EV calculation for turn semibluff

[yourface]

I did this while reviewing a session of mine. I thought that this was an interesting spot because with all of villain’s Ax hands having a gutshot we aren’t going to fold them out, so our semibluff is targeting a small range of hands that beat us.

Hopefully there aren’t any math errors and it makes sense [img]/images/graemlins/smile.gif[/img]
Thanks to everyone who looked it over for me

Limit Holdem Ring game
Limit: $5/$10
2 players
Converter

Pre-flop: (2 players) yourface is SB with J[img]/images/graemlins/spade.gif[/img] 5[img]/images/graemlins/spade.gif[/img]
<font color="#cc0000">yourface raises</font>, <font color="#cc0000">BB 3-bets</font>, yourface calls.

Flop: 4[img]/images/graemlins/spade.gif[/img] 2[img]/images/graemlins/heart.gif[/img] 2[img]/images/graemlins/club.gif[/img] (6SB, 2 players)
<font color="#cc0000">BB bets</font>, yourface calls.

Turn: 3[img]/images/graemlins/heart.gif[/img] (4BB, 2 players)
<font color="#cc0000">BB bets</font>,

So the question is should I call or raise. To do this I am going to do two EV calculations; one for calling and one for raising. I will be using pokerstove to figure out my and villains equities.

DETERMINING EQUITIES AND DISTRIBUTIONS

I am going to assume villain is pretty tight, with a preflop 3 betting range of { 55+, A5s+, KTs+, QTs+, A7o+, KJo+ }. This is 16.9% of total hands.

On this board I expect villain to fire the second barrel 100% of the time.



Pokerstove says my equity vs that range is ~22.2%


If I raise villain can call reraise or fold. What I need to do an EV calculation for this case are my equities vs his calling and raising hand ranges, and what fraction of the time he does those things.

He will likely only call with any ace, and any heart draw. { A6s+, KhQh, KhJh, KhTh, QhJh, QhTh, A7o+ }, 9.2% of all hands


My equity vs those hands is ~21.7%

I just noticed that KTcc snuck in there, but I’m not redoing this [img]/images/graemlins/smile.gif[/img]

Villain will likely reraise with any TPTK+. { 55+, A5s }, which is 4.8% of total hands


My equity vs those hands is ~19.2%


He will likely fold with his other broadway hands. { KcQc, KdQd, KsQs, KcJc, KdJd, KsJs, KcTc, KdTd, KsTs, QcJc, QdJd, QsJs, QcTc, QdTd, QsTs, KJo+ }, 2.9% of total hands.


The fraction of the time that villain takes either of the three actions when you raise the turn is calculated by dividing the % of hands that take that action by the % of hands that he had initially when he bet the turn.

POT AND IMPLIED ODDS

The pot size is obviously very important; it is 5BB when the action is on us on the turn.

Implied odds also need to be considered. You can get a very good idea for implied odds by looking at the weightings of different hands in villain’s range and how many bets they will go on the river when we improve.

When we just call the turn, I estimated the following implied odds scenarios. For the sake of simplicity I am going to assume that villain won’t cooler us by making a flush when we hit our hand. Note that there are different cases for improving to a straight and improving to a pair of jacks.


Again using pokerstove we can break down villains hand range into different types of hands that will pay us off different amounts on the river. The implied odds for each case are calculated by summing the products of the implied odds and weightings for each hand type. The average implied odds of ~1.3BB is calculated by taking a weighted average for both cases.


That took a while so I’m not going to do it for when we raise the turn, but you get the idea. For us raising and getting called I will estimate our implied odds at 1BB, and for raising and getting 3bet I will estimate our implied odds at 2BB.

EV CALCULATIONS

Now I have everything I need to do the calculations.
First put everything into some spreadsheet software. You can do it by hand as well, but this is much faster and it lets you mess around with the numbers.


Calculating the EV for calling is the easier one to do. The form of the equation is
EV = (hero’s equity)*(pot size + implied odds) - (1 - hero’s equity)*(cost of call)
As you can see, calling gets us ~0.62BB.


The EV calc for raising is tougher because we need to account for all of villains possible actions. The equation takes this form
EV = (fraction of the time villain will call our raise)*(EV when villain calls) + (fraction of the time that villain will 3bet our raise)*(EV when villain 3bets) + (fraction of the time that villain folds)*(EV when villain folds)

Where,
EV when villain calls = (pot size (including villains call) + implied odds)*(hero’s equity vs villain’s calling range) - (cost of raise)*(1 - hero’s equity)

EV when villain 3bets = (pot size (including villain’s 3bet) + implied odds)*(hero’s equity vs villains 3betting range) - (cost of raising and calling a 3bet)* (1 - hero’s equity)

EV when villain folds = (pot size)

From these calculations we can see that the EV of raising is slightly higher, ~0.63BB.


So versus a villain with a tight 3bet range, these calculations show that semibluffing the turn to fold out part of villain’s range that beats us is slightly more profitable. I don’t think this is necessarily true because the calculations don’t take into account that we could probably bluff out all of those hands on the river if villain gives up and checks. However versus a villain with a wider range preflop, or versus a villain who likes to fire the last barrel, semibluffing will go up in value.

Hopefully this can be used as a reference for doing your own EV calculations.

[secretprankster]

This is a pretty cool post. Could only skim right now because I'm working, but I just wanted to say I think you are overestimating the times Villain folds immediately on the turn.

[gehrig]

yourface looks like u have the right idea but u really need to weight ranges. ppl dont 3bet qts 100% and qjo 0%. they also dont fold kq 100% on turn

[Leader]

[ QUOTE ]
yourface looks like u have the right idea but u really need to weight ranges. ppl dont 3bet qts 100% and qjo 0%. they also dont fold kq 100% on turn

[/ QUOTE ]

This is true, but I think the idea of this post is to show the basic structure of hand analysis in this situation. A completely actuate and realistic analysis of even one situation would be time consuming and highly subjective. Assumptions make analysis such as this more accessible. So, while it's less accurate, it yields some result, which, for the most part, is better then none. Even if you don't agree the process in yourface's post can easily be extended to create more realism (accounting for the flush possibility, non-dichotomous hand ranges ect.)

[Volkan-20]

Gosh why do I suck so hard at math? I have a hard time even understanding those easy EV calculations I just feel like I'm an idiot sometimes. I think this is a great post though and I will do my best to work myself through it!
Thx

[yourface]

bump

I had initially planned on doing this for a wider 3bet range as well but it ended up taking longer than expected

gehrig I've never considered weighting postflop calling ranges. I'll have to put more thought into that