a quote

from The Mathematics of Poker:

bluffing in optimal poker play is often not a profitable play in and of itself. instead, the combination of bluffing and value betting is designed to ensure the optimal strategy gains value no matter how the opponent responds. opponents who fold too often surrender value to bluffs while opponents who call too often surrender value to value bets. 


obviously. but still, at the table, i don't often fully consider my hypothetical value betting or bluffing frequency in a spot while considering the opposite action.

seems like an easy way to stay out of trouble when the exploitive play isn't clear. also, few opponents play optimally, so when we do, we essentially let them choose how they want to pay us.

Flat Barrel Reverse Squeeze: Wisdom from a BE $100 NL player

The Flat Barrel Reverse Squeeze is a cool little sequence that I came upon by accident. The play is made generally from the blinds but it could certainly work in other positions if the opportunity presents.
I misclick called preflop in the SB with a hand that I would have called a single raise with, in this situation 22, however since this time the button three bet I would have normally folded. This time I misclick called the three bet out of position with 22. Not a seemingly +EV situiation. However, because the three bettor was a thinking reg and my image is tight, cold calling a three bet made my hand look very strong in the the eyes of the three bettor, I made a smallish 50% or so Cbet on a dry flop and the reg insta-folded.
It got me thinking that this would be a fun and tricky defense against regs who were three betting light in late position. It doesnt come up all that often but in the right spot the FBRSQ is a good way to disguise your range and f with your opponents head a bit.
The key is using this play against an opponent that knows you and is thinking enough that they would put you on a super strong range when you flat the three bet.

privatization

this blog was not originally intended to be open to the public. i opened it up recently because few members were reading or posting and i wanted to get input from some new people. i'll be closing it down again soon, so if you'd like to be involved, please leave a comment on this post so i can contact you via pm on leggopoker or duecescracked.

btn v. bb: 3b/4b/shove

here are some sims that are similar to the 5/6-bet stuff below, but where players have smaller stacks:

• btn opens to 3bb w/ top 50% 
• bb 3bets to 11bb w/ top x%
• btn 4bets to 26bb w/ [JJ+, AK, var1% of others] 
• bb shoves 100bb w/ [TT+, AK, var2% of others]
• btn calls [TT+, AQ+]

if we vary the 3bet range of bb, btn 4-bet air range, and bb shove air range, we get the following (notice scale changes):

notice that there is not equilibrium point for btn 4-bet range. that is, v. a 3b range this tight, 4-betting w/ any air is exploitable, ldo.

pretty light post, but i havent been able to play all week and dont want to spend too much time on this stuff right now...

[i also wanted to clarify something i wrote earlier - relevant to this and previous posts - about the GTO strategy being independent of the opponent (by definition, a GTO strategy occurs when a player cannot increase his expectation by acting unilaterally). i went on to say that strategies are dependent on stack sizes and the hands in hero's range. for example, i stated that the optimal frequency to 5-bet bluff, was dependent on hero's 3-bet range. that statement isn't strictly true, the optimal bluffing frequency is actually dependent on the number of combinations of value/nut hands, but since i had defined the bluff frequency as a % of non-value hands, it sort of looks like it's dependent on the range of hands going into the decision point.]

4/5/6 betting continued

i realize that my assumptions may not be realistic. so, here are some charts that should give an idea for how the different inputs change the situation:

the top chart is the original scenario, the bottom uses a tighter opening range for co/btn:

you can see that the game-theoretical optimal strategy does not depend on co/btn opening range, while the performance of any strategy does.

if the bb has different 3b ranges (as klink pointed out, most probably will), the optimal strategy will change. here are some charts that show different ranges v. different co ranges:

i didn't take the time to find the optimal strategy for each, but you should be able to approximate from these.

does 5-bet/folding make sense 200bb deep?

during a group sweat session yesterday MattUK asked that question of the player, but we didn't get back around to fully addressing it.

