Fundamental Theorem of Poker...
tling
There was a thread earlier discussing David Sklansky's theorem of poker (it was
more or less a whine thread; some guy got bad beated a lot and says there's no
way he's gaining anything even when his opponents are acting incorrectly.)
Anyways, I stated that the theorem is fundamentally wrong in regards to multi
way pots. I am reposting it here for all those who want to debate:
To disprove the theory as a whole, we only need to disprove one postulate
contained within the theory. to disprove the individual postulate, all we need
is one counterexample.
Chosen Postulate: "every time opponents play their hands differently from the
way they would have if they could see all your cards, you gain"
situation to disprove... blinds 5/10 cutoff and button limp in, small blind
calls and you check... all have 1000 chips
SB: AhKh
BB(You): 5c5d
Cutoff: 7h6d
Button: Th9s
Pot:40
Flop comes 8h 3s 4h
SB with AK pushes all in (990 more) with 2 overs and a flush draw.
Pot: 1030. To call: 990. Pot Odds: 1.0404:1
Now, applying sklansky's theorem:
if you see all the other player's cards, you should call because you would see
that player 3 and player 4 should not call regardless of your action. thus you
would in essence be all in vs AhKh heads up as a 50.854%-49.146% dog
(1.0348:1against you... pot odds are laying you slightly higher than that making
the call +EV)
All is good so far.
But then... the two fish after you think for some reason they might be ahead
(because everyone's bluffing with 25o of course!) and call.
The hand equities are now:
SB(AhKh): 50.366%
BB-You(5c5d): 19.878%
Player 3(Th9s): 16.829%
Player 4(7h6d): 12.927%
uh oh... spaghetti-o.
your seemingly +EV call that you made had you known all the other player's hands
backfired! they acted improperly, and in doing so, you're less than 20% to win
a 4 way pot, when you should've been close to 50% to win a 2 way pot. sure, you
in hindsight got 3010-990 pot odds (3.0404:1) but being only 19.88% to win (or
4.03:1) and thus your call turns into a negative EV play because of schooling
fish.
Restatement of postulate in logical syntax:
"For all situations where your opponents make a mathematically improper play
given your hand, you gain EV."
Counterpositive: "To lose EV, your opponents must make a mathematically proper
play."
My example serves as a counterexample.
"There exists a situation where you lose EV but your opponents have made
improper plays." or
"There exists a situation where your opponents made an improper play, and you
lost EV"
Therefore, postulate is false, and as a whole, the theorem is false in multiway
pots.
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truushot2
For low limit holdem, bet when you think you have the best hand. Raise less,
other then to get more money in the pot and expect them to chase you with almost
anything. Even though you might not agree, making the pot bigger will make more
people chase with nothing. Why? They see the big pot and they want it, it
excites them to be in it even if the odds tell them to fold. Plan that they will
chase. Bet and hope your hands stand up. For the most part, even in the short
run they will pay you off often enough even while they do ocassionally hit their
hands, to still make it profitable.
"if it ain't rigged, I get the worst cards live"
tling
ok, so i guess i could've just saved all that time and rather suggested that he
should've changed the name to "the fundamental theorem of heads-up poker"
I've never read the book; i was just going off of what the theorem states. good
to know he took into account multiway pots.
On Nov 16 2005 8:11 PM, Sit-n-Go.com wrote:
> You forget to include this sentence from Sklansky's book before your
> "postulate theory":
> "The Fundamental Theorm applies universally when a hand has been
> reduced to a contest between you and a single opponent. It nearly
> always applies to multi-way pots as well, but there are rare
> exceptions, which we will discuss at the end of the chapter. My
> suggestion: go read that chapter again.
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Shrike
are of course multi-way situations (like the one described) where one
player's poor decision benefits another player to your detriment. SnG
is right, FTOP applies best to heads-up situations and limit games,
although it still has broad applicability to multi-way and NL games as
well.
idigbitches
On Nov 16 2005 6:51 PM, tling wrote:
tling
Sorry I haven't read the book or any of the other books that discuss this so I
wasn't aware people have already went on discussing it; I was just going off of
the thread and the statement of the theory. my post was mostly a reply to this
post:
Shrike:You don't lose when this happens, it merely reduces your chance of
winning on that particular hand. It still remains a +EV venture. Obligatory
example: You have AA. Against one random fish, you win six times out of seven.
Against five random fish you win significantly less often, but the times you do
win you take down a bigger pot. It's +EV either way.
d
Shrike
about the FTOP in all my decisions, but it can be effectively used to
arrive at correct strategy for a large percentage of poker situations.
That doesn't mean that those strategies cannot be arrived at in other
ways or that the FTOP is a substitute for thinking for yourself.
Black & White Plasma TV
of a pot, you are in fact often only encouraging them to stay in! It is
reverse psychology in a sense, is it not? In low stakes hold em, the
simplest, most basic strategy works best.
"truushot2" <4308...@recpoker.com> wrote in message
news:1132189160$670...@recpoker.com...
torx
your pair.
thus they probably would call (especially given the pot odds) if they
could see your cards.
thus they wouldn't play the hand differently from the way they would if
they could see your cards.
to make my point clear, they're both even just a slight underdog to the AK
guy, justified by the pot odds.
-Alexander Knopf
https://www.allinpoker.com/aip/registration/register.jsp?refCode=AKF040D
https://secure.pokerchamps.com/pokerpublic/arequest?acode=TORX
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tling
preflop bud.
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torx
torx
i know what you're trying to argue here, but sklansky probably argues that
they would be making the correct play if they saw the hand they were up
against. and that they're reasonable players that wouldn't make that
play....
On Nov 17 2005 4:40 AM, tling wrote:
____________________________________________________________________
tling
testing to see if unreasonable play by others can still lead to a loss in EV by
you.
_______________________________________________________________
Lou Krieger
stuff written a few years ago on Morton's Theorem.
"tling" <lin...@hotmail.com> wrote in message
news:1132188681$670...@recpoker.com...
Mark Rafn
>There was a thread earlier discussing David Sklansky's theorem of poker
>Therefore, postulate is false, and as a whole, the theorem is false in multiway
>pots.
Yup, and Sklansky says as much (though he claims, and I believe that it
applies in many multiway pots) in the book. The FToP rigorously applies only
to headsup situations.
Google for Morton's Theorem and Implicit Collusion for lots of information on
the topic.
--
Mark Rafn da...@dagon.net <http://www.dagon.net/>
A. Prock
>tling <lin...@hotmail.com> wrote:
>>There was a thread earlier discussing David Sklansky's theorem of poker
> ...
>>Therefore, postulate is false, and as a whole, the theorem is false in multiway
>>pots.
>
>Yup, and Sklansky says as much (though he claims, and I believe that it
>applies in many multiway pots) in the book. The FToP rigorously applies only
>to headsup situations.
It doesn't even apply to headsup situations rigorously.
- Andrew
Mark Rafn
>>applies in many multiway pots) in the book. The FToP rigorously applies only
>>to headsup situations.
A. Prock <proc...@pokerstove.com> wrote:
>It doesn't even apply to headsup situations rigorously.
No? I can imagine if stakes are big enough that you'd rather give up some EV
to reduce variance, it could be wrong. There are probably situations in a
multiplayer tourney where it's wrong, even if the specific hand is headsup.
Does it at least apply to all heads-up situations where the utility of
chips is fairly linear? Or have I missed another important caveat?
Shrike
A. Prock
The primary problem with it is that it focuses the
players attention on results oriented thinking. In
fact, you should never know what your opponent has.
So by focusing on your opponents actualy holdings the
FToP actually misses the primary goal of creating a
strategy.
You don't create a strategy to directly counter a
single hand, you create it to counter a complete
strategy.
A good illustration of this is the heads-up no-limit
preflop Jam or Fold game. In that game, you aren't
focused on your opponents specific holding, you are
focused on his distribution of hands.
A. Prock
>A good illustration of this is the heads-up no-limit
>preflop Jam or Fold game. In that game, you aren't
>focused on your opponents specific holding, you are
>focused on his distribution of hands.
A specific example of this from jam or fold is this:
With 1 2 blinds and a stack size of 20, it is correct
to jam from the small blind with 53s. Despite the
fact that your opponent may be jamming with this hand,
you should always fold 63o from the big blind. Even
in the cases when where he does *actually* have 53s.
That is to say, unless you are somehow psychic, the
optimal strategy is to fold here. Of course, if
you're psychic, it's not really poker anymore.
David Nicoson
> A specific example of this from jam or fold is this:
>
> With 1 2 blinds and a stack size of 20, it is correct
> to jam from the small blind with 53s. Despite the
> fact that your opponent may be jamming with this hand,
> you should always fold 63o from the big blind. Even
> in the cases when where he does *actually* have 53s.
So we see the value of playing 35s deceptively. He used deception to
induce his opponent to play his hand differently than he would have if
he could see the 35s.
The FTOP isn't a strategy. It's just a concept used for creating
stategies. It doesn't work multiway or make toast either, but that
doesn't mean it's not a useful idea.
garycarson
It's not a theorem, it's not a strategy, it's not a concept, and it's
not an idea. It's useful only in the sense that David used it to argue
that deception is important.
It's a definition. David used it to define the idea of mistake in a
way that made it easy for him to argue the value of deception.
It's of no use whatsoever in developing stratagy.
Raising with 53s doesn't have to be deceptive to cause your opponent to
fold some hands that beat it. You can tell your opponent your range of
raising hands, and include 53s in that range, it's still correct for
him to fold 63 even when he knows that.
The only time it's right for him to call is if he's cheating and knows
exactly what you have. Other than a situation where he's cheating he
never makes an actual EV mistake by folding 63. He's only making a
mistake withing the context of the defintion of mistake that's given by
FTOP. In the real world, where EV matters, he's not making a mistake.
Gary Carson
www.garycarson.com
Mark Rafn
>>>It doesn't even apply to headsup situations rigorously.
>>
>>chips is fairly linear? Or have I missed another important caveat?
A. Prock <proc...@pokerstove.com> wrote:
>The primary problem with it is that it focuses the
>players attention on results oriented thinking.
Ok, that's why it's not always helpful or relevant (and I'll agree that
something called "The Fundamental Theorem of Poker" should be more generally
applicable than Sklansky's perhaps is). However, it _IS_ correct in these
situations, even if not helpful.
>In fact, you should never know what your opponent has.
Are you saying that it doesn't generalize to a range of holdings? "If your
opponent plays differently than he should if he knew the exact probability
of each possible holding, you gain". Unweildy, but still correct, I think.
The basic premise that you profit from your opponent's mistakes, whether those
be mis-estimating your hand (or range of hands) or miscalculating what to
do given a holding (or range of holdings) still seems valid and useful.
I summarize the FToP as "help your opponent make mistakes."
>A good illustration of this is the heads-up no-limit
>preflop Jam or Fold game. In that game, you aren't
>focused on your opponents specific holding, you are
>focused on his distribution of hands.
I'd argue that the Jam or Fold game, where strategies are known and
followed flawlessly doesn't have the aspects of poker that the FToP
addresses. It's still correct, but both players are DEFINED not to
make FToP mistakes. It does make an argument that the theorem is less
fundamental than it claims, at least to the extent that JoF is still poker.
A. Prock
>>>A. Prock <proc...@pokerstove.com> wrote:
>>>>It doesn't even apply to headsup situations rigorously.
>>>
>>According to Mark Rafn <da...@dagon.net>:
>>>Does it at least apply to all heads-up situations where the utility of
>>>chips is fairly linear? Or have I missed another important caveat?
>
>A. Prock <proc...@pokerstove.com> wrote:
>>The primary problem with it is that it focuses the
>>players attention on results oriented thinking.
>
>Ok, that's why it's not always helpful or relevant (and I'll agree that
>something called "The Fundamental Theorem of Poker" should be more generally
>applicable than Sklansky's perhaps is). However, it _IS_ correct in these
>situations, even if not helpful.
>
>>In fact, you should never know what your opponent has.
>
>Are you saying that it doesn't generalize to a range of holdings? "If your
>opponent plays differently than he should if he knew the exact probability
>of each possible holding, you gain". Unweildy, but still correct, I think.
I'm not quite sure what you are saying here.
But at some level the FToP holds. Specifically, if you
know your opponents complete strategy. A hand does not
a strategy make.
>I'd argue that the Jam or Fold game, where strategies are known and
>followed flawlessly doesn't have the aspects of poker that the FToP
>addresses. It's still correct, but both players are DEFINED not to
>make FToP mistakes.
Actually, that's not right, in Jam or Fold the players violate
the FToP all the time.
Black & White Plasma TV
makes a mistake, you make money". This simply isn't true. It's almost
delusional. But maybe Sklansky didn't intend for anyone to take that
statement literally. His mind operates on a higher plane than the average
poker player, probably.
garycarson
If the statement is delusional, then it's probably a better bet that
the author is delusional than that the author is too smart to be able
to engage in rational thought.
When David wrote the FTOP he was a recent college sophomore dropout.
So phrases like Fundemental Theorem of Calculas were fresh in his mind.
So his use of the term basically reflects sophomoric thinking, which
it turns out is exactly the right plane of thought to impress the
typical reader of poker books.
Gary Carson
www.garycarson.com
Gary Carson
www.garycarson.com
David Nicoson
> makes a mistake, you make money".
