vpFREE2 Forums

Wheel Poker

#21

Bob Dancer wrote:

On this site, Brian, Harry, and I (all of us experienced
players and analysts) each expressed the belief that playing the 6th
coin MUST increase the EV. It wouldn't surprise me if I wrote that
somewhere in an article, although I don't specifically remember doing
so. But apparently that's not true. On Wheel Poker and certain other
new Action Gaming products, playing the 6th coin is a bad bet.

Well ... I expressed this in the context that I believed statutory
regulations in at least some jurisdictions (notably IL) required that
the 6th coin bet not degrade EV. But I certainly never meant that
there was anything that had been specifically defined about the game
that supported that this would definitely (MUST) be the case. Far
from it.

···

------

The math on this one is straightforward (far more so than for
MultiStrike, for example). I've separately outlined the basic
mechanism behind the math and have confirmed the BP ER that you stated
using a very basic spreadsheet set up.

Whether or not the 6th coin bet improves or degrades the ER of the
base paytable is strictly a relationship between the average bonus
payout and the quad cycle under optimized strategy.

I've explained that there are tradeoffs involved because WP optimized
strategy will reduce the ER derived from the base paytable (even
before factoring the 6th coin bet). I believe it can be said with a
certainty that so long as the bonus equals or exceeds the quad cycle
under the standard base game that ER/EV will be improved. (That
"certainty" may not be intuitively obvious given the reduced ER of the
base paytable strategy, but I find that it plays out if you think
about it.)

------

That said, it really requires a workup of the numbers to make a
definite finding for a given game. I've described why the numbers
yield a relatively strong 8/5 BP WP game vs. standard 8/5 BP despite
the fact that the bonus is roughly equivalent to the quad cycle under
standard 8/5 BP play.

Nonetheless, making a solid off-the-cuff conclusion about deuces WP is
a no-brainer. The information that the average bonus payout on deuces
remains at 423 is nothing but startling. Before strategy adjustments,
the quad cycle is 1939. A 423 bonus can only represent a very poor
6th coin wager. (I didn't carry forward with a recalculation under an
adjusted WP optimized-strategy cycle, but the assured negative EV of
the 6th coin bet means the quad cycle will increase, not decrease ...
probably only very modestly in terms of % change.)

Off the top of my head, I don't recall IGT introducing a 6th coin game
option that was anywhere near so bad as a 423 bonus would yield on a
game like deuces. In fact, I have trouble believing that we have all
the facts here. (But I'm not disputing that we do.)

I don't see that it's possible to introduce the game to IL (and
possibly other jurisdictions) without substantial increase (tripling
+) of the bonus. It was the restrictions in IL that necessitated a
particular fine tuning in the frequency of FREE RIDES in MultiStrike
to assure that adding additional Levels to play wouldn't degrade EV.

- Harry

#22

paladingamingllc wrote:

This is something I wouldn't play, but if the wheel isn't random,
certainly the average wheel payout could be adjusted to modify the ER
appropriately.

I doubt you mean to suggest that there would be a possibility that the
wheel bonus outcome might not be "random".

As in the multipliers in STP and the expected Free Ride occurence in
multistrike, the mechanics of the average wheel payout is all about
the frequencies that are programmed into the game.

Adjust those frequencies and you change the average value of the bonus
and thus the ER. I had really anticipated that IGT would handle this
game akin to multistrike, where frequencies are set specific to the
particular paytable that you're playing to make the ER come out as
desired. (Free Ride frequencies are set much higher in a low hit-rate
game such as 2pr JW.)

- Harry

#23

Paladin wrote: This is something I wouldn't play, but if the wheel isn't
random, certainly the average wheel payout could be adjusted to modify
the ER appropriately.

Harry addressed this previously, but I wanted to expand on it a bit.

I think you're confusing the concepts of "random" with "equally likely."
The wheel is random but some spaces are more likely than others. I don't
have access to the weights but hypothetically if 2000 was set to hit
0.02% of the time, 1000 was set to hit .06% of the time . . . And 150
was set to hit 0.15% of the time --- the numbers could be set so that
you have an average of 428 and yet what space hits next is entirely
random.

So it is definitely possible to adjust these numbers so that there could
be an average of, perhaps, 470 for Deuces Wild games. But IGT claims it
didn't do this.

You also surmised that I have access to IGT's par sheets to allow me to
write the articles. This is not true. I do have a source within IGT who
sends me pay schedules and returns for all games I'm working on --- and
the IGT Director of Video Poker, John Daley, gets cc'd on all
communications between this source and myself. I have specifically
brought up the question of whether the weights were the same for all
games. I've reported here what was given to me by a reliable IGT source.

Bob Dancer

For a 3-day free trial of Video Poker for Winners, the best video poker
computer trainer ever invented, go to //www.videopokerforwinners.com

#24

I wouldn't call it "surmised". But, at the end, same same but
different, you may not have access, but access finds you, so to speak.
If you don't have the ER info, it makes it tough to write an article
about many of their products.

···

--- In vpFREE@yahoogroups.com, "Bob Dancer" <bdancer@...> wrote:

You also surmised that I have access to IGT's par sheets to allow me to
write the articles. This is not true. I do have a source within IGT who
sends me pay schedules and returns for all games I'm working on --- and
the IGT Director of Video Poker, John Daley, gets cc'd on all
communications between this source and myself. I have specifically
brought up the question of whether the weights were the same for all
games. I've reported here what was given to me by a reliable IGT source.

#25

Paladin wrote: I did see a quarter NSUD Wheel Poker at Rail City in
Sparks recently, but I can't imagine the ER being over 100% (my guess
is 99.93%). Sounds like an article for Strictly Slots is in the
works.

Bob Dancer wrote:

You are correct about a Strictly Slots article, but wrong about NSU.
On Deuces Wild games, Wheel Poker LOWERS the EV if you play the 6th
coin. NSU is 99.73% for 5 coins and 98.44% for 6 coins. The reason
for this 1.3% dropoff is that the frequency of (natural quads +
one-deuce quints) is considerably less than the 428 average hit on
the wheel.

First, thanks to Mickey and Brian for refreshing my memory (in
separate posts) re my earlier calculation of the natural quad
frequency in deuces.

As I earlier calculated
(http://groups.yahoo.com/group/vpFREE/message/84016)
the normal NSUD cycle is 483 hands.

If in playing a Wheel Poker game you're going to pay an extra coin to
receive a bonus of 428 coins, then the sixth coin wager would have an
ER of 428/483 = 88.56%.

This means that if you play the game with no adjustment to strategy,
you should see a weighted overall return of 97.86%. [ (5*0.9972 +
.8856) / 6 ]

With strategy optimization, you always look to do a little better than
that. As I've noted in a another post, you can determine the
optimized strategy for the game and the resulting hand distributions
by adding 514 (1.2 x the 483 bonus) to the natural quad payouts (using
a program such as Wolf Video Poker, that permits such a split). The
resulting hand distributions can be used to manually recalculate ER
for that optimized strategy.

You'll look for such an optimized strategy to play harder for natural
quads, shortening the cycle. This substantially increases the value
of the 6th coin wager, while having a smaller impairment on the base
game 5-coin wager ER.

The numbers that fall out of that analysis are:

Adjusted quad cycle: 441
ER from the 6th coin wager: 97.07%
Adj ER from the 5-coin base game: 98.70%
Overall weighted average 6-coin return: 98.43%

The 98.43% value differs very slightly from the 98.44% Bob obtained
from his IGT source. I expect that this is due to the fact that Bob
has indicated that the bonus average is 483-484 (not the 483 used in
my calculation).

- Harry

#26

Harry wrote: The 98.43% value differs very slightly from the 98.44% Bob
obtained
from his IGT source. I expect that this is due to the fact that Bob
has indicated that the bonus average is 483-484 (not the 483 used in
my calculation).

Correct --- except that the number you used in your calculations was 428
rather than some number between 428 and 429. Good job at explaining how
you came up with the EV.

Bob Dancer

For a 3-day free trial of Video Poker for Winners, the best video poker
computer trainer ever invented, go to //www.videopokerforwinners.com

#27

Harry wrote: "The 98.43% value differs very slightly from the 98.44%
Bob obtained from his IGT source. I expect that this is due to the
fact that Bob has indicated that the bonus average is 483-484 (not
the 483 used in my calculation)."

Bob Dancer wrote:

Correct --- except that the number you used in your calculations was
428 rather than some number between 428 and 429. Good job at
explaining how you came up with the EV.

I've been hashing numbers right and left today :wink: Thanks for the
editorial catch.

···

------

After a mid-afternoon break relook, I have one correction to post
(hey, surely it's been clear that this was a "work-in-progress" :wink:

In my head I rationalized a 20% bump in the bonus as being appropriate
in running the game analysis ... some logic to do with a 5-credit game
paytable and a 6 credit wager. The logic is flawed; you just add the
bonus value itself to the natural quad-related pays to find
strategy/hand distribution.

The correct game analysis (very slightly shifted from the prior values):

Adjusted quad cycle: 441 (unchanged)
ER from the 6th coin wager: 96.96% (down from 97.07%)
Adj ER from the 5-coin base game: 98.73% (up from 98.70%)
Overall weighted average 6-coin return: 98.43%

(ER moved from 98.429 to 98.432 ... still not at the IGT 98.44, yet :wink:

- Harry

#28

Why would anyone with an IQ above 85 want to play a VP game with a
greater variance but an identical or lower payout, when the original
game is also available on the same machine for the same denomination?

IGT's marketing is designed to make the gambler THINK he is getting
more return on his gambling money; whereas, in fact, they are
increasing the take for the casino.

As for Bob Dancer's analysis: since Bob has, and is receiving
compensation from IGT, his postings are highly suspect.

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

> Harry wrote: "The 98.43% value differs very slightly from the 98.44%
> Bob obtained from his IGT source. I expect that this is due to the
> fact that Bob has indicated that the bonus average is 483-484 (not
> the 483 used in my calculation)."

Bob Dancer wrote:
> Correct --- except that the number you used in your calculations was
> 428 rather than some number between 428 and 429. Good job at
> explaining how you came up with the EV.

I've been hashing numbers right and left today :wink: Thanks for the
editorial catch.

------

After a mid-afternoon break relook, I have one correction to post
(hey, surely it's been clear that this was a "work-in-progress" :wink:

In my head I rationalized a 20% bump in the bonus as being appropriate
in running the game analysis ... some logic to do with a 5-credit game
paytable and a 6 credit wager. The logic is flawed; you just add the
bonus value itself to the natural quad-related pays to find
strategy/hand distribution.

The correct game analysis (very slightly shifted from the prior values):

Adjusted quad cycle: 441 (unchanged)
ER from the 6th coin wager: 96.96% (down from 97.07%)
Adj ER from the 5-coin base game: 98.73% (up from 98.70%)
Overall weighted average 6-coin return: 98.43%

(ER moved from 98.429 to 98.432 ... still not at the IGT 98.44, yet :wink:

- Harry

#29

Highly suspect of what?

···

On 4/23/08, William Canevari <wcanevari@yahoo.com> wrote:

As for Bob Dancer's analysis: since Bob has, and is receiving
compensation from IGT, his postings are highly suspect.

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

#30

William Canevari wrote: Why would anyone with an IQ above 85 want to
play a VP game with a greater variance but an identical or lower payout,
when the original game is also available on the same machine for the
same denomination?
. . . As for Bob Dancer's analysis: since Bob has, and is receiving
compensation from IGT, his postings are highly suspect.

It's not really about IQ. On a "normal" video poker machine where you
have both 9/6 Jacks and 9/6 Double Double Bonus, your comment says that
only people with very low IQs play DDB. Slot directors will tell you
that DDB is the most popular vp game in the country.

Your post seems to indicate that your view is that variance is a bad
thing and to be avoided in a lower-variance alternative is available.
That is a sensible point of view --- but it is hardly universal. Higher
variance implies more excitement. There are "action junkies" out there
who PREFER the higher variance games because of the greater excitement.
This is not a matter of IQ. It's a matter of preference.

IGT's (actually Action Gaming's) goal in this game is to appeal to
people who like this sort of excitement. If they are successful in this
appeal, the game will thrive. If they aren't not successful, the game
will not last. Sometimes Action guesses right (Triple Play, Spin Poker,
Super Times Pay) and sometimes they haven't done so well (Chase the
Royal, Matrix Poker). Time will tell how successful this game is.

The main points I've made are that the average wheel return is between
428 and 429, and the wheel has the same average for all games, including
DW. Which of those points do you find "highly suspect?"

Bob Dancer

For a 3-day free trial of Video Poker for Winners, the best video poker
computer trainer ever invented, go to //www.videopokerforwinners.com

#31

Bob Dancer wrote:

Your post seems to indicate that your view is that variance is a bad
thing and to be avoided in a lower-variance alternative is available.
That is a sensible point of view --- but it is hardly universal.
Higher variance implies more excitement. There are "action junkies"
out there who PREFER the higher variance games because of the greater
excitement.
This is not a matter of IQ. It's a matter of preference.