the answer obviously depends on the opponents ranges for each action leading up to and facing the 5-bet. the most important being their 4-bet and calling off ranges. if we have those accurate, exploiting any flaws should be fairly straightforward. so, here is a situation w/ approximate ranges for 'standard tag reg':

1. 200bb effective stacks
2. CO opens to 3.5bb w/ top 50%
3. BB 3bets to 11bb w/ [JJ+, Axs, T9s+, 55-22, AQo, AJo, A5o, KJs] ~12% of hands
4. CO 4bets to 27bb w/ [QQ+, AK, var1% of other hands] 4.6% of opening range for value + ~var1% as bluffs
5. BB 5bets to 56bb w/ [AA, KK, AK, var2% of other hands], 15.4% of 3betting range for value + ~0.8*var2% as bluffs
6. CO ships w/ [QQ+, AK], folds others
7. BB calls (144bb) w/ [KK+, AK], folds others {fwiw, EV(QQ, call) = +16bb if BB knows CO range above, EV(JJ, call) = +0.2bb}

note: these ranges are easy to tweak, so let me know if they seem inaccurate.

if we then vary the amount of 'air' in both CO (var1) and BB (var2) ranges, we get the following table:

you can see that CO is unexploitable if he 4-bet bluffs w/ between 5-6% of his non-value hands (EV(4b) is inversely proportional to var2 below 5%, but increases w/ var2 above 6%; equilibrium somewhere between).

so, we see that BB would benefit from a 5bet bluffing range v. players who 4-bet more than ~11% total (4.6% value + ~6% bluffs), and only ship a value range.

we then need to consider whether CO has a 6-bet bluffing range. so, we set CO 4-bet air frequency (var1 above) to 10%, give CO a 6-bet shoving range of [QQ+, AK, var3% of others], and find the EV(5b) for different values of var2 and var3. if we then use those values to make a table similar to the one above (i'm to lazy to embed it) we find that BB cannot be exploited by a 6-bet if he 5-bet/folds ~13% of 'air' hands (something like A5s-A2s, would do the trick).

finally, we can answer the original question by noticing that the EV of 5betting only for value is ~6.0bb, and the EV 5betting for value + 13% of air is ~7.7bb, to definitively prove that: YES, BB WOULD BENEFIT FROM A 5-BET/FOLDING RANGE (at least, v. this particular CO, given some assumptions and hoping that i didn't fuck it up somewhere).

response to comments: 

yes, var2 is defined as a % of non-value hands, so the absolute % gets discounted

i think the discrepency you noticed was due to a tweak i made in the decision tree when i was looking for a specific group of hands that would make up that ~13% air. so, for that final paragraph i had defined the bluff hands to be specifically A5s-A2s.

also, i posted this in a forum where a question was asked about the effect of 6-bet bluffing frequencies on the EV of a 5-bet. here is a chart that shows the equilibrium points more clearly:

the decision function

this might not end up being particularly useful, but i've noticed that i don't often take anything useful away from hand history discussions. in my experience, when faced with a question about a hand history, different people generally take a position and point out different aspects of the situation that provide support. if discussion continues at all it usually involves a lot of reiteration and little resolution...

so, i want to suggest a framework for considering poker decisions that would invite broad thinking, collaboration and finding a consensus. here it is:

D = C1X1 + X2X2 + .... + CnXn

where Xn represents the value of a condition (in +/-bb), and Cn the relative importance of that condition (for simplicity, let's say Cn is bound by 0 and 1). a bet is indicated when D is positive, and a check when D is negative.

as a simple example, consider the following hand:

SB ($312)

BB ($599)

CO ($40)

HERO ($207)

SB posts (SB) $1

BB posts (BB) $2

Dealt to HERO Kc  9d

fold,

HERO raises to $6

fold,

BB calls $4

FLOP ($13) 3s  4h  Ah

BB checks

HERO ...

in order to determine whether to bet or check, there are a number of conditions that hero could consider, some of which are represented in the following decision function:

