It is a commonly held belief that raising preflop
increases variance.  I have never seen any solid
reasoning for this commonly heald belief.

While this is something that I too have believed
to be true, some recent investigations (done by
Gary Carson) have lead me to believe that my own
intuition on the subject may be false.

Therefore I bring the question to RGP looking for
some foundation for my intuition to stand.

In general, does preflop raising increase variance?

Under what specific circumstances does preflop raising
reduces variance?

What I am looking for is more than just testimonials.
Rather, I am looking for something more experimental
or mathematical upon which to rest my intuition.

Anyone up to the challenge?

- Andrew

In the stereotypical low-limit games, where two or three bets won't drive
anyone out who would call a single bet, raising increases variance, because you
are increasing the amount you lose if beat, and increasing the amount you win
if not beat, while not affecting the odds of winning.

In the hypothetical game of educated players, my understanding is a bit
shakier, but I think it works like this: raising may actually decrease your
variance; by driving out players with hands that are worth one bet but not two
or three, you decrease your chances of being drawn out on. You therefore
increase your chances of winning (though you are increasing the amount of your
money at risk, without necessarily increasing the pot size, since one player
opponent paying two bets nets less than two or three opponents paying one bet.)

- JC -

-JC-

According to JChurch602 <jchurch...@aol.com>:

This *seems* correct.  It is actually what my intuition says
should happen.  But it does not convice my mathematical mind.
The problem of course is that raising is not independent of
the odds of winning a pot.

Actually, this seems true too.  There is another problem: *raising*
to knock out players seems like a high variance play.  It is often
stated that you should *raise* with the 2nd-best hand to knock out
other players.  But there is a finite probability that this won't
work.  If it doesn't then you've put *more* money in the pot with
a *worse* hand.  It seems to me that the variance of this play
depends on the liklihood that you will knock someone out.

I am starting to think about preflop raises as follows:

Preflop, the state of the game is very well defined.  That is
the probability of each hand winning is as independent as it
will ever be.  In particular, each hand has a "nofoldem" chance
of winning against a field of "random" hands.  In reality, the
actual chance of winning is distributed about this base value.

In general, I think that the distributions are "closest" (according
to some metric) to the base value preflop.  An interesting experiment
would be to determine the preflop variance of particular hands.

Anyways, I think that if you have a hand which is more or less
independent of the other starting hands, raising reduces variance.
I actually think that this holds whether the hand is a winner or
a loser, but I have no proof of this.

- Andrew

This game exists in theory only. There are always players that
can and do fold when it's raised and they are faced with a trash hand.
Finding 8 players that are calling robots is not possible, even in CA.
Ken Kubey will prove me wrong here ;-)

Reducing variance by limiting pre-flop raises is likely to damage
your expectation quite a bit. Find a game with the appropriate
level of action for your risk tolerance and you'll earn more.

   Best Luck,
                  Ed  (no, not that Ed!)

              "I used to play this game for fun. Now I
               play it for the sheer frustration"  -  TBill

news:7trdsa$51a@spool.cs.wisc.edu...

What you're really looking for is a mathematical model that doesn't exist.
Therefore, your intuition will prevail because you can't obtain solid proof
that you may be wrong.

If your play is based partly on "hunches," let me know when and where you
play. I want you in my game.

It also depends on the situation. Are you referring to low limit games?
There is more than one reason for raising. If you raise with the intention
of driving people out and it doesn't work (a common problem for low limit),
then that aspect of strategy is taken away from you. That increases your
variance. But to describe it in mathematical terms...?

Do you get "lucky" sometimes? Call anyway when you know you're behind? Does
beating the odds reinforce your strategy for playing the same way again when
you shouldn't in the long run? You already know the answers to these
questions, but getting "lucky" works too. Sometimes.

According to Gone Fishing <fishing@alldaylong>:

Why does it increase variance?  What do you base this on?  Remember that
you seldom have a situation where you know with 100% certainty that a
raise will (or will not) knock someone out.

Note, I think you are probably right, but the question is *why* is this
right.

- Andrew

In article <19991010233949.26567.00001...@ng-ch1.aol.com>,
increases > variance, because you

It doesn't have much to do with thinning the field.  Thinning the field
can help, but it's not the primary factor.

You can increase your odds of winning by raising even if you don't thin
the field.

Also, high variance comes from making bets that are close to even
money.  The larger money favorite you are, the smaller the variance
that a raise has.

I've gotta run take my girlfriend shopping (She thinks I've got a job)
so I'll explain this later.  Or maybe Andrew can explain the part about
large varance being associated with even money bets (binomial has max
varaince at p=.50)

Gary Carson

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In article <7tt2jm$...@spool.cs.wisc.edu>, jeffysr...@yahoo.com (Andrew

I'm not sure about any of this.  But, even though I think you're kinda
close above, I don't think it's really relevant.  You'r probablity of
winning can chance significantly with the number of callers.  For
example with AA it ranges from about .8 to about .3.

