Stud Action vs. Hold'em Action -- Tom McEvoy in CARD PLAYER
Alan Bostick
In Tom McEvoy's column in the 11/28/97 issue of CARD PLAYER, he answers
a reader's question about the difference in the level of action between
7-card stud and Texas hold'em at medium limits.
"It has been my general experience," McEvoy writes, "that a hold'em
game that is played at the same limits as a stud game is, without
question, the bigger game . . . for a very simple reason. Seven-card
stud is designed to isolate and try to get the hand heads-up very early,
if possible. . . . With more players to start in a hold'em game, you
will see far more multiway pots than in stud. For a long time now, I
have thought that most of the $10-$20 hold'em games in Las Vegas are the
equivalent of a $15-$30 seven-card stud game."
I've read many times here in r.g.p. that low-limit 7-card stud is a very
different animal from mid- and high-limit games. Since McEvoy surely is
correct about his experience at the betting limits he talks about, my
own opposite experience at low limits confirms this difference between
lower- and upper-limit stud games.
I'm using variance as a measure of the level of action. A big variance
means big swings in stack size, and a small variance means smaller
swings.
I find that after logging 58 hours of tracked play, my variance at $2-$4
7-card stud is 4250 (big bets)**2 per hour, while after tracking my $2-$4
hold'em play for 26 hours my variance is 1250 (big bets)**2 per hour.
This correlates with my subjective feel for the two games at this level,
that my wins and losses have been bigger at stud than at hold'em. I'm
comfortable with an initial buy-in of $40 in the hold'em game; but I get
edgy unless I start the stud game with $80 in front of me.
What makes the difference? I think it a combination of two factors
working together. First, the games I play are typical California
no-foldem games. The isolation at third street in stud that McEvoy
talks about just doesn't happen. While hands that are heads-up at the
river are more common in stud than hold'em, a majority of hands in these
games see at least three players at the river.
The second factor is the additional betting round in stud. With more
players going farther, those extra big bets add up, meaning that there
are bigger pots to be won in the stud games.
(Every math wonk who reads this post ought to notice that I haven't
logged very many hours with either game at this point. I am very much
aware of the degree to which this calls into question the validity of my
quantitative results.)
I would love to hear about other people's experience here.
--
Alan Bostick | "Try thinking of love or something. Amor vincit
mailto:abos...@netcom.com | insomnia."
news:alt.grelb | Christopher Fry, A SLEEP OF PRISONERS
http://www.alumni.caltech.edu/~abostick
Barbara Yoon
Alan Bostick:
> In Tom McEvoy's column in the 11/28/97 issue of CARD PLAYER,
> he answers a reader's question about the difference in the level of
> "It has been my general experience," McEvoy writes, "that a hold'em
> game that is played at the same limits as a stud game is, without
> question, the bigger game...for a very simple reason. Seven-card
> stud is designed to isolate and try to get the hand heads-up very early,
> if possible... With more players to start in a hold'em game, you will
> see far more multiway pots than in stud. For a long time now, I have
> thought that most of the $10-$20 hold'em games in Las Vegas are
> the equivalent of a $15-$30 seven-card stud game."
> I've read many times here in r.g.p. that low-limit 7-card stud is a very
> different animal from mid- and high-limit games. Since McEvoy surely
> is correct about his experience at the betting limits he talks about, my
> own opposite experience at low limits confirms this difference between
> lower- and upper-limit stud games. ... What makes the difference?
> I think it a combination of two factors working together. First, the
games
> I play are typical California no-foldem games. The second factor is the
> additional betting round in stud. With more players going farther...
Yes, the extra betting round in stud, the greater range of possibilities of
what an opponent might have, plus the fact that "chasing" is not as swiftly
and surely punished as in hold'em, giving more license to those players
who don't need much of an excuse...
Richard Mallozzi
Alan Bostick <abos...@netcom.com> wrote:
>
>I find that after logging 58 hours of tracked play, my variance at $2-$4
>7-card stud is 4250 (big bets)**2 per hour, while after tracking my $2-$4
>hold'em play for 26 hours my variance is 1250 (big bets)**2 per hour.
>This correlates with my subjective feel for the two games at this level,
>that my wins and losses have been bigger at stud than at hold'em. I'm
>comfortable with an initial buy-in of $40 in the hold'em game; but I get
>edgy unless I start the stud game with $80 in front of me.
>
Is that variance really 4250 (big bets)^2 per hour, or 4250 (dollars)^2
per hour? My own experience is similar if you mean 4250 (dollars)^2
per hour. I have even less data than you, though; only 32 hours. And
I don't play hold'em (yet). I believe I play exactly the same game
as you. $2-4 stud at the Oaks? That $80 comfortable buy-in is the
same for me as well. So either I have computed wrong, or your variance
is in (dollars)^2 rather than (big bets)^2.
By the way, in which game to you have a higher average win?
Rich
Alan Bostick
In article <65dseq$ci3$1...@agate.berkeley.edu>,
mall...@physics10.berkeley.edu (Richard Mallozzi) wrote:
> Is that variance really 4250 (big bets)^2 per hour, or 4250 (dollars)^2
> per hour? My own experience is similar if you mean 4250 (dollars)^2
> per hour. I have even less data than you, though; only 32 hours. And
> I don't play hold'em (yet). I believe I play exactly the same game
> as you. $2-4 stud at the Oaks? That $80 comfortable buy-in is the
> same for me as well. So either I have computed wrong, or your variance
> is in (dollars)^2 rather than (big bets)^2.
It is indeed (big bets)^2, not (dollars)^2. While I (of course) track
my performance in dollars, I do my statistical analysis in terms of big
bets. I do this so that I have a better handle on comparing my results
at different limits.
Let's make sure we're not comparing apples and oranges. To calculate
variance, I'm using the formula I dug out of r.p.g. with DejaNews that
I am told what Mason Malmuth presents as the maximum likelihood
estimator for win rate and variance thereof:
W[I] is the win or loss of the Ith session.
(counted in either big bets or dollars; it doesn't matter as
long as you're consistent)
T[I] is the duration in hours of the Ith session.
WSQ[I] = W[I] * W[i] / T[I] is the squared win rate per hour.
WTOT is total winnings = Sum( W[I] )
TTOT is total session time = Sum( T[I] )
Then Win Rate is simply WTOT / TTOT
and Variance is Sum( WSQ[I] ) - (WTOT * WTOT / TTOT)
Note that there has been considerable debate in r.g.p. as to whether
maximum likelihood is the best estimator, especially for a small number
of sessions. Let's not go there.
>
> By the way, in which game to you have a higher average win?
>
I am slightly ahead at $2-$4 Hold'em and rather behind at $2-$4 stud.
Most of my stud losses are due to a series of sessions last summer of
playing on tilt and losing big. Looking at graphs of my performance,
though (aren't computers wonderful?) I see that if I leave those
sessions out of consideration, my trend of winning at stud outstrips
that of winning at hold'em. Leaving sessions out, though, is cheating,
both statistically and in terms of actual bankroll.
Interestingly, when measured both in big bets and dollars, my
performance at the Oaks' $1-$2 Hold'em game outstrips both $2-$4 games.
I'm using it as a bankroll pump while I get my higher-limit games up to
snuff.
William Chen
Grr... I'm in a bad mood today so bear with me.
In article <ugve08m9...@netcom.com>,
abos...@netcom.com (Alan Bostick) wrote:
>In article <65dseq$ci3$1...@agate.berkeley.edu>,
>mall...@physics10.berkeley.edu (Richard Mallozzi) wrote:
>
>
>> Is that variance really 4250 (big bets)^2 per hour, or 4250 (dollars)^2
>> per hour? My own experience is similar if you mean 4250 (dollars)^2
>
>It is indeed (big bets)^2, not (dollars)^2. >
God--that's a standard deviation of around 65 BB/hour. That just cannot be, think about it,
your average swing is $260/hr in a 2-4 game? Even if you play every hand... I'm still
skeptical.
> W[I] is the win or loss of the Ith session.
> (counted in either big bets or dollars; it doesn't matter as
> long as you're consistent)
>
> T[I] is the duration in hours of the Ith session.
>
> WSQ[I] = W[I] * W[i] / T[I] is the squared win rate per hour.
>
> WTOT is total winnings = Sum( W[I] )
>
> TTOT is total session time = Sum( T[I] )
>
> Then Win Rate is simply WTOT / TTOT
>
> and Variance is Sum( WSQ[I] ) - (WTOT * WTOT / TTOT)
Wait, shouldn't you like divide the last result by the number of sessions?
I mean think about it, suppose you had 100 1 hr sessions, 50 where you win $10 and
50 where you lose $10. Shouldn't your variance be 100 and not 10,000 like it is here?
Don't really mean to get on your case but as a math TA it really gets on my nerves when
folks just use a math formula without a little common sense. I have had students find volumes
of solids and come up with answers that were clearly negative like 16sqrt(3)-100*pi.
Anyway the real formula is the formula you quoted divided by the number of sessions according
to Malmuth or the number of sessions-1 for an unbiased estimator.
>
>Note that there has been considerable debate in r.g.p. as to whether
>maximum likelihood is the best estimator, especially for a small number
>of sessions. Let's not go there.
We resolved this I thought.
>
>
>>
>> By the way, in which game to you have a higher average win?
>>
>
>I am slightly ahead at $2-$4 Hold'em and rather behind at $2-$4 stud.
>Most of my stud losses are due to a series of sessions last summer of
>playing on tilt and losing big. Looking at graphs of my performance,
>though (aren't computers wonderful?) I see that if I leave those
>sessions out of consideration, my trend of winning at stud outstrips
>that of winning at hold'em. Leaving sessions out, though, is cheating,
>both statistically and in terms of actual bankroll.
>
>Interestingly, when measured both in big bets and dollars, my
>performance at the Oaks' $1-$2 Hold'em game outstrips both $2-$4 games.
>I'm using it as a bankroll pump while I get my higher-limit games up to
>snuff.
As an aside:
There was some discussion in the Oaks 15-30 last time whether the 1-2 game was beatable.
I claimed it was and most people just looked at me like I was nuts. Actually, when you are
ready you should try the 6-12 stud they have been spreaing regularly. It's my favorite game
at the Oaks--I estimate I have made around 10K this year from that and the 9-18 game alone.
(At around 25 an hour since I started keeping stats in September). The players are not
too tough and the varaince should be about the same as the 4-8 game.
I believe the recent controversy at Oaks was about whether the 15-30 stud was a bigger game
than the 15-30 hold'em and that was the issue the McEvoy (sp?) addressed in Card Player.
My opinion is that many of the props jusst don't wanna play 15-30 stud and others were trying
to get an increase in pay, but there is some legitmacy in their complaints. I don't think
Oaks low limit results translates to Oaks mid limit (15-30) because the games are so different,
in both hold'em and stud. I have a higher variance at 15-30 stud (350/hr to 227/hr) but I
think there's a bias. I play the stud whehever they spread it (every Friday for folks who
want to come down) and generally play hold'em when it's favorable. Also I'm just more
aggressive at stud, but I think at Oaks the stud game is higher variance most of the time
unless the 15-30 gets capaholic before the flop because:
1) It's easier to get drawn out on in stud.
2) When you get drawn out on, you have to pay off more often because the river card is not shown.
In hold'em you can sometimes fold the river if you put your opponent on a flush draw. In stud
well he either made it or he didn't--does he have a tell?
3) because of 1) YOU have to chase in more situations where you know you are behind but it
costs too much to throw the hand away. The classic example is a small pair with a big kicker
where most cards are live. Generally in hold''em when you have a smaller pair against a
certain bigger pair on the flop, you can just muck.
4) The extra round of betting does matter--there are basically two turn cards instead of 1.
I think the most significant factor is the players--in the 15-30 stud most of the players are
not the usual nevada rocks--lots of action goes into those pots.
Bill
Bill
Barbara Yoon
Richard Mallozzi:
>>> Is that variance really 4250 (big bets)^2 per hour,
>>> or 4250 (dollars)^2 per hour?
Alan Bostick::
>> It is indeed (big bets)^2, not (dollars)^2.
William Chen:
> God -- that's a standard deviation of around 65 BB/hour.
> ...just cannot be...average swing is $260/hr in a 2-4 game?
> Even if you play every hand... Anyway the real formula is
> the formula you quoted divided by the number of sessions
> according to Malmuth or the number of sessions-1 for an
> unbiased estimator.
B.Y.:
Perhaps we could straighten this out if Alan would make up a
small example (say 3 sessions) to show us how he calculated...
Alan Bostick:
>> ...there has been considerable debate in r.g.p. as to whether
>> maximum likelihood is the best estimator...
William Chen:
> We resolved this I thought.
B.Y.:
Yes, Malmuth's variance formula, while "maximum likelihood,"
is always BIASED TOO LOW...
William Chen [on why action in stud more than hold'em]:
> 1) ...easier to get drawn out on in stud.
> 2) ...have to pay off more often because the river card is not shown.
> 3) ...chase in more situations where you know you are behind...
> 4) ...extra round of betting...
True...re-stating points by Alan and me in earlier posts...
Alan Bostick
In article <ugve08m9...@netcom.com>,
abos...@netcom.com (Alan Bostick) wrote:
> Let's make sure we're not comparing apples and oranges. To calculate
> variance, I'm using the formula I dug out of r.p.g. with DejaNews that
> I am told what Mason Malmuth presents as the maximum likelihood
> estimator for win rate and variance thereof:
>
> W[I] is the win or loss of the Ith session.
> (counted in either big bets or dollars; it doesn't matter as
> long as you're consistent)
>
> T[I] is the duration in hours of the Ith session.
>
> WSQ[I] = W[I] * W[i] / T[I] is the squared win rate per hour.
>
> WTOT is total winnings = Sum( W[I] )
>
> TTOT is total session time = Sum( T[I] )
>
> Then Win Rate is simply WTOT / TTOT
>
> and Variance is Sum( WSQ[I] ) - (WTOT * WTOT / TTOT)
Bill Chen is right: this should be
Variance = ( Sum( WSQ[I] ) - (WTOT * WTOT / TTOT) ) / N
I've updated my spreadsheets accordingly. My new estimates for
my variance are 200 BB^2/hr for $2-$4 stud and 120 BB^2/hr for $2-$4 Hold'Em.
Really, I put these "mistakes" into my posts on purpose, just to find out
who's on their toes. ;-)
Andrew Morton
William Chen wrote:
> As an aside:
> ... the 6-12 stud they have been spreaing regularly. It's my favorite game
> at the Oaks--I estimate I have made around 10K this year from that and the 9-18 game alone.
> (At around 25 an hour since I started keeping stats in September). The players are not
> too tough and the varaince should be about the same as the 4-8 game.
I don't understand why the variance in the 6-12 stud should be the same as the variance in the 4-8
stud. I also don't understand why you lump your 6-12 stud results in with your 9-18 (stud?)
results. Of course, I agree that if you're making 25/hr after 400 hours (ie, 10K) in a 6-12 anything
game, then it's very likely that it's an excellent game.
> I don't think
> Oaks low limit results translates to Oaks mid limit (15-30) because the games are so different,
> in both hold'em and stud.
This makes a lot of sense to me, _especially_ when trying to compare 1-4 stud with 15-30 stud and
15-30 holdem.
> I have a higher variance at 15-30 stud (350/hr to 227/hr) but I
> think there's a bias. I play the stud whehever they spread it (every Friday for folks who
> want to come down) and generally play hold'em when it's favorable. Also I'm just more
> aggressive at stud, but I think at Oaks the stud game is higher variance most of the time
> unless the 15-30 gets capaholic before the flop because:
>
This was for me the most interesting part of your post. I'll admit that I have been one of those
guys who thought that 15 stud was about as big as 12 holdem or so. I don't really have quite enough
data at 15stud to meaningfully calculate my SD in that game, though. But your difference is so large
I have to ask how many data points you're using to get your 350/hr figure. eg, in my experience, 30
data points (ie, sessions) is not really enough to pin down your SD using mason's formula, although
it would certainly be enough to distinguish the number 350 from a number like 227.
Also, it's always been my impression that at the 15-30 level, aggression is much less appropriate in
7stud than in holdem. winning stud players who come to my holdem games usually seem to play fairly
passively, and winning holdem players who go to the stud game often appear to play too aggressively,
although this is my own subjective judgment and i am no stud authority.
> 1) It's easier to get drawn out on in stud.
> 2) When you get drawn out on, you have to pay off more often because the river card is not shown.
> In hold'em you can sometimes fold the river if you put your opponent on a flush draw. In stud
> well he either made it or he didn't--does he have a tell?
> 3) because of 1) YOU have to chase in more situations where you know you are behind but it
> costs too much to throw the hand away. The classic example is a small pair with a big kicker
> where most cards are live. Generally in hold''em when you have a smaller pair against a
> certain bigger pair on the flop, you can just muck.
> 4) The extra round of betting does matter--there are basically two turn cards instead of 1.
>
> I think the most significant factor is the players--in the 15-30 stud most of the players are
> not the usual nevada rocks--lots of action goes into those pots.
Again based solely on my own subjective impressions, this last reason is more compelling than all the
other 4 reasons. Typically, these 4 are not sufficient to make stud a bigger game than holdem,
unless the ante is raised proportionally much higher than it is at the 15-30 level.
Having said all this, I'll try to calculate my stud variance as soon as I can; this thread has really
piqued my curiosity.
Andy
"And I thought McEvoy had finally written something that made sense..."
>
>
> Bill
>
> Bill
MasonM...@twoplustwo.com
Barbara Yoon wrote:
>
> Yes, Malmuth's variance formula, while "maximum likelihood,"
> is always BIASED TOO LOW...
The following repeats a previous post since there still must be some
question as to the validity of the maximum likelihood estimator of the
variance (and therefore standard deviation) that is presented in my book
GAMBLING THEORY AND OTHER TOPICS. Here is what I wrote in a previous
post.
I thought I would take a moment to settle the controversy concerning
the maximum likelihood estimator that I use in my book GAMBLING THEORY
AND OTHER TOPICS to estimate the standard deviation for a particular
poker game. When I was in graduate school one of the statistical texts
that I used was STATISTICAL THEORY AND METHODOLOGY IN SCIENCE AND
ENGINEERING by K. A. Brownlee. This text is part of the Wiley Series in
Probability and Mathematical Statistics. On page 91 it says the
following about this estimator:
"A method of estimation which usually in practice works out
satisfactoily is the method of maximum likelihood"
"Maximum likelihood estimators have the desirable properties of being
consistent and asymtotically normal and asymptotically efficient for
large samples under general conditions. ... Maximum likelihood
estimators are often biased, but frequently the bias is removable by a
simple adjustment."
What this means is that for a large sample size this method will give
you a good estimate of the standard deviation. On page 61 in the fourth
edition of GAMBLING THEORY AND OTHER TOPICS I wrote:
"A good rule of thumb is to have at least 30 observations (playing
sessions) for the estimate to be reasonably accurate. However, the more
the better, unless for some reason you think the game for which you are
trying to estimate your standard deviation has changed significantly
over some particular period of time."
I think it should be clear what the above means. But to set the record
straight it means that this is a good estimator as long as you collect
the required data as specified. Using a sample size of 2 to attempt to
show that this estimator is inaccurate is just not good statistics.
If any of you would like to discuss this some more with me or discuss
any of the results that I have published based on this estimator you can
respond to our forum at www.twoplustwo.com.
Barbara Yoon
B.Y.:
>> Yes, Malmuth's variance formula, while "maximum likelihood,"
>> is always BIASED TOO LOW...
Mason Malmuth:
> ...since there still must be some question as to the validity of the
> maximum likelihood estimator of the variance (and therefore
> standard deviation) that is presented in my book...
>
> [quoting from statistics text book]: "Maximum likelihood estimators
> have the desirable properties of being consistent and asymtotically
> normal and asymptotically efficient for large samples under general
> conditions. ...Maximum likelihood estimators are often biased, but
> frequently the bias is removable by a simple adjustment."
>
> I think it should be clear what the above means...
Yes, it means that maximum likelihood estimators are generally good
enough for large samples, but they are often BIASED, as is in fact the
case with the formula at issue here...
Alan Bostick
In article <65guqp$3...@dfw-ixnews11.ix.netcom.com>,
William Chen <w_c...@ix.netcom.com> wrote:
> In article <ugve08m9...@netcom.com>,
> abos...@netcom.com (Alan Bostick) wrote:
> > W[I] is the win or loss of the Ith session.
> > (counted in either big bets or dollars; it doesn't matter as
> > long as you're consistent)
> >
> > T[I] is the duration in hours of the Ith session.
> >
> > WSQ[I] = W[I] * W[i] / T[I] is the squared win rate per hour.
> >
> > WTOT is total winnings = Sum( W[I] )
> >
> > TTOT is total session time = Sum( T[I] )
> >
> > Then Win Rate is simply WTOT / TTOT
> >
> > and Variance is Sum( WSQ[I] ) - (WTOT * WTOT / TTOT)
>
> Wait, shouldn't you like divide the last result by the number of
> sessions?
Ayup. I already posted a correction.
>
> Anyway the real formula is the formula you quoted divided by the number
> of sessions according to Malmuth or the number of sessions-1 for an
> unbiased estimator.
>
>
> >
> >Note that there has been considerable debate in r.g.p. as to whether
> >maximum likelihood is the best estimator, especially for a small number
> >of sessions. Let's not go there.
>
>
> We resolved this I thought.
I don't think we have.
I've been boining up on statistical inference this morning. My (only)
reference is some lecture notes handed out in a mathematical methods
class long ago in my misspent youth as a grad student: LECTURES ON
PROBABILITY AND STATISTICS by G. P. Yost (Lawrence Berkeley Laboratories
technical publication no. LBL-16993, 1984).
I haven't read Malmuth's GAMBLING THEORY AND OTHER TOPICS, so I'm not
prepared to assess his presentation of Mark Weitzman's derivation of
his expressions for poker win rate and variance. (Let's call it the
Malmuth-Weitzman, or M-W, estimator. But I am willing to take their
word for it that it is a maximum-likelihood estimator.
Note that constructing a maximum-likelihood estimator demands assuming a
particular form of the probability distribution function of the data one
wishes to model. Trying to imagine the p.d.f. for the outcome of a
single hand of hold'em makes my brain hurt, but fortunately the Central
Limit Theorem tells us that the more hands one plays in a session, the
more the p.d.f. for the whole session's outcome approximates a Gaussian.
I would guess (without seeing the derivation) that the M-W estimator is
in fact the maximum-likelihood estimator for a Gaussian distribution.
You are quite correct that the M-W estimator is biased. But in the
limit of many sessions, that bias gets asymptotially small, and it and
your unbiased estimator (where 1/n is replaced by 1/(n-1) ) converge.
Moreover, a biased estimator is not necessarily a bad estimator.
Sometimes one wishes to introduce a bias into an estimator deliberately.
Consider the mean-squared error, MSE, defined as the expectation of
(V - Vtrue)^2, where V is the estimated variance of one's sample data
and Vtrue is the actual variance of the underlying p.d.f. If one
constructs an estimator of form V = A *sum(( Xi - Xtrue)^2) where Xtrue is
the true mean of the underlying p.d.f. and A is a parameter of our own
choice.
If we compute the MSE of this V, and differentiate it with respect to A,
it can be shown that the A that minimizes MSE is 1/(n+1), resulting in
an estimator for variance with even more bias than the M-W estimator;
but is *better* than either the M-W estimator or the unbiased estimator,
if one considers the mean-squared error to be a figure of merit for
evaluating estimators. Note that in the limit of many sessions, all
three estimators converge.
In order for any of these estimators to be useful, they have to be based
on enough samples of the data. For the M-W estimator, Mason Malmuth
recommends at least thirty sessions. For N=30, the difference between
these three estimators is only a few percent. This is going to be quite
small compared to the expected error in our estimate.
(If V is our best guess of the actual variance, and if sessions are long
enough for the Central Limit Theorem to apply, then our best estimate
for the *variance of V* will be given by 2 * V^2 / (n-1), and the square
root of this quanitity will give us an indication of the error in our
guess of V. For thirty play sessions, this will be rather larger than a
few percent.)
And all of these estimators may be inappropriate for predicting
real-life play. Suppose, for example, an otherwise solid player is
given to occasional sessions-on-tilt, rife with bad decisions and
significant losses. If this player plotted a histogram of her results,
she might see a broad main cluster of wins centered in the positive
area, with a handful of outliers deep in the negative.