D = C1*(stack size) + C2*(flop texture) + C3*(hole cards) + C4*(opponent tendencies) + C5*(perceived image) + ...

if i asked for opinions on whether or not hero should bet, some players would likely respond 'yes, that's a great flop to cbet', implicitly setting C2 = 1 and all other Cn ~=0. other players might consider the value of K9o, how frequently the opponent tends to call, whether we have an aggressive image, etc. to arrive at a decision. the following table illustrates these different approaches:

D (player type)	C1 (stack size)	C2	C3	C4	C5	...
texture expert	0	1	0	0	0	0
soul reader	0	0	0	1	0	0
deep thinking lag	0	0.5	0.1	0.7	0.2	0
fish	0	0	1	0	0	0

...you get the idea.

by identifying and considering the relevant conditions individually, we get in the habit of looking for additional bits of information and (trying) to objectively determine the relevance of those bits. as opposed to playing on auto pilot and focusing in on a single factor that is typically biased/tilted by recent hands or the weather or whatever we've been thinking about recently.

here's another example with more (and more complicated) conditions/factors:

SB ($289)

BB ($123)

UTG ($211)

MP ($203)

CO ($121)

HERO ($202)

SB posts (SB) $1

BB posts (BB) $2

Dealt to HERO 4s  2s

fold, fold,

CO calls $2

HERO raises to $7

fold,

BB calls $5

CO calls $5

FLOP ($22) As  8h  3s

BB checks

CO checks

HERO ...

both CO and BB appear fishy, but were essentially unknown at the time. hero had a clean standard tag image (if anyone was paying attention).

the decision function should look something like this:

D = C1*(stack size) + C2*(flop texture) + C3*(hole cards) + C4*(CO tendencies) + C5*(BB tendencies) + C6*(perceived image) + ...

my initial estimates are in the following table:

condition	Cn	Xn	Cn*Xn
stack size	0.5	-10	-5
flop texture	1	+2	2
hole cards	1	+2	2
CO tendencies	0.1	-2	-0.2
BB tendencies	0.1	-2	-0.2
percieved image	0.1	+2	0.2
total			-1.2

so, i checked back.

obviously, this isn't meant to be as formulaic as it might appear from that last example. but from there it would be easy for somebody to point out where their thinking differed and for both players to use that disparity to improve their thinking.

to cbet or not? if so how much?

during my session from this morning, i was trying to pay close attention to good/bad spots to cbet. i marked several to ask for opinions on whether to bet and, if so, how much...

hand 1:
asolone ($47.30)
BodystainTattoo ($200)
beatis ($330)
robyguida ($119)
LBrits ($200)
BearUK ($200)

asolone posts (SB) $1
BodystainTattoo posts (BB) $2

Dealt to beatis Ad  9d
beatis raises to $6
fold,
LBrits calls $6
BearUK calls $6
asolone calls $5
fold,
FLOP ($26) 2c  Td  9s
asolone checks
beatis ???

hand 2:
DaviBoy337 ($40)
The58Maker ($80)
Instinkt83 ($244)
maxxll22 ($143)
beatis ($258)
DDice511 ($206)

DaviBoy337 posts (SB) $1
The58Maker posts (BB) $2

Dealt to beatis Ts  Tc
fold, fold,
beatis raises to $6
DDice511 calls $6
fold,
The58Maker calls $4
FLOP ($19) 3h  5d  Qd
The58Maker checks
beatis ???

hand 3:
Maximus446 ($172)
Jorisa ($206)
D1scoInferno ($1,299)
kingkevin87 ($200)
beatis ($360)
chapichapo30 ($848)

Maximus446 posts (SB) $1
Jorisa posts (BB) $2

Dealt to beatis Ts  Kc
fold, fold,
beatis raises to $7
chapichapo30 calls $7
Maximus446 calls $6
fold,
FLOP ($23) 7c  Ac  Ah
Maximus446 checks
beatis ???

hand 4:
BenHogan ($230)
nbh52 ($100)
resurepus ($230)
Wretched84 ($286)
fkraise ($127)
beatis ($200)

