vpFREE2 Forums

Please explain "equation"

#1

On the vpFREE Yahoo Groups home page is the formula

EV = [ER] X [coin-in]

I'm wondering just what this means. The abbreviations that have been
commonly used are
EV = Expected Value
ER = Expected Return

The Expected Value of a play is always expressed in units, not coins.
That's why the EV of the dealt hand Qd-5d-Ad-Qs-Js when holding the
pair of queens on a 5-coin 9/6 Jacks or Better game is given as
1.53654 rather than as 7.68270 coins.

I use the term ER as the Expected Return of a game. A game analyzer
assumes perfect play to come up with ER = 99.544% for this game.
Jazbo has shown that the ER with my Precision Play rules is less than
0.01% off of perfect, so I quote 99.53% ER with those rules.

Since the EV of each play before the cards are dealt is equal to the
ER of the game, some people use these terms interchangeably, which is
OK.

Some may define ER differently, to mean the expected return of a play
in coins. In that case, the above equation should instead be ER = EV
x [coin in].

Apparently the vpFREE administrator has something else in mind. I
would appreciate an explanation.

Thanks,
Dan

···

--
Dan Paymar
Author of best selling book, "Video Poker - Optimum Play"
Editor/Publisher of VP newsletter "Video Poker Times"
Developer of VP analysis/trainer software "Optimum Video Poker"
Visit my web site at www.OptimumPlay.com

"Chance favors the prepared mind." -- Louis Pasteur

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

#2

Dan Paymar wrote:

On the vpFREE Yahoo Groups home page is the formula

EV = [ER] X [coin-in]

I'm wondering just what this means. The abbreviations that have been
commonly used are EV = Expected Value ER = Expected Return

<<< SNIP >>>

Apparently the vpFREE administrator has something else in mind. I
would appreciate an explanation.

Please read the Dogma section of the FAQ:

<http://members.cox.net/vpfree/FAQ.htm#Dog>

and FAQ #8:

<http://members.cox.net/vpfree/FAQ.htm#8>.

If you still have questions or comments after reading
the FAQ, I'll be glad to address them.

vpFae

#3

Dan Paymar wrote:
> On the vpFREE Yahoo Groups home page is the formula
> EV = [ER] X [coin-in]

> I'm wondering just what this means. The abbreviations that have
> been commonly used are EV = Expected Value ER = Expected Return

vpFae responded:

Please read the Dogma section of the FAQ:
<http://members.cox.net/vpfree/FAQ.htm#Dog>

and FAQ #8:
<http://members.cox.net/vpfree/FAQ.htm#8>.

Dan's question is reasonable; I've never been comfortable with the use
of "EV" around these groups. As defined here, EV is a reference to
expected coin-out. Alternatively, frequently it's casually used to
indicate the expected net win/loss of a play (i.e. coin-out - coin-in,
where some might say that the EV of $10K through on a 1% advantage
play is $100).

The problem stems from the fact that while ER (when defined as a %) is
a very well defined term, EV is a generic statistical reference for
the expected outcome of any phenomenon. It would be best if we always
specifically defined what "V" we were referring to ... "expected coin
out", "expected net win", "expected return", and "expected number of
chair bumps per hour by passing foot traffic" are all EV's.

In the context of game analysis, Dan's full post is dead on in stating
the standard definition of EV -- expected win (payout) from a hold,
expressed in bet units.

Any time a general term is used, the definition is dependent upon
context. That leads to confusion at times, but if that were the worst
of it around here, this'd be a utopia :wink:

- Harry

#4

Yes, it's a reasonable question.

There are (as far as I understand) several different concepts floating around:

-When analyzing a given deal in a given game, the average payoff of
each of the 32 plays. That is what Dan calls EV of a play. It is
reasonably expressed in units.

-For an entire game and for a given strategy, the average payoff of
the game before the deal (i.e. the average value of the EV of the play
indicated by the strategy over every single possible deal). That's
what Dan calls the ER. I'll call it the "net ER" for now.

-In the (simplified) context of infinitely long play with an infinite
bankroll, comps are taken into account. Adding the "net ER" for a game
and the comp rate at the time and place where that game is played gets
the total ER, and that's what the vpFree formula calls [ER].

-Because what actually matters is cold hard cash, the choice of a
game, of a time and of a place is also affected by the actual value of
a "unit". That's what the vpFree formula calls [EV]. It could be
called "cash EV"

-Finally, once again assuming infinite bankroll, what ultimately
matters is the net result when playing - i.e. how much more (or less)
money you expect to have in your wallet after playing. It could be
called "absolute cash EV".

(You could even go further and multiply that by the speed at which a
game can be played, and the cost of going to play and being there).

Approximate examples (I hope I got my numbers right):

5-coin quarter 9/6 JoB with no comps: net ER 99.54%, ER 99.54%, cash
EV $1.244, absolute cash EV -0.6c

1-coin quarter 9/6 JoB with no comps: net ER 98.37%, ER 98.37%, cash
EV $0.246, absolute cash EV -0.4c

10-coin quarter FPDW with 0.75% comps: net ER 100.77%, ER 101.52%,
cash EV $2.538, absolute cash EV +38c.

5-coin $5 10/7 DB with 0.75% comps: net ER 100.17%, ER 100.92%, cash
EV $25.23, absolute cash EV +23c.

I'm certain that Dan has no problem with all those concepts, and that
the only problem is a matter of vocabulary.

There's a lot of imprecision in figuring out the actual value of
comps, except of course for direct cash back, and it varies from one
person to the other.

JBQ

···

On 11/21/05, Harry Porter <harry.porter@verizon.net> wrote:

Dan's question is reasonable

#5

Of course I had to get the numbers wrong. That's +3.8c for 10-coin quarter FPDW.

JBQ

···

On 11/21/05, Jean-Baptiste Queru <jbqueru@gmail.com> wrote:

Approximate examples (I hope I got my numbers right):

10-coin quarter FPDW with 0.75% comps: net ER 100.77%, ER 101.52%,
cash EV $2.538, absolute cash EV +38c.

#6

Jean-Baptiste Queru wrote:

-In the (simplified) context of infinitely long play with an infinite
bankroll, comps are taken into account. Adding the "net ER" for a game
and the comp rate at the time and place where that game is played gets
the total ER, and that's what the vpFree formula calls [ER].

-Because what actually matters is cold hard cash, the choice of a
game, of a time and of a place is also affected by the actual value of a
"unit". That's what the vpFree formula calls [EV]. It could be called
"cash EV"

The vpFREE formula output depends on the input and applies to:

game ER or EV

or comp ER or EV

or cash ER or EV

or total ER or EV etc.

Otherwise I agree with your post.

vpFae