That gets precisely to the heart of the matter. Hoping it's not
impertinent, I'd like to place it into one additional perspective --
to seek out higher variance and a lower return game (i.e. 9/6 DDB over
9/6 Jacks) can be an "intelligent" decision.

A recreational gambler can find that they enjoy play much more if they
come out ahead on a session more frequently ... even if it means in
the longer term their prospects are poorer. It's the session to
session experience that counts, and a good many gamblers have a very
optimisic nature -- they greatly value the wins, and take losses with
a grain of salt.

When playing a negative expectation game such as the examples above
(before factoring other play incentives), if the return is reasonably
close the higher variance game will yield the greater percentage of
winning sessions. Anyone who plays Jacks knows that it's frequently a
matter of "death by a thousand cuts" except when an unusually
remarkable run of quads is hit.

The thrill of the big hits of DDB set aside, and DDB can still prove
to be a more satisfying game for some. (For myself, I get off on the
"In the long run ... :wink:

- Harry

#32

Not a logical conclusion William.

Bob posts frequently on many subjects, and because of his high profile
everything he says is scrutinized.

He provides much excellent information to this community.

Mac
www.CasinoCamper.com

···

--- In vpFREE@yahoogroups.com, "William Canevari" <wcanevari@...> wrote:

As for Bob Dancer's analysis: since Bob has, and is receiving
compensation from IGT, his postings are highly suspect.

#33

Is that really true for those wheel games? or any VP game?. Are you advocating that if I play
a higher variance game with the same EV (as the lower variance game) I am more likely to
win? And if I play higher variance game I will have more winning sessions?? I can feel my IQ
dropping below 86 as I rush out to find one of those wheel games. Ok, seriously... people
play higher variance games because of the increased possibility of larger wins in spite of the
higher likelihood of a losing session.

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

if the return is reasonably
close the higher variance game will yield the greater percentage of
winning sessions.

- Harry

#34

Harry Porter wrote:

> if the return is reasonably close the higher variance game will
> yield the greater percentage of winning sessions.

cdfsrule replied:

Is that really true for those wheel games? or any VP game?. Are you
advocating that if I play a higher variance game with the same EV (as
the lower variance game) I am more likely to win? And if I play
higher variance game I will have more winning sessions?? I can feel
my IQ dropping below 86 as I rush out to find one of those wheel
games. Ok, seriously... people play higher variance games because of
the increased possibility of larger wins in spite of the higher
likelihood of a losing session.

When a reply of this nature is offered up by someone I respect as much
as I do you, I have to sit up and take notice ... maybe I've put my
foot into it (yet again :wink:

Re respective probabilities of a winning session (low variance vs.
high), let me offer up an example, on the extreme (applies to any game):

Take two 99% ER games -- one has 0 variance, the other has 200
variance. Isn't it the case that the "200 variance" presents a
tremendously greater expectation that a given session (of, say, 2
hours) will be profitable?

FWIW, my phrasing never involved advocating such play ... I merely note
that for some players the choice of a higher variance game (even if at
a modest ER expense) can be a very rational choice, depending upon
their personal play priorities. As long as the tradeoffs are
appropriately weighed, it's not surprising that some people might
sacrifice some EV for something else that enhances the pleasure they
get from play. (And, on occasion, I've sacrificed EV in a casino to
play a less smoke-ridden bank.)

···

------

Re your last point: There's no mistaking that the adrenaline rush of
big hits is what makes games such as DDB popular. However, that rush
isn't the only factor that leads people to play such games.

Face the fact that during a day's play of 9/6 Jacks, once you've lost
1000 credits, your hopes for a profitable day are pretty much down the
drain. However, the optimism of a 9/6 DDB player is likely to still be
running strong -- with a respectable amount of reason behind it.

I sense that for some people a prospect of winning the days battle
holds great value. Therefore a game that does a better job of keeping
that prospect alive may best suit those people.

And, finally, just to be clear -- higher variance doesn't mean a
greater likelihood of a losing session ... as I've stated, it's just
the opposite (assuming EV's are reasonably close). It does mean,
however, that losing sessions tend to be more costly.

- H.

#35

Harry,

You are making some excellent points and I've done a rather poor job of explaining my
point. Frankly I'd have to say in reviewing my post that I plain misspoke (or is it mis-
wrote ?). Surely increasing the variance CAN increase the % of winning sessions. That's
true as your simple example shows. But it is not always the case, and I was primarily
objecting to your phrase "will increase...". Plenty of simple examples can show this.
Consider two 100% games, both with a perfectly normal distributions (no such games
exist!). You can increase the variance of one game and not change the % of winning
sessions.

The important thing to remember here is that the "area" under the PDF is conserved. That
is, while we are allowed to change the shape, the PDF must always have the same area. In
these examples we are also approximately fixing the mean, which adds more
constraints.... So, if you increase the area above 100%-- which is what you do in you
example--, you must decrease it somewhere else. But you don't have to increase the area
above 100% to increase the variance. That is, you can increase the variance in other ways
that do not affect the % of winning sessions at all -- for example, just by "stretching" out
the tails of the distributions, leaving the part below 100% unchanged (vp example: reduce
the payout of a RF a wee bit and ad in a payout for a sequential RF that keeps the mean
the same, but increases the variance, but does not change the % of winning sessions)

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

Take two 99% ER games -- one has 0 variance, the other has 200
variance. Isn't it the case that the "200 variance" presents a
tremendously greater expectation that a given session (of, say, 2
hours) will be profitable?

F
And, finally, just to be clear -- higher variance doesn't mean a
greater likelihood of a losing session ... as I've stated, it's just
the opposite (assuming EV's are reasonably close). It does mean,
however, that losing sessions tend to be more costly.

- H.

#36

I agree, Harry. I've also sacrificed some EV to flee to a quiet
corner, in the back of a casino (notably Silverton) when they are
playing mega loud hard rock in the bar near the Optimum Bank.

I will also leave a high, upright 100%+ machine in favor of a comfy
slant-top with a <100% game when my back begins to vigorously
protest.

I do believe that when a player is distracted by smoke, noise, pain
or any annoyance that affects concentration, that maximum EV is
sacrificed by staying in that uncomfortable situation.
~Babe~

···

=========================================================
-In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

......(And, on occasion, I've sacrificed EV in a casino to play a
less smoke-ridden bank.)

#37

cdfsrule wrote:

Harry,

You are making some excellent points and I've done a rather poor
job of explaining my point. Frankly I'd have to say in reviewing
my post that I plain misspoke (or is it mis-wrote ?). Surely
increasing the variance CAN increase the % of winning sessions.
That's true as your simple example shows. But it is not always the
case, and I was primarily objecting to your phrase "will
increase...". Plenty of simple examples can show this.
Consider two 100% games, both with a perfectly normal distributions
(no such games exist!). You can increase the variance of one game
and not change the % of winning sessions.

In my original post containing that phrase the statement was prefaced
with the words, "When playing a negative expectation game".

You're absolutely right -- for a B/E game variance has relatively
insignificant impact on probability of a win (it has some, because
games aren't normally distributed), and in playing a positive game
variance will reduce rather than increase the likelihood that a
session will come out ahead (and a player who would sacrifice return
to seek out greater variance when "postive" plays are involved is in
need of an intervention ;).

You go on to note some particularly exceptional hypothetical cases
that could be constructed that would be neutral in terms of session
win probability without the constraint that the game be b/e. I'll
simply say that I sought to address the vp games that present
themselves in the casino. While I'm falling back on generalization
to an extent, it's a strong representation of the realities of actual
play choices.

- Harry

#38

Harry, do you have any PDF (or CDF's) to share with use for the wheel games? Perhaps you
have computed them for games that are in an actual casino?

I'm sure you are familiar with Jazbo's curves, PDFs and CDF's here: http://www.jazbo.com/videopoker/curves.html

BTW, It's easier for me to make reference to them, than post my own pictures here.
Please take a look at Jazbo's last plot on that page. It compares the CDF (cumulative
distribution function) for 5000 hands for set of different games (ignoring going broke
before playing 5000 hands).

You can read the probability of having a winning session right off that graph. What's
interesting here is the % of having a wining session for all the game studied here except
for JoB is about the same, 55-56% even though the variances and EV are significantly
different. Clearly, increasing the variance and increasing the EV are not enough to insure
an increased % of winning sessions!

Sure, you can argue that these positive EV games may not be found in many casinos anymore-- so they aren't actual play choices now-- but I think that if you re-did these
computations for games that are available now, you would find quite similar results:
despite what we seems to be common sense, increasing the variance and EV doesn't necessarily mean more winning sessions. [Aside: all it means is that when you do have a
winning session, it will likely be a larger win.]

