3betting from Blinds - Is my math correct?

[johnnythemoss]

The scenario is: You are in BB facing a 2.5x raise from the Button (assuming 50% opening range). You decide to 3bet resteal with a range of 7.5% (JJ+, AKs, AQo, bluff with A5s, A4s, J7s-J9s, etc). You get called. Now what do you do??

Is the following math correct: In the blind facing the raise, the pot is 4bb (SB+BB+raise of 2.5). Let's say you 3bet to 8bb. You are betting 8 to win 4 so you are giving yourself odds of 1:2. This means that you need to win the pot 66% of the time in order to break even. I used Flopzilla to compare that 3bet range to see what to continue with. To get 66% equity approx, you have to continue on a WIDE range of boards, i.e. any top pair or better, any pocket pair less than top (TT on Q73), ALL straight and flush draws, any middle pair. That''s a lot of poker to play out of position in a 3bet pot, if my assumptions and math are correct. And I don't know how to continue the calculation to the Turn and River.

Please correct me if something is wrong in that analysis.

 

[vinnie]

First, you're risking 7 to win 4. Your raise to 8 only cost you 7xbb because you had 1 in there already. That's 63.6% of the time you need to win.

How much you need to continue with, on the flop, is based on the flop texture and what range your opponent calls with. Say your opponent calls with 16.6% of their hands, 4bets 3.5%, and folds the rest (29.9%).

They are folding 59.8% of the time to your raise. You only need 63.6%, so you're only short 3.8% that you need to really capture. That's not a huge amount.

How much you need to defend will depend on the flop and your opponent, and it might be very high. If you check and your opponent bets something small like 3-4xbb, you will need to defend a large amount of your range to prevent them from showing an automatic profit. If you check and they bet larger, like 8-10xbb, you will need to defend less often.

You will probably lead some of the time, so you'll have some fold equity as well. Playing 3-bet pots out of position isn't the best spot to be in, but your range should be pretty strong, which will compensate.

 

[vinnie]

I realize that I never did answer your question about how much equity you need in that pot, after getting called, to turn a profit.

The formula for this is complicated. It needs to account for many situations:

How often he folds to your 3 bet, how often he 4bets and to what amount, how often you fold to his 4bet (it seems to be about 47.3% from the ranges you gave), if you ever just call a 4 bet your equity against his range on those flops, how often he folds to your shove after 4 betting, how often he 4bets and then calls your shove and the range he has when he does and your equity against that range, and how often he just calls.

Based on your numbers, and some very reasonable estimates, you might only need to get 8% of the pot on the flop. That is, you only need to win an average of 1.3 bb from the pot to break even over all the possible ways the hand could play out.

Considering how strong your range is, especially compared to a calling range, you should be able to get more than that much on average from the pot. Of course, this gets very complicated because more money is likely to go into the pot, and that will also impact things. You will want to make sure that decisions are all averaging more than 1.3 bb net over the course of the hand.

The real issue here is that a lot of your equity comes from the folds that normally happen, and when you get called, you only need to make up for a small amount of equity to make the overall raise profitable. Long term, it should be easy to get the right amount in this spot.

 

[UkoChebuko]

First, I don't think in reallity someone folds 2/3 form 50% range with this pot odds (2.5x OR and 8bb 3bet). But we are talking about the math. My math is weak . But if he folds 66%, you don't need 66% equity to be BE. This pot is for free. When he calls or 4bet. All this is "for free". Very profitable 3bet obv. You are talking about BE.
And I don't use polarized ranges. By default. I don't care much for the FE. 50% OR, 50% FE, cool, easy 3bet ATs , 99, AJo, KQo. Why call? I prefer 3bet. And this "A5s, A4s, J7s-J9s", I am calling with this. If he folds 60% +, I will use this for 3bet as well. Maybe...There are lot of reasons..To use polarized range...To use depolarized range, you need only high OR percentage. And you can see this very easily.

If you invest 8bb to take this 4bb, then the 3bet is 9bb. To 9bb...Not 8bb. And yes, there are some nits, they will fold 66% from 50%. Very profitable 3bet. You can 3bet even with ATC. if he is "blind". You not expect a "defend", "adaptation".

 

[johnnythemoss]

First, you're risking 7 to win 4. Your raise to 8 only cost you 7xbb because you had 1 in there already. That's 63.6% of the time you need to win.

I'm not following your logic here. The blind has already been posted and is in the pot. The pot is exactly 4bb when the action reaches me. If I 3bet to 8bb, I am putting in an additional 8bb as well the 1bb I posted at the beginning of the hand.

 

[johnnythemoss]

First, I don't think in reallity someone folds 2/3 form 50% range with this pot odds (2.5x OR and 8bb 3bet). But we are talking about the math. My math is weak . But if he folds 66%, you don't need 66% equity to be BE. This pot is for free. When he calls or 4bet. All this is "for free". Very profitable 3bet obv. You are talking about BE.
And I don't use polarized ranges. By default. I don't care much for the FE. 50% OR, 50% FE, cool, easy 3bet ATs , 99, AJo, KQo. Why call? I prefer 3bet. And this "A5s, A4s, J7s-J9s", I am calling with this. If he folds 60% +, I will use this for 3bet as well. Maybe...There are lot of reasons..To use polarized range...To use depolarized range, you need only high OR percentage. And you can see this very easily.

If you invest 8bb to take this 4bb, then the 3bet is 9bb. To 9bb...Not 8bb. And yes, there are some nits, they will fold 66% from 50%. Very profitable 3bet. You can 3bet even with ATC. if he is "blind". You not expect a "defend", "adaptation".

First, how can an investment of 8 to win 4 be considered 9? The 1 blind was already in the pot, whether I call fold or 3bet.

Second, the question was more to do with how to continue on the flop after I am called. I feel like the 3bet is profitable but trying to justify it with math is not so easy since you have to continue with such a wide range out of position. You can't just 3bet preflop and check fold every time you don't hit top pair or better.

 

[UkoChebuko]

Mate, my English is bad, I can't really understand. Sorry for that. I just want to help, not to argue.
"Investment of 8b", then you are on big blind. I understand this like "9bb 3bet". 8 blinds to win 4 blinds. This big blind is not a "investment". You already pay this. This is a "dead money". In my eyes...

For this below..."How to continue"...Mate, I already explain this. If the people fold too much, then you can do whatever you want. You can check-fold or bet. If you see profitable bet for value, then bet. As bluff, profitable bluff, then bet. If you are not sure, just check-fold then. You don't need a balance or "not giving up", "not exploited".
Let's say , you see some player, who fold too much from BB. You raise from SB with 83o. How to continue!? I will look for "fold to Cbet", I will bluff (maybe) on some boards. I will continue ofc with pair, even a bottom pair. At least OTF. But my plan is not to "making money from 83o", this "monster hand". I will hope for big FE and for something postflop. Sometime. The hand is pretty bad, you know. But still can be profitable in long run., Exactly vs this player. And with 3bet is just the same. But let's say if I have KJo, then I will continue more often. My plan is different. I can even play for stacks with this hand. And that's why I am already not looking for high FE. That's I mean. In the first post. All is connected. Preflop play and postflop play. The profit from every street is very little in a long run. All is conected. You have a profit only one blind for a hand. Most likely... For "all" hand...

I can't explain better. "How to continue". Well, show some hand, give some info, I try to explain better.

 

[vinnie]

I'm not following your logic here. The blind has already been posted and is in the pot. The pot is exactly 4bb when the action reaches me. If I 3bet to 8bb, I am putting in an additional 8bb as well the 1bb I posted at the beginning of the hand.

You said you were 3-betting TO 8bb. That means you are putting in 7bb more on top of the 1bb that is already in front of you. The 1bb that is in front of you does not count as money you're risking, as it's already invested and is gone. It's not your money any more. It's the pot's money. There is 4bb out there (SB's 0.5bb, BB's 1bb, BTN's 2.5bb) and you are putting in 7bb more to try and win it. Yes, I know you're the BB and already put in 1bb, but that's not your money any longer. You are risking 7bb to win 4bb.

Like I said, you only need to win 63.6% of the time. Most of that 63.6% is going to come from him folding to your 3bet. The rest of it represents a tiny fraction of the pot. You don't need to win the pot (when he calls) 63.6% of the time.

 

[johnnythemoss]

You said you were 3-betting TO 8bb. That means you are putting in 7bb more on top of the 1bb that is already in front of you. The 1bb that is in front of you does not count as money you're risking, as it's already invested and is gone. It's not your money any more. It's the pot's money. There is 4bb out there (SB's 0.5bb, BB's 1bb, BTN's 2.5bb) and you are putting in 7bb more to try and win it. Yes, I know you're the BB and already put in 1bb, but that's not your money any longer. You are risking 7bb to win 4bb.

Like I said, you only need to win 63.6% of the time. Most of that 63.6% is going to come from him folding to your 3bet. The rest of it represents a tiny fraction of the pot. You don't need to win the pot (when he calls) 63.6% of the time.

Let me put it like this. Let's say I have 100bb and then I post 1bb in the big blind. I have 99bb and there's 1.5bb in the pot (SB+BB). The raiser in late position puts in 2.5bb, making the pot 4bb. I 3bet by betting 8bb from my stack, making the pot 12bb. My stack is now 91bb. I don't count the 1bb in the big blind as part of my 3bet because, as you said, the money is gone the moment the blind is posted. It's not my money anymore so I can't count it as part of my 3bet. It's a 3bet to 8bb but it has nothing to do with the 1bb I posted in the bb.

 

[vinnie]

Let me put it like this. Let's say I have 100bb and then I post 1bb in the big blind. I have 99bb and there's 1.5bb in the pot (SB+BB). The raiser in late position puts in 2.5bb, making the pot 4bb. I 3bet by betting 8bb from my stack, making the pot 12bb. My stack is now 91bb. I don't count the 1bb in the big blind as part of my 3bet because, as you said, the money is gone the moment the blind is posted. It's not my money anymore so I can't count it as part of my 3bet. It's a 3bet to 8bb but it has nothing to do with the 1bb I posted in the bb.

This is a language issue. When you say that you raise TO 8bb, it means you make the current bet 8bb. If you were to say that you raised 8bb more, that means you add 8bb to the last bet (making it 10.5bb in this case). There's no consistent way to say what you're trying to say in the way you're trying to say it. The best way would be to say that you raised to 9bb. Yes, it's 8bb more from your stack, but you're making the current bet 9bb because of the 1bb already in the pot from you during this round.

In that case, you would need 66.7% equity, but it really doesn't change much.

Imagine you played this situation 1000 times. That means you put in 8,000 chips. 598 times you will get 12 chips (4 + the 8 you risk) because your opponent folds. That's 7,176 chips back. You only need to win 824 more chips from the remaining 402 pots that are 18.5bb. You don't need to continue 67% of the time. If you bet 12% of the time and your opponent always folds and you just give up the rest, you'll show a profit. And, you probably play this spot better than that.

Now, this assumes you never get 4bet, but if you include that it doesn't take much equity from this whole situation. And, that also assumes that you don't win a bigger pot when you flop really well. But, all that's really not your original question. The main point is that you don't need to continue anywhere near 67%.

 

[johnnythemoss]

This is a language issue. When you say that you raise TO 8bb, it means you make the current bet 8bb. If you were to say that you raised 8bb more, that means you add 8bb to the last bet (making it 10.5bb in this case). There's no consistent way to say what you're trying to say in the way you're trying to say it. The best way would be to say that you raised to 9bb. Yes, it's 8bb more from your stack, but you're making the current bet 9bb because of the 1bb already in the pot from you during this round.

In that case, you would need 66.7% equity, but it really doesn't change much.

Imagine you played this situation 1000 times. That means you put in 8,000 chips. 598 times you will get 12 chips (4 + the 8 you risk) because your opponent folds. That's 7,176 chips back. You only need to win 824 more chips from the remaining 402 pots that are 18.5bb. You don't need to continue 67% of the time. If you bet 12% of the time and your opponent always folds and you just give up the rest, you'll show a profit. And, you probably play this spot better than that.

Now, this assumes you never get 4bet, but if you include that it doesn't take much equity from this whole situation. And, that also assumes that you don't win a bigger pot when you flop really well. But, all that's really not your original question. The main point is that you don't need to continue anywhere near 67%.

I understand now. I was mistakenly assuming that I have to realize the 67% equity postflop and that if I can't do that then the 3bet is bad. But I see that combining the equity from the preflop folds with the equity from when I hit the flop, it should be profitable. Thanks for the explanation.

 

[vinnie]

Yeah, that is what I was trying to explain above in the first post I made, sometimes it is easier to think of it as playing 1,000 hands instead of as percents. It just makes it more clear.

As an aside, when you are only called (he didn't 4-bet), your hands should be stronger than his on average. That's because he would have 4-bet with the best hands. So, it should be pretty easy to win more than your share of the pots.

 

[BatOneHat]

Never Bluff the Fish

i agree with the three bet with the 7.5%, but i do not understand why you would try to bluff in this position. I know you are trying to defend, but I would fold a lot of those hands unless I knew the other players were playing very, very lose.

 

[vinnie]

i agree with the three bet with the 7.5%, but i do not understand why you would try to bluff in this position. I know you are trying to defend, but I would fold a lot of those hands unless I knew the other players were playing very, very lose.

Your typical button will raise-first-in 45-60% of their hands. Often they will even raise more often. You 3-bet your value hands, of course, and you call with the hands that will do well against his range. But, you also want to 3-bet the hands that are on the weaker side because they gain EV when he folds too much. Those hands should still have equity when called (like A5s) and having an Ace is nice because it makes it harder for the button to have a hand like AA or AK.

The other benefit of this is that getting caught 3-betting A4s makes your opponent more likely to call your 3-bets with worse hands, because they know you aren't raising only KK+.

 

[UkoChebuko]

As an aside, when you are only called (he didn't 4-bet), your hands should be stronger than his on average. That's because he would have 4-bet with the best hands. So, it should be pretty easy to win more than your share of the pots.

Do you mean range vs range advantage? If you do, that's is not like that. Too simple to be true. This I tried do explain, but It's not so easy for me obv . You don't need "range advantage" to make this 3bet profitable. And sometime even with range advantage this 3bet still can't be profitable. It is not so simple, guys. Like I said, this is all connected. Preflop profit from the aggro move, postflop profit. At any street. And "overall" you must have profit. With bottom of your range for 3bet it is often one blind or less. If you use only obv hands for 3bet or OR (with "range advantage"), then you never will have a good win rate. This spots with borderline profit will made you a crusher. No matter NL5, NL10 or NL50. Ofc this comes with higher variance. But this is "the poker", this is always like that. This spots are not rare. Most of the profitable spots are "borderline", with very little profit. This is because NL Holdem is very "luck dependent", your edge is small. That's why this format is so popular.

Ok, an example. Let's say some guy opens 40% from the BTN. 50% FE vs resteal. We have QJs from the SB. We don't have an "autoprofit", we don't have a "range advantage" vs his calling range. Still it is not too hard to make a profitable 3bet. Still be bad call (SB vs BTN). Most likely...At least the 3bet will be more profitable. Than call..This is a "depolarized" range. You can make a profit with call with bottom of your range for 3bet. You still choice 3bet. For this one blind extra profit. Or half of blind, whatever. If you have ten spots in 100 hands, you can see the difference. Ten "borderline spots".

 

[BatOneHat]

Makes Sense

That makes a lot of sense.

 

[UkoChebuko]

That makes a lot of sense.

Is this ironic? I know, I can't explain, sorry.
I wrote a huge article about this. "3bet, depolarization vs polarization". But in my community, in my native language. Many people liked my article. I tried in English, but I can't. I must learn this language. I never learned English. I mean lessons. I learn some English from the movies and the PC games.

 

[UkoChebuko]

I look at my posts now and it is very unclear. I mean this "all math" for the 3bet spots, equity, fold equity, "autoprofit" , "enough equity for call vs 3bet", this all is pretty stupid. Polarized ranges, calling ranges with hands with "enough equity". I never met someone, who use that. And who play for a living. This is all just a theory. Useless theory...It same like then you open raise. 2bet...For 3bet, 4bet, 5bet is just the same , but with narrow ranges and different SPR. Then you open raise with some hand , you don't think about the "autoprofit", you don't think about the "range advantage" vs his calling range. You just play this hand, because you think is good enough. Also you don't use open limp. Or over limp...The raise is the better option. Enough good hand for a raise. But you don't limp with some "enough good hand for limp" and raise in the same position with very good hands and trash (polarized range). No one does that. But still they use polarized ranges for 3bet. As default, without info. With some weird math...

And this question "How to continue?"...How to continue , then you use 2bet, someone calls and you are OOP!? Play only good hands, don't use trash and "the continue" will be pretty obv. Use trash only vs some players, who fold too much. And then no need "for continue", you already take enough profit. The same like SB, BTN OR. How to continue with 72o!? No need for "continue" obv...Still I use this hand very often at this positions. This is a profit...