BenHogan posts (SB) $1
nbh52 posts (BB) $2

Dealt to beatis 7h  4h
fold, fold,
fkraise calls $2
beatis raises to $9
BenHogan calls $8
fold,
fkraise calls $7
FLOP ($29) 3s  3d  Ts
BenHogan checks
fkraise checks
beatis ???

hand 5:
BenHogan ($289)
Tutti99 ($123)
resurepus ($211)
Wretched84 ($203)
fkraise ($121)
beatis ($202)

BenHogan posts (SB) $1
Tutti99 posts (BB) $2

Dealt to beatis 4s  2s
fold, fold,
fkraise calls $2
beatis raises to $7
fold,
Tutti99 calls $5
fkraise calls $5
FLOP ($22) As  8h  3s
Tutti99 checks
fkraise checks
beatis ???

hand 6:
yashdonk ($615)
beatis ($200)
Tina first lady ($310)
green100b ($511)
kurokitty ($200)
Puyol77 ($275)

yashdonk posts (SB) $1
beatis posts (BB) $2
yashdonk antes $0.30
beatis antes $0.30
Tina first lady antes $0.30
green100b antes $0.30
kurokitty antes $0.30
Puyol77 antes $0.30

Dealt to beatis Kh  Qc
fold,
green100b raises to $6
Puyol77 calls $6
fold,
beatis raises to $28
green100b calls $22
Puyol77 calls $22
FLOP ($86.80) Qs  Qh  Ac
beatis ???

anyone care to give an opinion?

T87t, QJo oop when agro btn raises my cbet...

so, here's a hand i played yesterday where i way overweighted a stat read (and ignored the results of recent posts):

i dont recall any recent history or have any specific reads on GambitMJ. the relevant stats i looked at were:

vpip/pfr = 20/18

3b from btn = 9%

cc from btn = 7%

raise cbet = 35%

http://www.holdemmanager.net

NL Holdem $2(BB) Replayer Game#15729854641

ALFeRICH ($247)

ure a towel ($270)

beatis ($243)

kewl99 ($117)

pRip43 ($40)

GambitMJ ($203)

ALFeRICH posts (SB) $1

ure a towel posts (BB) $2

pRip43 posts (SB) $1

Dealt to beatis Qh  Jc

beatis raises to $7

fold, fold,

GambitMJ calls $7

fold, fold,

FLOP ($18) 8h  Th  7c

beatis bets $14

GambitMJ raises to $40

beatis raises to $236 (AI)

i posted this in the leggopoker forum where people said to c/f this flop. i fully agree v. a player who isn't raising cbets so often, but v. this guy i thought it would be better to give him an opportunity to spaz out so that i could then respaz out.

so, i imported the hand into stoxev and assigned him some ranges:

• preflop call w/ [22-TT, 54s-JTs], 10% weight on [AA, KK, AK, suited 1-gap], 20% weight on [JJ-QQ, AQo, AJo, KQo, other suited broadways] = 7.5% of hands
• raise cbet w/ [1pr+, fd, oesd, var1% of all others], 
• call shove w/ [tp+, fd, oesd, pr+gs]

i then varied how often he raises the flop w/ 'air' to get the following graph of the ev of a shove v. var1%:

obviously, my line is terrible v. these button ranges. but i wasn't ready to give up entirely, so i adjusted the cbet raising range to exclude some 1pr hands by defining a calling range as [1p+bdfd, 1pr+gs] to see if that might help me justify my play. in order to get anything meaningful out of the sim, i need to continue the tree out to the end in a reasonable way. i attempted to do that and see that it just shifted the redline up by ~5bb (orange line above). so, it helps to remove some of the 1pr hands from btn's raising range, but not nearly enough to make the shove profitable.

just to belabor this a bit more, if btn raises 100% and only calls w/ a range as tight as [tp-K kicker, fd, 1pr + oesd], the cbet nets -$7.52.

i suck.