That's the whole of it.
> This simply isn't true. It's almost
> delusional. But maybe Sklansky didn't intend for anyone to take that
> statement literally. His mind operates on a higher plane than the average
> poker player, probably.
I can't really figure out why people want to argue with it. It seems
trivial and obvious to me.
Black & White Plasma TV
news:1132280837....@o13g2000cwo.googlegroups.com...
I take it you don't share the same high opinion of Sklansky as the fanboys.
Based on amazon.com reviews, I expected The Theory of Poker to be the
definitive book on poker. It's OK, but not great. It's poorly written. I
feel Lee Jones' Winning Low Limit Hold Em was more helpful to me and I don't
even play limit very often. I just bought your book, but haven't finished it
yet.
garycarson
Black & White Plasma TV wrote:
>
> I take it you don't share the same high opinion of Sklansky as the fanboys.
Actually I think highly of Sklansky. I think he has some tendencies
towards bipolar disorder, particularly a delustional sense of self, but
I like David very much and respect most of his work.
> Based on amazon.com reviews, I expected The Theory of Poker to be the
> definitive book on poker. It's OK, but not great. It's poorly written.
It's a good book, certainly not definitive, it's real claim to
greatness is that it was the first of it's kind.
I
> feel Lee Jones' Winning Low Limit Hold Em was more helpful to me and I don't
> even play limit very often.
The Jones book is another that's pretty good.
>I just bought your book, but haven't finished it
> yet.
Jones and Sklansky both did a better job at picking catchy titles.
Gary Carson
www.garycarson.com
Black & White Plasma TV
garycarson
Black & White Plasma TV wrote:
No.
At one time I suggested it was worth reading if for no other reason
than most of your opponent have read it.
But, I don't think that' the case any more and there' just no reason to
subject yourself to that nonsense.
It's chapter on loose games is the worst writing on poker that's ever
seen print, from the point of view of quality of analysis and quality
of writing both.
Read the Feeney' book Inside the Poker Mind and you'll get some of the
better ideas contained in HEFAP and Feeney both thinks and writes
better than Malmuth.
Gary Carson
www.garycarson.com
Black & White Plasma TV
> Read the Feeney' book Inside the Poker Mind and you'll get some of the
> better ideas contained in HEFAP and Feeney both thinks and writes
> better than Malmuth.
OK thank you for the suggestion. I'll check it out.
TD Lowball
"Black & White Plasma TV" <pokerp...@virginal-dominance.com> wrote:
>
> I take it you don't share the same high opinion of Sklansky as the fanboys.
> Based on amazon.com reviews, I expected The Theory of Poker to be the
> definitive book on poker. It's OK, but not great.
The 2+2 echo chamber has created sense that TOP is the best book ever. I
didn't mind it, but frankly I havent seen a any fascinating insights in
it except for one or two tangential comments by Sklansky. If your going
to buy 2+2 books, you owe it to yourself to get them on Overstock.com .
> It's poorly written. I
> feel Lee Jones' Winning Low Limit Hold Em was more helpful to me and I don't
> even play limit very often. I just bought your book, but haven't finished it
> yet.
If you want a Math-ey treatment of poker, I recomend Science of Poker,
by Mahmood N Mahmood. Very good book covering Hold'em, Stud and High
omaha in both limit and Pot limit versions. The PL Hold'em section is
worth the price of the book.
TD Lowball --
TD Lowball
"garycarson" <garyc...@alumni.northwestern.edu> wrote:
> Black & White Plasma TV wrote:
> > Gary, do you recommend Hold Em Poker For Advanced Players?
>
> No.
>
> At one time I suggested it was worth reading if for no other reason
> than most of your opponent have read it.
>
> But, I don't think that' the case any more and there' just no reason to
> subject yourself to that nonsense.
>
I think the section on shorthanded play is good, otherwise Middle Limit
Hold'em + How good is your limit hold'em (Which is like MLHE only much
much more aggresive) is I think the best set of two books on Hold'em.
But Bobby Baldwin's+Jennifer Harman's sections are also excelent
coverage and in all ways better than HEFAP.
TD Lowball --
TD Lowball
"Shrike" <sch...@gmail.com> wrote:
> I stand corrected. As I've said, I don't sit at the table thinking
> about the FTOP in all my decisions, but it can be effectively used to
> arrive at correct strategy for a large percentage of poker situations.
But it can be very wrong in certain common situations. This drasticly
lowers it's overall value.
> That doesn't mean that those strategies cannot be arrived at in other
> ways or that the FTOP is a substitute for thinking for yourself.
For alot people that's what FTOP is.
TD Lowball --
TD Lowball
proc...@pokerstove.com (A. Prock) wrote:
> The primary problem with it is that it focuses the
> players attention on results oriented thinking. In
> fact, you should never know what your opponent has.
> So by focusing on your opponents actualy holdings the
> FToP actually misses the primary goal of creating a
> strategy.
>
> You don't create a strategy to directly counter a
> single hand, you create it to counter a complete
> strategy.
Sklansky is going to argue that you apply FTOP to each probable holding
(or class of holdings) that opponent has and then reach a conclusion
about an action based on the aggregate evaluation.
Not that anyone would do all of that, but the way FTOP is presented is
on a holding by holding basis. Not on the basis that there is 65% chance
that my opponent has this, 20% that he has that, and 15% percent that he
has that and I should choose the action that maximises EV over all cases.
TD Lowball --
TD Lowball
da...@dagon.net (Mark Rafn) wrote:
> I summarize the FToP as "help your opponent make mistakes."
Or that
$PROFIT == Opponents mistakes
mistakes == devations from the maxEV play with perfect information.
Helping your opponent make mistakes is a strategy that is derived from
from the FTOP. It is not the FTOP it'self.
TD Lowball --
garycarson
But, as Andrew pointed out elsewhere, making mistakes as defined by the
FTOP aren't neccesarily mistakes that make you money.
Mistakes that make you money are deviations from what they should do to
maximize EV given the information available to them.
The more information they have, the better they can theoretically do,
if they don't take advantage of that information they're making a
mistake, if you provide them too much information you're making a
mistake.
Deception is a way to reduce the information they have, which sometimes
reduces their win potential.
Gary Carson
www.garycarson.com
Michael Sullivan
Well that would be the approach that Latto (IIRC) used in formulating
the Probabalistic FTOP.
IOW, whenever an opponent deviates from the strategy he would use if he
knew exactly what you could hold given your actions (i.e. he knows your
metastrategy completely), then you gain.
That's a much better translation to poker of the Von Neumann principle
you posted earlier. It works with Prock's example here, for instance.
The FTOP as Sklansky states it seems to be measuring the effect of
"seeing into your soul", which is should be small except against really
weak players in person.
Michael
Mark Rafn
>>I'd argue that the Jam or Fold game, where strategies are known and
>>followed flawlessly doesn't have the aspects of poker that the FToP
>>addresses. It's still correct, but both players are DEFINED not to
>>make FToP mistakes.
>
>Actually, that's not right, in Jam or Fold the players violate
>the FToP all the time.
You're correct. In retrospect, I'm reading the FToP far too liberally, simply
as a restatement that "poker is zero-sum". The actual statement it makes
about playing as if you know specific hands is wrong.
TD Lowball
use-re...@spambegone.null (Michael Sullivan) wrote:
>
> Well that would be the approach that Latto (IIRC) used in formulating
> the Probabalistic FTOP.
>
> IOW, whenever an opponent deviates from the strategy he would use if he
> knew exactly what you could hold given your actions (i.e. he knows your
> metastrategy completely), then you gain.
This then suggests that a "balanced" strategy is a powerful tool. I.e
you play different hands the same way this reducing the amount of
"information leakage" in your play of hands. Ofcouse the information
leakage must be balanced with instantious EV.
> That's a much better translation to poker of the Von Neumann principle
> you posted earlier. It works with Prock's example here, for instance.
>
> The FTOP as Sklansky states it seems to be measuring the effect of
> "seeing into your soul", which is should be small except against really
> weak players in person.
If you slightly modify the FTOP to say that it's about deviations from
the ideal max EV strategy given perfect information then it becomes
generaliseable again.
TD Lowball --
A. Prock
>If you SLIGHTLY modify the FTOP to say that it's about deviations from
>generaliseable again.
Yes, unfortunatly the difference between hand-vs-hand maximization
and strategy-vs-strategy maximization is so great that you'll end
of missing the forest for the trees if you try and do the first
with out regards to the second.
For that reason, I would replace the term SLIGHTLY above
with the term FUNDAMENTALLY.
TD Lowball
proc...@pokerstove.com (A. Prock) wrote:
Great Minds think alike,
How does this FTOP strike you?
1. Mistake == deviations from the ideal max EV strategy given perfect
information.
2. Your profit == your proportionate share of sum of the of aggregate
forfeited EV.
3. Strategies that encourage others to make FTOP mistakes can increase
your profit.
TD Lowball --