Set on the Flop

Sets on the flop are tricky to play. The correct amount of aggression
is board dependent.
On dry boards the set is very strong. A set against top pair is over
98% favorite. It's safe to bet small and attempt to string opp along.
You: 6s6h
Flop: 9s6c4d
Opp with As9h is way, way behind. Needs runner/runner to beat you.
As boards become more coordinated they become more dangerous.
Sets should fear flush and straight draws. Plan a betting
scheme which denies opp both pot odds and implied odds. On
these types of board sets want to be all in by the turn.
The river betting favors the chaser.

tiptoeing thru the turn

There are threads stating that many successful fixed limit
players have problems winning at no limit. No particular
reasons were given. The difference in turn play could be
the reason. In SS2 there's almost no space devoted to
turn play. The short turn section only discuss odds for
chasing. Nothing on way ahead/way behind situations.

Opening raiser misses the flop. She makes the continuation
bet. The defender calls. There's a void in the literature.
What should she do next? Why did he call? Occasionally
it's a big hand. Usually it's a pair or a draw. Should
she follow up with a turn bet? That's the mystery. Some
defenders call the flop with second pair and then fold on
the turn. Others call all three streets. Some call with
draws once and others twice. How do you know one from the
other?

In FL raiser has TPTK on the flop. She bets the flop and
is called by the defender. The turn is a blank. She bets
and is raised. In FL she can now be stubborn and call this
turn raise and a river bet. This will costs her two big
bets. In NL the defender can raise much more. He can bet
the pot or more on the river. In FL she is getting odds
to call. In NL she is giving odds to call. In a SnG the
stacks are usually small. Top pair makes one pot-committed.
Against aggression TPTK is harder to play in NL than FL
or a SnG.

Example A. She: As Qh
Flop: Qs Td 7c
She bets and he calls.
Turn: 5:c:
This card is very unlikely to improve defender's hand.
She bets. He raises. What can he have? In NL she has
to wonder why he called. In FL she doesn't care. She
knows it will only be two big bets to find out. In NL
it may costs the entire stack to find out.

The books say open raise first in. Then make a c-bet. But
what if the opponent calls? What does he have? What if
you have missed the flop and have nothing? What do you
do next?

That is the next phase of the game to investigate.

Cold calling

The current thinking on cold calling says you must hold
the top half of raiser's range. I believe they are all
wrong. They're focusing on the wrong statistic. The
critical statistic is raiser's continuation bet percentage.
When raiser rarely makes a continuation bet, he is playing
like an open book. It's possible to call with a vast
range of hands. Even greater than raiser's range. When
the raiser c-bets 100%, never call. It's too dangerous.
These pots always become larger pots than the other hands.
Also larger pots with you having at most a marginal EV
advantage.
All these pokerstove calculations are a waste of time.
The perceived ranges can't be trusted. The vector
doesn't include raiser's c-bet%. It doesn't measure
implied odds. It just gives the ex-showdown values.
There's no accounting for betting. None for future
chips at risk.
In the future a new vector in orthogonal space will be
developed. This vector include raiser's c-bet%, implied
odds and all other statistics which has measurable
effect on $EV.

MOP19.3. The pot size case.

The problem on 19.3 is resolved using geometric growth with
pot size bets.
Clare, the clairvoyant, will be dealt one card. If it's
an ace or king she wins, else she loses. Dean will be the
defender. There are three streets of betting. Clare may
bet or give up. Dean may call or fold. Both will ante
five units. Clare's bets will be pot size.

Question.
If both Clare and Dean are playing optimally, what's the
value of the game?

Answer.
Clare has a +EV of 0.19231 units.

The ex-showdown value of the game is -3.46. This is from
MOP 19.3. The game is solved by linking three matrices in
series.
First the three matrices are solved separately. On street
one Clare bluffs about 9% of her losers. If this were a
one street game, Dean would call 50% of the time. Since
this is a three street game, Dean can improve on his
-0.19231 EV by just folding to every bet. The game value
would be 5*(.76923)-5*(.23077)=2.6923. That's 2.6923
in Dean's favor.
To force Dean to call more often Clare must overbluff
street one. To produce +0.19231 EV Clare must bet so
that if Dean folds to every bet, she would still get
her +0.19231.

5*(x-(1-x))=0.19231
2x-1=0.19231/5
2x=1+.038462
x=.519231

Plug these numbers in and Clare is betting about 40% of
her losers instead of 9%.
On street two Clare had to overbluff again. She bets 35%
of her remaining losers instead of 21% suggesting by the
one street matrix.
By street three the game has been reduced to a one street
game. Clare bets losers at the suggested optimal strategy
frequency.
Clare overbluffs by over 300% on street one. This suggests
in a real game where Clare starts with 50-70% winners the
100% continuation bet may be viable. She only overbluffs
about 60% on street two.
Dean calls at the 50%(pot/{pot/bet}) frequency thruout all
three streets.

geogrowth overbluff
S1 Cgives 0.48077 __-5 ____-2.40385
S1 Dfolds 0.25962 __ 5 ____ 1.29808
S2 Cgives 0.11857 _-15 ____-1.77862
S2 Dfolds 0.07052 __15 _____1.05781
S3 matrix 0.07052 __28.63 __2.01888
____________________________0.19231
On street one Clare gives up 48% of the time. She loses
5 units on those. Dean folds about 26% of the time.
The street three matrix is played out as a one street
matrix game.