I think that your preflop probablity of winning is as independent of
actual hands your opponents hold then it will ever be.  But, it's not
independent of the range of hands they might have.  For example, I
recently did some sims with with AQ offsuit on the button with three
passive limpers.  If you call (and it matters whether you raise or
call), your probability of winning is .2 if they are tight players, .3
if they are typical players, and about .36 if they are very loose
players.

I think this is true and I suspect that's it's important.  But, I can't
really put my finger on exactly why it's important.

Hands don't have variance.  Sitiuations, (defined by your hand, the
range of hands they have, and how many of them are gonna call) have
variance.  The kind of experiment you're talking about can get real
complex, real quick.  But, I agree it would be interesting.

That's an interesting thought.  I don't know if it's true or not.  It
might be true.

I do think that much of what passes for knowledge about variance in
gambling is misconceived and often wrong.

Gary Carson

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In article <19991010233949.26567.00001...@ng-ch1.aol.com>,
increases > variance, because you > are increasing the amount you lose
if beat, and increasing the > amount you win > if not beat, while not
affecting the odds of winning.

But, it does effect the odds of winning.  You can increase your odds of
winning even though you aren't thinning the field.

How does that work?  Well, think of the argument about keeping the pot
small you sometimes here.  Although, I think he's usually talking about
keeping it small on the flop, Sklansky argues that it's sometimes best
to keep the pot small so that they won't have odds to chase you with
thin draws.  He argues that waiting until the turn to raise cut's their
odds down enough so that it's often not right for them to call, where
if you would have raised on the flop they would have odds to call.
Some people have extended that idea to preflop -- thinking that raising
is more likely to give them odds to draw to overcards or gutshots on
the flop.  For example, say you've got AQ and raise with 3 or 4
callers.  Then if you flop a queen a player with KJ has odds to call a
bet (the overcard and backdoor straight).  Or if you flop two-pair the
KJ has odds to draw to the gutshot.

Well, that's all true.  But, if you're best before the flop then your
more likely to benefit from getting odds to draw yourself on the flop.
Just like the KJ would be getting odds, so do you if a king flops or if
KJ flops.  In fact, your AQ is more likely to see a flop where you're
getting the odds to draw to overcards than the KJ would, if you raise
preflop.  If you don't raise preflop then the pot will often be too
small to chase if it misses you.

Some TTH sims I've specifically done with AQ suggests that your chances
of winning increase by as much as 10% simply by raising preflop.
Specifially, against 3 tight limpers, you increase your win
probablility from 20% to 22% by raising.  Against 3 typical, slighly
loose limpers, you increase your win probablility from 30% to 33%.
That's a lot.  And, it's not from thinning the field.  It's from making
the pot big enough, when you've got the best of it, so that calling
later with weak draws to protect what equity you've got even when the
flop misses you.  If you've got the best of it preflop then it's more
likely that you'll benefit from picking up weak draws later than a
player with a weaker hand.

Raising just has all kinds of good things that can result.  Some of
them are a little surprising.

Gary Carson

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In article <19991010233949.26567.00001...@ng-ch1.aol.com>,
increases > variance, because you > are increasing the amount you lose
if beat, and increasing the > amount you win > if not beat, while not
affecting the odds of winning.

But, it does effect the odds of winning.  You can increase your odds of
winning even though you aren't thinning the field.

How does that work?  Well, think of the argument about keeping the pot
small you sometimes here.  Although, I think he's usually talking about
keeping it small on the flop, Sklansky argues that it's sometimes best
to keep the pot small so that they won't have odds to chase you with
thin draws.  He argues that waiting until the turn to raise cut's their
odds down enough so that it's often not right for them to call, where
if you would have raised on the flop they would have odds to call.
Some people have extended that idea to preflop -- thinking that raising
is more likely to give them odds to draw to overcards or gutshots on
the flop.  For example, say you've got AQ and raise with 3 or 4
callers.  Then if you flop a queen a player with KJ has odds to call a
bet (the overcard and backdoor straight).  Or if you flop two-pair the
KJ has odds to draw to the gutshot.

Well, that's all true.  But, if you're best before the flop then your
more likely to benefit from getting odds to draw yourself on the flop.
Just like the KJ would be getting odds, so do you if a king flops or if
KJ flops.  In fact, your AQ is more likely to see a flop where you're
getting the odds to draw to overcards than the KJ would, if you raise
preflop.  If you don't raise preflop then the pot will often be too
small to chase if it misses you.

Some TTH sims I've specifically done with AQ suggests that your chances
of winning increase by as much as 10% simply by raising preflop.
Specifially, against 3 tight limpers, you increase your win
probablility from 20% to 22% by raising.  Against 3 typical, slighly
loose limpers, you increase your win probablility from 30% to 33%.
That's a lot.  And, it's not from thinning the field.  It's from making
the pot big enough, when you've got the best of it, so that calling
later with weak draws to protect what equity you've got even when the
flop misses you.  If you've got the best of it preflop then it's more
likely that you'll benefit from picking up weak draws later than a
player with a weaker hand.

Raising just has all kinds of good things that can result.  Some of
them are a little surprising.

Gary Carson

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According to GaryCarson  <garypokerNOgaS...@email.msn.com.invalid>: