Hi,

it's a classic situation: We're playing no-limit 6-max and villain defends his big blind aggressively against open raises from the small blind - in this case he calls 35% and 3-bets 18%.

Should we 4-bet 88 in this spot?



With the aid of the Funnel Principle and by considering the right things at showdown you can narrow his 3-bet range down as follows:



red = 3-bet / all-in
green = 3-bet / call 4-bet
blue = 3-bet / fold
yellow = You do not know exactly if and with which range villain is capable of bluff shoving.

What do you consider the EV of a 4-bet with 88 to be in the following scenarios?

1) Villain shoves only TT+, AK
2) Villain additionally shoves 55-44
3) Villain shoves all pairs

Here is my quick calculation:

Results:

A)
4b/call = 0bb
4b/fold = 3.3bb

B)
4b/call = 2.5bb
4b/fold = 1.8bb

C)
4b/call = 5.3bb
4b/fold = 0.29bb




EV - Approximation 4-Bet with 88


Villains - Range- TT+,55-2,AJs+,KJs+,K2s,QJs,Q2s,JTs,J3s-J2s,T4s-T2s,94s-92s,84s-83s,74s-73s,64s-63s,53s+,42s+,AQo+,A4o-A2o,KQo
(#234)

Assumptions:
Betting Sequence: 3 - 9 - 21

Villain 3-Bet / Call 4-Bet
Range = AQs-AJs,KJs+,QJs,JTs,AQo,KQo
(#48)
Equity(88 vs Call-Range) = 0.53

You're not going to realise your entire equity because you're going to often be made to fold the best hand. So we need to discount our equity, using the Equity Realisation Faktor

Equity Realisation Faktor in 4-bet pot (KTU) = 0.75
Equity Realisation Faktor in 4-bet pot (lnternet) = 1 (* I personally feel this would be too optimistic *)



In[17]:=
evcall N[ 48 / 234 * (0.53 * 0.75 * 42 - 18)]
Out[17]=
-0.267692

Case:
Villain only shoves TT+,AK

In[36]:=
villainnobluffrange = 46;
equityvsvillainnobluffrange = 0.31;
wskvillainfold = N[(234 - 46 - 48) / 234];
wskvillainallinnobluff = 46 /234;
ev4betcall = wskvillainfold * 12 + evcall + wskvillainallinnobluff(0.31 * 200 - 97)

Out[40]=
0.031453
In[41]:=
ev4betfold wskvillainfold * 12 + evcall + wskvillainallinnobluff(-18)

Out[41]=
3.37333

Case:
Villain shoved TT+,55-44,AKs,AKo

In[65]:=
villainfewbluffsrange = 58;
equityvsvillainfewbluffs = 0.41;
wskvillainfoldfewb1uffs = N[ (234 - 58 - 48)/234];
ev4betcallfewbluffs =
wskvillainfoldfewbluffs * 12 + 58 / 234 * (equityvsvillainfewbluffs * 200 - 97) + evcall

Out[68]=
2.57846

In[58]:=
ev4betfoldfewbluffs = wskvillainfoldfewbluffs * 12 + 58 / 234 * (-18) + evcall

Out[58]=
1.83487

Case:
Villain shoved TT+,55-22,AKs,AKo

In[73]:=
villainbluffrange = 70;
equityvsvillainbluffrange = 0.48;
wskvillainfoldb1uffs = N[(234 - 70 - 48) / 234];
ev4betcallvillainbluffs =
wskvillainfoldbluffs * 12 + evcall + 70 / 234 * (equityvsvillainbluffrange * 200 - 97)

Out[76]=
5.38188

In[77]:=
ev4betfoldbluffs = wskvillainfoldbluffs * 12 + evcall + 70 / 234 * (-18)

Out[77]=
0.29641


And this is an illustration of the whole scenario: