Spoony Exercise 7: Bluffing in a Vacuum

In Exercise 6 we made sure everyone knew how to count up hand combinations. Now we're going to apply that knowledge to simple bluffing situations in a vacuum.

For a pure bluff to be +EV in a vacuum when we bet some amount S into some pot P, our opponent needs to fold more often than S/(S+P) for the bluff to be +EV. Or you can remember this as bet/(bet+pot). We figure out how often our opponent is folding in our analysis by putting him on a range, deciding what part of that range folds to our bet or raise, and counting up the hand combinations to see what percentage of the time he's folding.

For example, if there's some spot where the total pot is $6 when it's your turn to act and you bet $4 as a pure bluff, you need your opponent to fold more than 4/(6+4) = 4/10 = 0.40 = 40% of the time for it to be +EV. If we hold 43o on a board of J95r and our opponent's range (as a simple example) is {99+, AJ+, KQ} and he folds everything that doesn't make top pair or better, that means he's folding {TT, AQ+, KQ}. His starting range is 90 combinations if I counted it right, and he's folding 54 of those combinations (again, if I counted it right), so he's folding 54/90 = 0.60 = 60% of the time. We need him to fold more than 40% of the time, so this would clearly be a +EV bluff in a vacuum.

Now here are today's exercises:

1. Find a situation where you 3-bet bluffed pre-flop, or could have 3-bet bluffed pre-flop and chose not to. Analyze whether the bluff would have been profitable in a vacuum.
2. Find a situation where you made a c-bet bluff. Analyze whether it would have been profitable as a pure bluff in a vacuum.

When doing these exercises, you should write out your opponents entire ranges, how many combinations each hand is when finding your totals, and how often you would need him to fold based on the bet sizing and pot size. Then make your conclusions.

Afterward: Pure bluffing assumes you'll never win the pot if your opponent doesn't fold. Bluffing in a vacuum assumes that your play won't change how your opponents play in the future. You'll rarely be betting on a pure bluff, and sometimes your bluffs will change your opponents' play in later hands even at microstakes. We'll look at these ideas in greater detail in the future.

Here's the hand:

Villain was opening 16% of hands from CO and I had him folding to a high % of 3bet's when OOP. (Basically a great guy to be sitting to the left of)


PokerStars No-Limit Hold'em, $0.25 BB (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

UTG+1 ($26.50)
MP1 ($20.35)
MP2 ($26.05)
MP3 ($25)
CO ($40.55)
Hero (Button) ($34.10)
SB ($25.10)
BB ($20)
UTG ($19.25)

Preflop: Hero is Button with ,
5 folds, CO bets $0.75, Hero raises to $2.25

Let's say a guy with these stats opens from the CO with a range of:

22+,A2s+,KTs+,QTs+,JTs,ATo+,KTo+,QTo+,JTo = 240 combos

and only continuing with say:

77+,AQs+,AQo+ = 69 combos

I am betting $2.25 (S) into a $1.10 pot (P), so I need him to fold $2.25/($1.10+$2.25) ---> 67% of the time.

Since he opens 240 combos, but only continues with 69 of them, my 3Bet pre-flop will make him fold 240-69/240 ----> 71% of his hands

SDKL:GJSLKJ

HEM decided it doesn't want to open my database anymore so it might be a little while before I can do this.

Situation 1

Full Tilt No-Limit Hold'em, $0.05 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

Button ($4.30)
Hero (SB) ($5)
BB ($5.36)
UTG ($5.24)
MP ($12.64)
CO ($3.24)

Preflop: Hero is SB with A, 9
1 fold, MP calls $0.05, CO bets $0.25, 1 fold

Hero 3bets in theory but actually doesn't

Alright, so his CO Iso/Raising range here may be something like (he was a bit tight): 66+, ATo+, A8s+, KTs+, KJo+, QTs+, 78s+, JT, QTo, QJo.
66(6), 77(6), 88(6), 99(3), TT(6), JJ(6), QQ(6), KK(6), AA(3), AK(12), AQ(12), AJ(12), AT(12), A9s(3), A8s(3), KTs(4), KJ(16), KQ(16), QTs(4), QJ(16), JT(16), 78s(4), 89s(3), T9(3) = 184 combos (probably calculated wrong or forgot something but it's close I think.

Probably continuing with 42 combos: AK(12), AA(3), KK(6), QQ(6), JJ(6), TT(6), AQs(3) **I decided to reduce AQ to AQs on second thought.**

Being OOP with one limper I'd probably be 3betting about 1.05 here.
1.05/.32+1.05 = 76.6%

42/184 = 23% continuation or 77% fold. I needed 76.6% fold and therefore the 3bet would have been extremely close but +EV technically.

Situation 2

Full Tilt No-Limit Hold'em, $0.05 BB (5 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

MP ($11.43)
Button ($4.93)
SB ($9.41)
Hero (BB) ($5.83)
UTG ($5.04)

Preflop: Hero is BB with 8, A
3 folds, SB calls $0.03, Hero bets $0.20, SB calls $0.15

Flop: ($0.40) 7, 3, 5 (2 players)
SB checks, Hero bets $0.25

So, Villain was a very loose passive player 64/0/1.5 to be exact. So really his range here is MASSIVE.
In the interest of speeding this up a bit I'll just use Pokerstove's definition of 64% of hands.
22+,A2s+,K2s+,Q2s+,J2s+,T2s+,95s+,84s+,74s+,64s+,5 4s,A2o+,K2o+,Q4o+,J6o+,T7o+,97o+,87o,76o
Okay, so... Every hand that is not a PP and doesn't include an 8 or an A has 16 combinations.
This comes out to be 24*16+21*4+11*12+72+72+18= 762 hands he is calling with.

Now I should note that he had only folded 1/6 hands to cbet and 2/3 turns to cbet so right there is pretty much my answer of whether this is a good cbet or not, however I'll do this as if I have no reads since it is in a vacuum.

I'd expect him to continue with all suited broadways, A3+, 33+, broadways QJo+, all 7x hands, 64s, 54s, 84s. 33+(69), A3+(129), 7x "x=8+"(68), 74,5,6s(3), 64,5s(2) = 271

271/762 = 36% = 64% fold rate.

.25/.65 = 38% = 62% fold rate needed. Move is again close but +EV.

Hey which 51 do you think he's continuing with and why

3-bet bluff-

weaktight | Hand Poll | KTo - $0.02/$0.05 No Limit Holdem - Hero 3bets to 45 cents PF.

9/5/9 over 483 hands 26% ATS, 100% fold to 3bet (2 hand sample).

Villains range for opening in the CO is something like: { 22+, A2s+, K9s+, Q9s+, J9s+, T8s+, 97s+, 86s+, 75s+, 65s, A8o+, KTo+, QTo+, JTo } which is 338 combos. (Taking blockers into consideration obv.)

He's continuing OOP to a 3bet with: {AQo+, 99+, KQs, } which is 61 combos.

.45/(.45+.30) = 60% of the time he needs to fold for this 3bet bluff to be breakeven.

He continues with 61 out of 338 starting hand combinations, so he's folding 277 combos.

277/338 = 82% of the time, making this a very profitable 3bet bluff.

C-bet bluff-

weaktight | Hand Poll | KQs - $0.02/$0.05 No Limit Holdem

Villain is 13/7/4 over 234 hands. His VPIP for MP is 13% his PFR is 10%. Fold to c-bet is 71% over 7 samples, hasn't 3bet yet in 54 spots.

Villain appears to be a weak/tight TAG/nit that plays pretty straightforward pre and post flop. Considering his ATS is 26%, I can assume he is at least somewhat positionally aware. Considering this we can discount a lot of stronger hands like AQ+, KQ, TT+ from his limping range, especially with a limper in front of him.

For his limp/calling range PF I'll give him {22-99, TJ, QT-QJ, KT-KJ, AT-AJ, 89s-T9s} for a total of 152 combos.

On this flop he's probably not donking anything.

He's probably continuing one street with: {55-99, AT-AJ, 89s} for a total of 51 combos.

I'm risking .45 to win .72 so, .45/(.45+.72) = 38% of the time he needs to fold for this c-bet to be breakeven.

He's continuing with 51 combos out of 152 starting combinations, so he's folding 101 combos.

101/152 = 66% he's folding to a c-bet making this an extremely profitable c-bet bluff.

1-

$0.10/$0.25 No Limit Holdem
PokerStars
7 Players
Hand Conversion Powered by weaktight.com

Stacks:
UTG mikeH13 ($30.85)
UTG+1 C-R4Z0R ($26)
MP JayKos666 ($22)
CO T0NT0-CRO ($37.40)
BTN Hero ($25)
SB Maanu3L ($25.80)
BB stackbuilder ($33.70)

Pre-Flop: ($0.35, 7 players) Hero is BTN
3 folds, T0NT0-CRO raises to $0.75, Hero raises to $2.75


Vill is / over hands. He steals % of the time so he is positionally aware.