These outliers can pose significant problems for estimating future
results. They are real data with real effect on the player's bankroll.
But they can invalidate the assumptions that go into constructing
estimators -- outliers can be big trouble for maximum likelihood, for
example. Dealing with data like this can require considerable
statistical savvy.
> As an aside:
> There was some discussion in the Oaks 15-30 last time whether the 1-2
> game was beatable. I claimed it was and most people just looked at me
> like I was nuts. Actually, when you are ready you should try the 6-12
> stud they have been spreaing regularly. It's my favorite game at the
> Oaks--I estimate I have made around 10K this year from that and the 9-18
> game alone. (At around 25 an hour since I started keeping stats in
> September). The players are not too tough and the varaince should be
> about the same as the 4-8 game.
I'm not ready. I've played the 4-8 game three times, and in all three I
spewed away my buy-in much more quickly than I ought to have if I were
on top of the game. Building up my skills is going to take some time.
The big hole in my game, both stud and hold'em, is reading other
players' hands.
The $1-$2 hold'em game at the Oaks *can* be beat, and I'm beating it.
It's time for me be more adventurous in the $2-$4 and $3-$6 games.
>
>
> I believe the recent controversy at Oaks was about whether the 15-30
> stud was a bigger game than the 15-30 hold'em and that was the issue the
> McEvoy (sp?) addressed in Card Player. My opinion is that many of the
> props jusst don't wanna play 15-30 stud and others were trying to get an
> increase in pay, but there is some legitmacy in their complaints. I
> don't think Oaks low limit results translates to Oaks mid limit (15-30)
> because the games are so different, in both hold'em and stud. I have a
> higher variance at 15-30 stud (350/hr to 227/hr) but I think there's a
> bias. I play the stud whehever they spread it (every Friday for folks
> who want to come down) and generally play hold'em when it's favorable.
> Also I'm just more aggressive at stud, but I think at Oaks the stud
> game is higher variance most of the time unless the 15-30 gets
> capaholic before the flop because:
>
> 1) It's easier to get drawn out on in stud.
> 2) When you get drawn out on, you have to pay off more often because the
> river card is not shown. In hold'em you can sometimes fold the river if
> you put your opponent on a flush draw. In stud well he either made it
> or he didn't--does he have a tell?
> 3) because of 1) YOU have to chase in more situations where you know you
> are behind but it costs too much to throw the hand away. The classic
> example is a small pair with a big kicker where most cards are live.
> Generally in hold''em when you have a smaller pair against a certain
> bigger pair on the flop, you can just muck.
Why would one let oneself be caught in this situation in the first
place? Unless everyone else's upcards are low, the hand is liable to be
third-best or worse at third street. If one is drawing to a flush or
straight, catching a low pair hardly counts as improvement.
There are times when the pot and implied odds tell one to keep going
with a drawing hand. That's a positive-EV play, but it does raise one's
variance, it does indeed. The same is true in hold'em, but the extra
betting round in stud magnifies the effect.
> 4) The extra round of betting does matter--there are basically two turn
> cards instead of 1.
>
> I think the most significant factor is the players--in the 15-30 stud
> most of the players are not the usual nevada rocks--lots of action goes
> into those pots.
Don't tempt me. . . .
Barbara Yoon
Alan Bostick:
>>> Note that there has been considerable debate in r.g.p.
>>> as to whether maximum likelihood is the best estimator,
>>> especially for a small number of sessions.
William Chen:
>> We resolved this I thought.
Alan Bostick:
> I don't think we have. Malmuth-Weitzman...I am willing to take their
> word for it that it is a maximum-likelihood estimator. I would guess
> (without seeing the derivation) that the M-W estimator is in fact the
> maximum-likelihood estimator for a Gaussian distribution. You are
> quite correct that the M-W estimator is biased. But in the limit of
> many sessions, that bias gets asymptotially small...
RESOLVED -- Malmuth variance (standard deviation squared) formula
is "maximum likelihood" allright, but mathematically BIASED (too low)...
William Chen
In article <347CA12B...@ix.netcom.com>,
Andrew Morton <and...@ix.netcom.com> wrote:
>
>
>William Chen wrote:
>
>> As an aside:
>> ... the 6-12 stud they have been spreaing regularly. It's my favorite game
>> at the Oaks--I estimate I have made around 10K this year from that and the 9-18 game alone.
>> (At around 25 an hour since I started keeping stats in September). The players are not
>> too tough and the varaince should be about the same as the 4-8 game.
>
>I don't understand why the variance in the 6-12 stud should be the same as the variance in the 4
8
>stud. I also don't understand why you lump your 6-12 stud results in with your 9-18 (stud?)
>results. Of course, I agree that if you're making 25/hr after 400 hours (ie, 10K) in a 6-12
anything
>game, then it's very likely that it's an excellent game.
Well, I haven't played 4-8 but the variance should be the same because the antes are the
same--$0.50. Sure the betting on future rounds is higher but the pots are generally bigger
in 4-8.
Well I have only kept good per session records since September--before that I didn't really
have a job and didn't take the TA job that most grad students are offered, so it was relatively
easy to see how much I won without keeping records--my monthly expenses were mostly
fixed and I had a small bank account with no investments for around a year and a half.
The rate was for 110 hours since September for the two limits (I shouldn't play this
much poker now that I have a job). Basically, I lump the two games toghther because the
players are the same--often what happens is that a 6-12 gets "converted" to a 9-18 and
I am often too lazy to count how much I have in front of me when the game changes. So the
earn rate may *not* be accurate at all but the amount I quoted I would say is accurate to
within 2K--this was my "main" game earlier this year. Hmm actaully thinking about it
the earn rate is probably a bit *LOWER*...
Over the summer I started doing consulting (variable hours, variable pay) and because of the
extra income diversified some of my money, and I *think* I had a bad summer pokerwise, but
I couldn't tell--well I probably can if I get records from my bank and find out how much I
made consulting but... So I started to follow the advice that I have been giving everyone and
started keeping records.
I'm very bad at keeping records though (laziness). I balanced my checkbook for exactly two
months and then figured to hell with this--in college I always knew within $100 how much
money I had in any case.
>> I don't think
>> Oaks low limit results translates to Oaks mid limit (15-30) because the games are so different,
>> in both hold'em and stud.
>
>This makes a lot of sense to me, _especially_ when trying to compare 1-4 stud with 15-30 stud and
>15-30 holdem.
>
>> I have a higher variance at 15-30 stud (350/hr to 227/hr) but I
>> think there's a bias. I play the stud whehever they spread it (every Friday for folks who
>> want to come down) and generally play hold'em when it's favorable. Also I'm just more
>> aggressive at stud, but I think at Oaks the stud game is higher variance most of the time
>> unless the 15-30 gets capaholic before the flop because:
>>
Bill
Bill
William Chen
In article <65l5a2$eis$1...@winter.news.erols.com>,
"Barbara Yoon" <by...@erols.com> wrote:
>
>RESOLVED -- Malmuth variance (standard deviation squared) formula
>is "maximum likelihood" allright, but mathematically BIASED (too low)...
>
>
>
Since it seems only 3 people in the world are really interested in the intricacies of
this argument, this is the last I will say about this subject for a while unless something
new comes along.
The M-W formula can be made unbiased by multiplying by n/(n-1). The M-W or the new revised
forumla does a decent job (in my opinion--since these are poker sessions and not just
samples form a gaussian I can't offer a proof) for 30+ samples. Which formula is
better? Well, define "better" and I can tell you. If being unbiased is a major criterion
then well...
Bill
Bill
Alan Bostick
> RESOLVED -- Malmuth variance (standard deviation squared) formula
> is "maximum likelihood" allright, but mathematically BIASED (too low)...
Many maximum likelihood estimators are biased. This does not prevent them
from being useful.
Paul R. Pudaite
In article <65ibj8$r8q$1...@winter.news.erols.com>, "Barbara Yoon" <by...@erols.com> wrote:
>Yes, it means that maximum likelihood estimators are generally good
>enough for large samples, but they are often BIASED, as is in fact the
>case with the formula at issue here...
For any sample size, the bias will be less than the variance estimate's
standard error. Unbiasing the formula isn't difficult, but it doesn't
make your estimates substantially more accurate.
Paul R. Pudaite
pud...@pipeline.com