Ok-- as noted already, Jazbo's computation ignores going broke (ruin) before reaching
5000. It's a little more involved, but one can easily enough repeat these computations (of
the PDF & CDF) taking into account ruin by assuming some starting bankroll. If the
starting bankroll is reasonable (ie, big enough so you have a high liklihood of playing the
desired # of hands), you will find that increasing the variance, somewhat paradoxically,
just makes things worse for the player-- in other words, the if the EV's are similar, a
larger variance just doesn't increase the % of winning sessions. Now, to be fair, I don't
have these curves for Wheel Poker. So I might be wrong regarding that game, with and
without the 6th coin. But that would be at odds with what I have computed for other
games.

The moral here is that the CDF just doesn't lie. Sure its best to compute the CDF for a
finite bank roll, taking ruin into account-- but as a quick-and-dirty approximation, the
straight-forward to compute simple CDF (like Jazboz's graphs) give a good-enough
answer, much better than an assumptions based on the EV and VAR alone. I'd go so far as
to say using the EV and VAR alone and "conventional wisdom" can be quite misleading
and amount to choosing facts to fit the pre-determined and sometimes erroneous
conclusions Likewise, I would strongly encourage those who do bother to compute all
the EVs and VAR's for the every growing variation of games out there then go on to
compute the CDF's for various sessions lengths (and RoR's). Its a straight forward process
that requires just a table of the final hand probabilities and payouts. Information gleaned
from these results (rather than the plots themselves) could be clearly presented to the
group and would go along way towards educating the VP playing public.

cdfsrule (ok, I can't resist: this is why I chose the moniker cdfs rule, well, because they
do, at least over the EV and Var, lol)

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

I'll simply say that I sought to address the vp games that present
themselves in the casino. While I'm falling back on generalization
to an extent, it's a strong representation of the realities of actual
play choices.

- Harry

#39

cdfsrule wrote:

Harry, do you have any PDF (or CDF's) to share with use for the
wheel games? Perhaps you have computed them for games that are in
an actual casino?

I'm sure you are familiar with Jazbo's curves, PDFs and CDF's here:
http://www.jazbo.com/videopoker/curves.html

You can read the probability of having a winning session right off
that graph. What's interesting here is the % of having a wining
session for all the game studied here except for JoB is about the
same, 55-56% even though the variances and EV are significantly
different. Clearly, increasing the variance and increasing the EV
are not enough to insure an increased % of winning sessions!

Sure, you can argue that these positive EV games may not be found
in many casinos anymore-- so they aren't actual play choices now--
but I think that if you re-did these computations for games that
are available now, you would find quite similar results:
despite what we seems to be common sense, increasing the variance
and EV doesn't necessarily mean more winning sessions. [Aside: all
it means is that when you do have a winning session, it will likely
be a larger win.]

There are a couple of clarification re the context of my original
statements you reference that should be made:

···

------

The topic we've been discussing was an tangential offshoot to the
Wheel Poker thread (and likely should have been retitled at some
point). The comment that initiated my first reply in this breakaway
thread was:

William Canevari wrote:

Why would anyone with an IQ above 85 want to play a VP game with a
greater variance but an identical or lower payout, when the original
game is also available on the same machine for the same
denomination?

All my comments since have be in reference to vp generally, not
specific to Wheel Poker.

------

The context in which I used the phase "exceptionally hypothetical
cases" (with the implication of "not generally found" was in reply to
your following statement:

That is, you can increase the variance in other ways that do not
affect the % of winning sessions at all -- for example, just by
"stretching" out the tails of the distributions, leaving the part
below 100% unchanged (vp example: reduce the payout of a RF a wee
bit and ad in a payout for a sequential RF that keeps the mean
the same, but increases the variance, but does not change the % of
winning sessions)

That's simply to say that your observations in the last paragraph
above doesn't directly address something I've said ... but it does
raise a very pertinent point to the discussion

------

The core example I've cited in asserting that variance increases
session win % when playing a negative expectation (for sessions of a
couple hours or so) is the extreme example of a hypothetical 0
variance game vs one of high variance (or any variance at all, for
that matter). I know you won't argue that it's not true of that
special case. I've gone on to suggest that it's also true in
comparing a low variance and high variance game such as 9/6 JB and
9/6 DDB.

My gut sense is that it's still true when you're talking 1000-3000
hands (the general sense of a "session" for most casual gamblers).
I'm thinking in terms of being down $600 or $800 30%-50% the way
through a session playing $1 vp ... it's seems much more likely that
you might end up with a winning session playing DDB than JB (mind
you, you success percentages in either case are fairly modest, but I
look for DDB to double or higher).

I don't know that to be the case ... it would clearly be helpful to
review Jazbo's charts closely ... however, I'm writing during down
time on a "non-play" LV trip (now isn't that an oxymoron ... what can
I say ... we're at CP on my wife's 6-day conference and I welcome the
break from play, not having to "earn our keep" :wink: Don't look for me
to follow up to confirm my gut sense here.

But you may be correct, when it comes to vp, generally speaking
variance may not be sufficient to shift the CDF curve when the
specific variance of the games involved is factored. That's
certainly true in most games for periods of 20,000+ hands, for
example.

However, the gist of my first sentiments here is that many gamblers
are motivated by, place derive the greatest value from, their session
to session experience. It's that specific scenario in which I've
asserted that I can see where play of a game such as DDB rather than
JB (to cite an example fitting WC's post) could be quite "rational".

------

In the balance of your post you make a few observations about CDF's.
I don't have the time to address those specifically, but I will say
that I agree: In coming to grips with the realities of vp play,
CDF's have a strong role to play ... in many respects giving a deeper
understanding of play than simple stats such as ER and variance.

- Harry

#40

Harry,

I was responding to something your wrote in message 87890.
Here it is again:

When playing a negative expectation game such as the examples above
(before factoring other play incentives), if the return is reasonably
close the higher variance game will yield the greater percentage of
winning sessions.

I was taking some issue with your statement (above), which I believe is false in general for
VP games. Sure, one can certainly find plenty of hypothetical situations, like the zero-
variance game you sited, for which your statement is true, but those situations are just
not, well, relevant to any casino VP games I know.

It is pretty easy to show how your statement isn't always true for a real VP game. But first
let me make sure I have what you were claiming correct...

You seem to be saying that, for 2 VP games, both with EV < 1 (or 100%) and both EV's
reasonably similar, that the game with the higher variance has a higher probability of
producing a winning session-- or equivalently, it produces a greater percentage of
winning sessions.

I am saying that is certainly not always true, and is therefore false (or not a general result)

Perhaps the easiest way to see is to to take our favorite EV < 1 game. I'll take pick'em. I
like it better than JoB.. and I won't use and CDF's!

Here's the pay table for FP pick'em, EV = 99.95% = 0.9995,

2-3-5-11-15-18-120-239.8-1200

When you play pick'em you can either lose your bet, or win more than 2 bets.
If you have a bankroll of 1 bet, after 1 hand you either have 0 bets left, or 2 or more bets
in you bankroll.
The probability of having won (or having a winning session after this first hand), is easy to
compute.
Its 1 minus the probability of losing your bet.
Interestingly, the variance plays NO direct role in determining the probability of having
won that hand!
It is simply just the probability of getting "nada" that you need to know.
So, imagine that I alter the variance of the game a bit.
I'm free to do it in anyway that I want to, so that the EV is about the same (whatever that
means!).
Indeed, I can do it so the EV is exactly the same if I am careful and not worry about what
"almost the same" means.
But that doesn't matter. What matters is whether or not increasing the variance increases
the likelihood of winning.
Well, that's an easy question to answer for this simple case.
Nope, increasing the variance doesn't increase the likelihood of having a wining session.
The only thing that affects the likelihood of winning is the probability of losing or getting
nada.
So for your statement to be true (that is, never false), increasing the variance would always
have to decrease the probability of getting nada.
That's not going to happen.

Ok, I know what you are going to say, 1 hand is not a session. Well, that's silly.
One hand can be session. But assume it isn't a session. Assume we need more hands to
make a session.
I don't know how many we need, but assume its more than 1. Say a few thousand.
What do you think the result will be for this case (assuming you have enough money to
play such a session, which is another red herring, btw) ?
Well I suggest you calculate it.. because you probably won't take my word for it.
The problem is when you calculate this, you will end up with a CDF (or the integral of the
PDF).
So I guess I'll stop here. Offline I'll work on a general "proof" that doesn't require a CDF.

If any can come up with a simple (or complicated!) argument that shows that longer
sessions always behave differently,
I certainly like to see it.