He opens on the CO in a short table. I put him on a {22+, ATo+, KTo+,QTo+,JT, T9s-45s, A5s+}
That's 6*11 (PP - AA 55) + 3*2 (AA 55)+ 12*4(ATo+) + 16*6(KTo+,QTo+,JT) + 4*4(T9s-76s) + 3*2 (56s-45s) + 3*5 (A9s-A5s)
= 253 combos
or 19% of starting hands, which is consistent with his HEM PFR stat for the CO.

We 3b bluff him, raising to 2.75$. (and I don't remember why I picked this size over a simple 3x).

He has a high fold to Cbet (90%), and is generally weak, so I expect him to fold a lot of hands here. We can put his continuation range at : {77+, AK} which is 7*6 + 3 + 12 = 57 combos
So he folds to our bluff (253-57)/253 = 77% of his opening range.

We risk 2.75$ in a 1.10$ pot, so we need him to fold 2.75/(2.75+1.1) = 71% of the time. The bluff is +EV with a relatively wide continuation range. If we estimate that he'll continue only with {JJ+,AK} the bluff becomes even more profitable.

2-

$0.10/$0.25 No Limit Holdem
PokerStars
9 Players
Hand Conversion Powered by weaktight.com

Stacks:
UTG Teenycow ($25.50)
UTG+1 Hero ($58)
MP1 PhysicalTilt ($22.65)
MP2 Puzzzi ($25.45)
MP3 reaknis ($27.50)
CO supermigl ($25)
BTN leoninas ($25)
SB amamaasuntxi ($12.05)
BB Rak00 ($50.30)

Pre-Flop: ($0.35, 9 players) Hero is UTG+1
1 fold, Hero raises to $1, 2 folds, reaknis calls $1, 4 folds

Flop: ($2.35, 2 players)
Hero bets $1.75

Vill in this hand is 12/10 over 300 hands.

His PF calling range would be like : {22-JJ, T9s-54s} which is 9*6 + 1 + 4*6 = 79 combos.
His PF 3b is 2.5% so I expect him to 3b with {QQ+, AK} which is why I excluded them from his calling range.

The flop Is K high and rather dry, so I expect to fold most of his hands (also his fold to Cbet is 100% over 10 occurences). I expect a continuation range of {66, JJ, TT} which is 12 combos. He folds (79-12)/79 = 84% of the time.

We bet 1.75 into 2.35 so for the bluff to be +EV he has to fold 1.75/(1.75+2.35) = 42%

As a little extra exercice, I'm going to throw in some EV calculation to see if I'm still doing it right (it's been a while).

So in the first example : we bet 2.75$ to win 1.10$. we take it down 77% and give up 23% of the time so :
EV = 0.77*1.1 + 0.23*(-2.75) = 0.21$

in the second example we bet 1.75$ to win 2.35$
EV = 0.84*2.35 + 0.16*(-1.75) = 1.7$

Donachello- Nitpicking here a bit, but in your 3bet bluffing example, I have a couple of things I want to point out:

1.) Nevermind I'm retarded, just realized he isolated a limper.

2.) Your sizing here is far too large imo. 1.15/.25 = 4.5x as a 3bet bluff? The 'standard' for 3bet sizing is typically 3-3.5x. I have no problem making my 3bets 4x+ if I'm doing it for value and villain is calling with a wide enough range to make it worthwhile, but 4.5x as a bluff is far too much.

Cant find a hand where I'm 3bet bluffing pre but lots of cbets the flop. I chose to do a reraise of a donkbet instead of a straight cbet....

Villain was 18/12/2.7 over 123 pretty fit or fold style
No 3bet preflop and always cbet after raising pre. Didnt play a lot of hands in EP but more in LP but also oop in the blinds.

Range I put him on on the flop is 22-JJ, QJ+, KT+, A9+
22(3), 33(6), 44(3), 55(3), 66-TT(6), JJ(3)
QJ(9), KT(16), KJ(12), KQ(12), AK(16), A9(16), aT(16), AJ(12), AQ(12)
Total hands= 165

PokerStars No-Limit Hold'em, $0.10 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com
MP1 ($36.80)
MP2 ($21.65)
CO ($10.05)
Hero (Button) ($10.40)
SB ($12.75)
villain (BB) ($12.05)
UTG ($6.50)
UTG+1 ($1.85)
Preflop: Hero is Button with Q, J
2 folds, MP1 calls $0.10, 2 folds, Hero bets $0.50, 1 fold, villain calls $0.40, 1 fold
Flop: ($1.15) 5, 2, 4 (2 players)
villain bets $0.20, Hero raises to $0.80, 1 fold
Total pot: $1.55 | Rake: $0.05


Continues after my reraise with 22(3),33(6),44(3),55(3),TT(6), JJ(3), AQ(12),AK(16) or 52 hands out of 165 and folds 68% of the time

Need him to fold .8/(1.35+.8)= .38% of the time.
I calculate this bluff as +EV.

