there's much more of general interest.

- Harry