p**********1
发帖数: 1458 | 1 Just came across this theorem again, and want to share it with you guys. It'
s an interesting theorem that is not in poker books AFAIK.
It basically says sklansky's fundamental theorem of poker cannot be extended
to multi-way pot. I remember there was a simpler example to explain it,
kinda like prove by contradiction using a toy game.
the setup is like this, 3 players with same stack size, and they can only
push/call/fold. AND, after push/call, a player must turn his cards face up.
Button(hero) push and show TT.
Small blind call and show KJs. it's a mistake, as KJs
Big blind call and show AQo.
NOW, hero actually is in worst shape, TT 31.357% KJs 33.661% AQo 34.982%. So
, sb's mistake cost hero's equity, which cannot be true if sklansky's
theorem holds true in multi-way pot.
http://en.wikipedia.org/wiki/Morton's_theorem
conclusion:
It is the existence of this middle region of pot sizes, where a player wants
at least some of their opponents to fold correctly, that explains the
standard poker strategy of thinning the field as much as possible whenever a
player thinks they hold the best hand. Even opponents with incorrect draws
cost a player money when they call their bets, because part of these calls
end up in the stacks of other opponents drawing against them.
One conclusion of Morton's theorem is that, in a loose hold'em game, the
value of suited hands goes up because they are precisely the type of hand
that will benefit from implicit collusion. | p****r
发帖数: 9164 | 2 A nice one! thanks for sharing. I definately agree with thinning field line.
Even in short stack heads up situation, getting FE is so important as well
. Even when play against some really bad/loose aggro opponent in short stack
headsup our winning rate is not as good as passive opponent who fold a lot.
It'
extended
.
So
wants
a
draws
【在 p**********1 的大作中提到】
: Just came across this theorem again, and want to share it with you guys. It'
: s an interesting theorem that is not in poker books AFAIK.
: It basically says sklansky's fundamental theorem of poker cannot be extended
: to multi-way pot. I remember there was a simpler example to explain it,
: kinda like prove by contradiction using a toy game.
: the setup is like this, 3 players with same stack size, and they can only
: push/call/fold. AND, after push/call, a player must turn his cards face up.
: Button(hero) push and show TT.
: Small blind call and show KJs. it's a mistake, as KJs: Big blind call and show AQo.
| p**********1
发帖数: 1458 | 3 Thanks. now that I think about it, we probably don't need the "a player turn
his cards face up" assumption, but the "same stack size" is still needed to
avoid side pot. I don't quite remember the exact example, it's from an old
2p2 post. yet the idea is the same as in morton's example, you got a made
hand (a pair or better pair) against two drawing hands and you are ahead,
with the difference being preflop or on the flop. (a made hand is not always
ahead though, i.e., 33
line.
well
stack
lot.
【在 p****r 的大作中提到】
: A nice one! thanks for sharing. I definately agree with thinning field line.
: Even in short stack heads up situation, getting FE is so important as well
: . Even when play against some really bad/loose aggro opponent in short stack
: headsup our winning rate is not as good as passive opponent who fold a lot.
:
: It'
: extended
: .
: So
: wants
| p****r
发帖数: 9164 | 4 does this theorem mainly focus on preflop equality. what about post flop?
Say we have a suited Ace, do we want to see more ppl in the pot to get
better implied odds when we make nuts flush?
turn
to
old
always
【在 p**********1 的大作中提到】
: Thanks. now that I think about it, we probably don't need the "a player turn
: his cards face up" assumption, but the "same stack size" is still needed to
: avoid side pot. I don't quite remember the exact example, it's from an old
: 2p2 post. yet the idea is the same as in morton's example, you got a made
: hand (a pair or better pair) against two drawing hands and you are ahead,
: with the difference being preflop or on the flop. (a made hand is not always
: ahead though, i.e., 33:
: line.
: well
| p**********1
发帖数: 1458 | 5 I think it started out like this, lots of reg complained there were so many
loose callers in limit games that it was hard to beat. morton looked at some
of the examples/hh and eventually got to his example. the conclusions as
stated in wikipedia http://en.wikipedia.org/wiki/Morton's_theorem), are something we're all familiar with. the value of suited connectors (incl. AXs) goes up in multi-way pot, preflop or postflop; it's correct strategy to thin the field when you got a vulnerable made hand like TPTK in multi-way pot (conversely you want more players around with a drawing hand); etc.
About postflop, I am not good at it at all, so I will cite what windstormm
once said "有鱼的锅reg一般打得比较直白“。I guess it has something to do
with this theorem in that you sometimes don't want to trick another reg into
making a mistake that might actually cost you equity and benefit the fish
in the pot.
【在 p****r 的大作中提到】
: does this theorem mainly focus on preflop equality. what about post flop?
: Say we have a suited Ace, do we want to see more ppl in the pot to get
: better implied odds when we make nuts flush?
:
: turn
: to
: old
: always
| T********n
发帖数: 528 | 6 Good find - but to clarity it's not as if Sklansky doesn't know this or
doesn't try to educate this. Something close to Morton's Theorem is also
discussed in HEFAP, right after the section on Sklansky's Fundamental
Theorem of Poker, where it says blah blah exception blah blah multiway blah
blah. What Morton's Theorem does though is it gives practical (game example
) ways to think about how to benefit from this. Such as the part about why
suited connectors go up in value, etc. | f*****g
发帖数: 15860 | 7 谭老师最近忙啥子？贴个万元session来提提人气？
blah
example
why
【在 T********n 的大作中提到】
: Good find - but to clarity it's not as if Sklansky doesn't know this or
: doesn't try to educate this. Something close to Morton's Theorem is also
: discussed in HEFAP, right after the section on Sklansky's Fundamental
: Theorem of Poker, where it says blah blah exception blah blah multiway blah
: blah. What Morton's Theorem does though is it gives practical (game example
: ) ways to think about how to benefit from this. Such as the part about why
: suited connectors go up in value, etc.
| W********m
发帖数: 7793 | 8 This is interest. I will add my 2 cents.
In a multi-way pot situation, someone's mistake can cost you equity. I think
it is fairly straight forward to understand this if we don't worry too much
about hand strength, but think about the hands in a framework of odds/
combination of hands.
Look at the example you give:
"Button(hero) push and show TT.
Small blind call and show KJs. it's a mistake, as KJs
Big blind call and show AQo.
NOW, hero actually is in worst shape, TT 31.357% KJs 33.661% AQo 34.982%. So
, sb's mistake cost hero's equity, which cannot be true if sklansky's
theorem holds true in multi-way pot."
Why would a made hand TT becomes an underdog if KJ AQ both call? KJ
46.2%/53.8%. We all know that what it really means is that among all
possible 5 cards dealt 46.2% of the combination can make KJ a winner while
the rest of the 53.8% of the combination can make TT a winner. The current
hand strength really means nothing when it comes to odds after all in. so we
separate all hand combination to two winning regions. Now the involvement
of the AQ changes the whole game. It will take some winning region from both
TT and KJ. THe reason TT turns a winner equity-wise into a loser is because
AQ takes more combinations from TT's winning region than from KJ's winning
region. KJ's mistake does not give TT more equity, because it enables AQ to
be the favorite by unbalance the original regions of the winning hands
combination. So in a multiway situation, when someone makes a mistake, not
everyone in the pot gain, but someone will gain and someone will even lost
equity (it should happen very often) depending on which winning region it
took more hand combination from the HU situation. (slightly different from
the fundamental theory, but in my opinion it is close enough) In this case
AQ is the gainer and TT lost equity because of KJ's mistake.
Now this is the preflop situation. post flop situation can changes a lot as
well from HU to multiway situation. a lot of times, it is because of dead
money. under multiway pot situation, there are normally a lot more dead
money in the pot, this create a situation where everyone is +ev to call than
fold even though someone lose money overall. Additionally hands with nut
draws should be more powerful ev-wise in a multi-way situation than others
hands simply because they do not lose your winning region as much as other
hands. The simplest example, if you have a nut flush draw on the flop, you
obviously want as many people in the hand as possible if you already decide
to go all in, because you have locked winning region and the rest of the
player would take each other's equity much more often, and the most you
would lose is 2 outs (but with much more combination from your winning
region) when someone else is also holding a flush draw. This seems fairly
easy to understand if we stop looking at the current hand strength and start
to look at the winning odds by what possible hand combination can make our
hand a winning hand at showdown. This approach is very common in PLO game
because many times in PLO, the current made hand is in fact behind a draw
hand significantly and people would pay more attention to odds and
combinations. but in holdem game, people do not do that often because it is
more proportional between the current hand strength and winning odds except
a few extreme cases.
It'
extended
.
【在 p**********1 的大作中提到】
: Just came across this theorem again, and want to share it with you guys. It'
: s an interesting theorem that is not in poker books AFAIK.
: It basically says sklansky's fundamental theorem of poker cannot be extended
: to multi-way pot. I remember there was a simpler example to explain it,
: kinda like prove by contradiction using a toy game.
: the setup is like this, 3 players with same stack size, and they can only
: push/call/fold. AND, after push/call, a player must turn his cards face up.
: Button(hero) push and show TT.
: Small blind call and show KJs. it's a mistake, as KJs: Big blind call and show AQo.
| T********n
发帖数: 528 | 9 Been playing playing Diablo 3 (Big Pineapple) :) LP says I should write up a
Q2 wrap-up, which I will, but just so happens the only free non-Diablo 3
time I get is at work, where I can't type Chinese.
【在 f*****g 的大作中提到】
: 谭老师最近忙啥子？贴个万元session来提提人气？
:
: blah
: example
: why
| f*****g
发帖数: 15860 | 10 期待，盼望，翘首。
a
【在 T********n 的大作中提到】
: Been playing playing Diablo 3 (Big Pineapple) :) LP says I should write up a
: Q2 wrap-up, which I will, but just so happens the only free non-Diablo 3
: time I get is at work, where I can't type Chinese.
|
|