HOW BOUT DEM FLOP 3BETS

Someone run some ranges and maths on this so you get the feel:

$0.50/$1 No Limit Holdem
8 Players
Hand Conversion Powered by weaktight.com

Stacks:
UTG ($104.20)
UTG+1 ($185)
MP1 ($306.40)
Hero ($100)
CO ($111.20)
BTN ($107.55)
SB ($60)
BB ($105.65)

Pre-Flop: ($1.50, 8 players) Hero is MP2
3 folds, Hero raises to $3, 1 fold, BTN calls $3, 2 folds

Flop: ($7.50, 2 players)
Hero bets $5, BTN raises to $14, Hero raises to $35, BTN folds

Final Pot: $56.50

Hero wins $54.75 (net +$16.75)

BTN lost $17

also, I guess $32 would effectively change nothing about his continuing range.

Lucky for me, M2M knows how to get me to do work. So long as i dont have to search my database to find a hand i can do the maths. Thx m2m

Flop 3bet, we're risking 30 to win 7.5+5+14=26.5 when he folds, and risking 30+ to win 26.5+21=47.5+ when he doesnt.

Im gonna split it up into two things. 1st assuming we have 0 equity

taking b/b+p we need him to fold 53% of the time.

Assuming some stuff about btn, id say he can really only be raising with flush draws, 22, 77, and maybe AJ...maaaaaybe. Thats 6 for sets, 9 for AJ (discounted to like 4) and lets say 10 combos of straight draws. Then he just needs to be bluffing with 22 combos for us to be making a b/e play WITHOUT any equity. If he only bluffs with A2 (9) and say 98 (16) and always folds then we're good.

However, against his flushy draws, we have a good deal of equity so we probably dont even need him to fold as much as that to be ok.

Lets say we actually have 4% equity (cuz villain haz 22), lets also assume we shoved all in for 35 instead and that villain still folds that 53% of the time.

Then we have an expected value of $1.57. Of course we're done with the hand when villain does anything but fold...but its cool anyway!

2nd part: we actually bet like 32

7.5+5+14=26.5 still, so assuming 0% equity (shown to be false) we need him to fold about 50% of the time. Thats def significant, and means he probably only needs to be b/fing A2 and like 76(no diamond) or something.

What ive learned here
-if u can bruff smaller without changing nothing, do it (ldo)
-we probably still have equity against a guy's continuing range, so if we find we're breakeven assuming 0% equity then our breakeven play is actually +EV
-i should 3b bruff flops more against ppl that fold to much

Part 1 - 3bet Bluff.

PokerStars No-Limit Hold'em, $0.05 BB (5 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com
SB ($5.93)
BB ($5.32)
UTG ($12.24)
MP ($3.61)
Hero (Button) ($6.20)
Preflop: Hero is Button with 9, 9
1 fold, MP bets $0.10, Hero raises to $0.35, 3 folds
Total pot: $0.27 | Rake: $0


Villian stats over 50 hands: 63/27/0 ATS= 59% total and 80% 'Raise 1st' from the CO.
Villians Fold to 3bet% is 100% with 2 examples.

I'm using the 80% 'Raise 1st' from the CO stat for his range. The table was short-handed, villian was in the CO.

According to Pokerstove, I have 69% equity versus 31% equity for villian. That being the case, you may not call this a bluff, but 99 is not in my typical 3bet range, so meh.

He would raise only 2bb, trying to steal the blinds cheaply. I should have adapted better and 3bet him more with air but I didn't check his stats closely enough while playing. Also, 50 hands is still a small sample.

Since his raising range is so wide, I'm going to shortcut figuring out the hand combinations by taking 80% of the total possible combinations.
So, 80% of 1326 possible combo's is (1326 x .8) = 1060 combinations. Is that method correct?

--------------------------------------------------------------
There hasn't been a discussion on the difference of suited or unsuited hand combinations. For unsuited, there is a maximum of 16 per 2 unpaired cards. If we're counting suited cards, there are only 4 combos per any 2 unpaired cards. I would guess that the method used for unsuited cards takes into account any suitedness automatically, but the reverse isn't true.

