|
It seems you have 72% equity on the range that you put him on for his 3-bet so certainly raising makes sense?
I'd like to try and calculate this but I' m not sure how.
(7x5 + 1) +(6) + (24) total combos that he 3-bets with.
= 66 combos that he 3-bets with.
Of which 7 he shoves, 8 he calls, and 51 he folds.
He shoves 10.5%, he calls 12%, he folds 77% of the time.
Pot is 77.5
So what is the minimum bet that is EV?
If B is the bet and P is the pot then:
-(10.5% x B) + (77% x P) (+/-?) (12% x B+P) = 0
Do we add the percentage of times he calls because we beat those combos or what?
Or is that segment of the equation in fact:
(the equity percentage that hero would have against his calling range multiplied by the 12% multiplied by Villain' stack) - (the equity percentage of Villain's calling range hand multiplied by his stack multiplied by the 12%)
I wish I knew.
Note: the below is just an example to explain to Tasha, it's not meant to justify plays in the hand above.
First, I am holding KK, so keep in mind these two K's cannot participate to the combos in his range.
Say he 3-bets with 88+,AQ+:
- there are 6 each combos of 88-QQ and AA = 6x6 = 36
- there is 1 combo of KK
- there are 16 combos of AQ (4 of them suited)
- there are 8 combos of AK (2 of them suited)
Total 61 combos
Yes I am ahead of his 3b range. This is the relevant range if I call. But if I 4b (say to $1.50), and he calls or shove, the range I will be up against is his 4b calling or his shoving range. In other words, it only makes sense to raise if I am ahead of his 4b calling range AND 5b ranges together, called his "continuing" range.
So let's suppose his continuing range is QQ+,AKs. That's 6 QQ combos, 1 KK combo, 6 AA combos and 2 AKs combos only. Total 15 combos. So he continues 15/61 = 25% of the time when I 4b. He folds 75% of the time.
When he continues, let's assume he shoves only KK+. I would have to fold because I don't have the odds to call (22.6% equity < 30.7% pot odds). KK+ is 7 combos, so that's 7/15 = 50% of his continuing range. The rest calls, and against his calling range QQ,AKs I have 78% equity.
It's not finished. Now you have to use the above numbers to calculate the EV of 4-betting and the EV of calling and see which one is higher.
Currently in the pot is $0.73. Let's say I 4b to $1.25 (adding $1.05 in the pot)
4-bet EV =
- 75% of the time he folds and I win $0.73
- 12.5% of the time he shoves, I fold and I loose the $1.05 I added in the pot
- 12.5% of the time he calls. Let's imagine for the sake of the exercise that none of us will put more money in the pot on further streets (or if one of us does, the other knows he is an underdog and folds). So 78% of the time I will win the $0.73, but 12% of the time I will loose my $1.05 investment.
So the equation is 0.75*$0.73 - 0.125*$1.05 + 0.125*(0.78*$0.73-0.12*$1.05) = $0.50 The EV of 4betting is $0.5
Now need to calculate the EV of just calling his 3b: if we only call he 3b, we are sort of underrepresenting our hand (he cannot put us on a range as narrow as if we 4b), so there is a better chance that more money will go in the pot (this is made more likely if you have position on him, that is why in general it is better to consider calling when you have position, on top of all the other advantages of position). Let's say that the stacks will go in to simplify. If we call we are now up against his whole 3b range, 88+,AQ+, against which we have 70% equity.
So EV of calling (stacks will go in after the flop, effective remaining stack is $3.44, dead money in the pot is $0.73 and the call costs $0.30):
- 70% of the time we win $3.44+$0.73
- 30% of the time we loose $3.44+$0.30
0.7*$4.17-0.3*$3.73=$1.8 >> $0.5
However if no more money went in the pot when just calling, then the EV would only be 0.7*$0.73-0.3*$0.30=$0.42 < $0.50, but not by much. This is to show that it doesn't take that much more extra money in the pot to make calling a superior play (you can calculate how much more money exactly should go in the pot to make calling a better play).
Another way of seeing it is that the 4b has the effect of defining our range very narrowly, allowing him to play almost perfectly against our range.
Or yet another way to see it is that we could have a better chance of extracting by just calling.
Now that's all theory. At 2/5NL, pretend to be a donkey and insta-shove all your stack over his 3b. You'd be surprised how often you get called...
Hope this helps. It helped me also to refresh these concepts. If anyone has good links to articles about the theory of 3/4-betting, please ship.
|