So, for instance, if we figure a range of {KTs+, KJo+},
we would have KJo (16) + KQo (16) + KAo (16) + KTs (4) = 52 total combos (assuming no blockers)
Does anyone know if this is correct?
--------------------------------------------------------------

After my 3bet, Villian's continuing range is: {88+, A2s+, ATo+, KTs+, KJo+}
So, 88+ = 37 combos, ATo+ = 64 combos, A2s+ = 30 additional combos, KJo+ = 36 combos, KTs+ = 4 additional combos, for a total of 171 combos.

That means villian is folding (1060-171) = 889 combos or 889/1060 = 84% of the time.

He needs to fold to the 3bet .35/(.35+.27) = 56% of the time for the bluff to be breakeven.
So, the 3bet is very +EV.

I'll wait for feedback on my method of counting suited hand combinations before trying part 2.

Full Tilt No-Limit Hold'em, $0.10 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

MP ($10.39)
CO ($15.04)
Hero (Button) ($9.85)
SB ($12.06)
BB ($10.16)
UTG ($10.24)

Preflop: Hero is Button with ,
2 folds, CO bets $0.40, Hero raises to $1.20, 2 folds, CO calls $0.80

villain is 37/11 his fold to 3b is 63

his opening range is 22+,A8s+,KTs+,QTs+,JTs,ATo+,KQo 160 (?) combos and he continues with 99+,AJs+,KQs,AKo 51 combos

im betting 1.20 into 55 (40+10+5) 120/120+55

he needs to fold 68% of the time, he continues with 55/160 = 34% that means he folds 66% wich makes my 3bet slightly -EV

lol awesome, the one i just did in ex 5 was basically this exact situation (at least part b) and i already did count it out and proved it was a profitable bluff. either way heres part a


Part A.
ok in this hand villain is 16/14 tag that loves to steal (ats of 40). He also has a fold to 3bet of 100 lol so you can already see why this is going to be an EV+ play before it even starts. either way though, here it goes


Full Tilt No-Limit Hold'em, $0.05 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

UTG+1 ($1.77)
MP1 ($5.03)
MP2 ($2.72)
MP3 ($5.73)
CO ($1.33)
Button ($5.26)
SB ($7.11)
Hero (BB) ($6.20)
UTG ($4.03)

Preflop: Hero is BB with Q, 6
4 folds, MP3 bets $0.20, 3 folds, Hero raises to $0.62, 1 fold

Total pot: $0.42 | Rake: $0

hes opening about 40 % of hands here, we'll say 30 because theres the btn still to play and to make things a little easier on me . thats roughly 22+,A2s+,K9s+,Q8s+,J7s+,T8s+,98s,A7o+,K9o+,Q9o+,J9 o+,T9o which is

22,33,44,55,77,88,99,tt,jj,kk,aa x 6= 66
66 qq= 6
a2s+= 12 * 4= 48 - 2( my q 6)= 46 (remember to subtract from a7o)
k9s+ = 4* 4 - 1 (queen of spades) = 15
q8s+= 4 *3= 12
j7s= 4 *4 = 16
t8s t9s 89s= 12
a7o+= 16*6+ 12= 108- 19 (the hands i already counted in the suited part)= 89
k9o+ = 3 * 16= 48 + 12= 60 - 15= 45
q9o+ = 12 * 3= 36- 9 = 27
j9o+ = 32-8= 24
t9o= 12

wow that was tedious, but it brings his combos to a grand total of 307 hands....basically a fuck ton.

of that, considering he has folded to all 3bets so far, i think he is only continuing with absolutely premium hands (unless of course i frequently 3b him and he adjusts (even without consciously adjusting, but tilt adjusting)) such as (tt+,AJs+,AQ+) which is a total of 59 hands.

59 hands out of his 307 is just under 20%.

i bet 60 into a pot of 27, so 62/(62+27)=62/89=.6966

which means because i put in such an overbet i need him to fold ~ 70% of the time for this to be break even. As you can see he is only calling with 20% of his range, so he is folding 80% of the time, so this is a winning EV+ play. Also if i increased his range to 40% like it likely is here, being as the btn was tighter than a virgins cornhole, then this is even more ev+

Could someone be a maddawg and post up a few hands without calcs so that newbs like myself without tracking software can just do the maths on a few example hands? Would be muchly appreciated.

<3