Don't fold, just ask: NL: Light 4 bets Part 2
by PokerStrategy.com
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There are moments in the life of every poker player in which the substantiated advice of a professional is extremely valuable. Going by the motto "together instead of alone" you can now get this well-grounded advice from our professional content team. This includes our content-chef, Onkel Hotte (Fixed Limit), Sammy (No limit, SNG), Wishmaster (Fixed Limit, Real-Life-Poker). Whether you are unsure about a hand, have questions about poker theory or any other matters - ask!
This time we present the second part of Sammy's analysis of the the question of Ghostmaster and joosP. You can find the first part here: Sammy answers part 1
| Question of Ghostmaster / joosP |
No-Limit
Two simple questions:
1. Under which circumstances should you make a light 4bet in reaction to a light 3-bet
2. When and against which opponents should you bluff-4bet (2,25 times)?
| Answer (part2) from sammy |
Having discussed the fundamental parameters in the first part and knowing what we have to look out for when we are thinking about bluff-4-betting an opponent, we will now deal with the concrete decision about the bet size of our 4-bet.
In no-limit holde'em players have the great advantage of choosing the bet size. This is an advantage because by choosing certain bet sizes we can manipulate the pot size to our advantage and animate our opponents to make mistakes.
After such an introduction some might think that I can provide some charts which enable you to make perfect 4-bet sizes. Unfortunately I have to disappoint you. There will not be any charts today.
| sammy |
 Jan Samuelsen aka sammy supervises the no-limit section from PokerStrategy. He was very successful as a player himself and reached the black member status. He is now teaching the following generation the art of, what he calls, big-balls-poker. |
If we are 4-betting preflop we should distinguish two different situations because we have to analyse them differently.
Case 1:
Our 4-bet is an all-in. It doesn't matter whether we are actually moving all-in or whether we have the opponent covered. The attribute is that there is no possibility to 5-bet either by our opponent or by us. He can only call the 4-bet or fold.
Case 2:
Our 4-bet is not an all-in. This is the normal case because we don't usually think about 4-bet pushing a strong hand by default. In general our intention is to protect our monsters but still keep the opponent in the hand preflop. A direct all-in as a 4-bet push would chase the opponents out of the hand too often when the stack sizes are very large.
Let's look at the option of putting our opponent all-in with our 4-bet or respectively to put our whole stack in the middle. Such all-in bets have to be analysed differently because they depend on the relative stack sizes. Sometimes we are even forced to move all-in.
4-Bet Push without fold equity
The first question, which I want to answer, is: When do we have to move all-in with our 4-bet preflop?
Speaking of being forced means that a push has a neutral EV at least. The results which the formula is going to calculate are the necessary parameters so that it wouldn't make any difference for us to fold or push. This means that we wouldn't make a mistake by pushing. We assume that a call has a lower total expected value than a fold.
You have to consider the following parameters:
- Our open raising range
- Dead money in the pot
- The effective preflop starting stacks
- Our equity expected against the range of our opponent
If we were able to put definite numerical values on all four parameters, it would be very easy to decide whether to 4-bet all-in or not.
Let's calculate the expected value and consider all variables to see what we can get from this.
Basic equation:
EV = 0 = ( pot size + calling size of the opponent) * equity + (1-equity) * (- own bet size)
This is a standard calculation of the expected value. We look at how much we would win and how much we would loose if the opponent calls our push.
Definition of the parameters:
Pot size = own open raise + opponent's reraise + dead money
Opponent's calling size = effective preflop stack - opponent's reraise
Own bet size = effective preflop stack - open raise
I assign algebraic letters to the important parameters. These are randomly chosen by me. You could assign completely different letters, I chose these...
Own open raise: α
Dead money : d
Opponent's reraise : r
Effective preflop stack : S
Equity : E
EV = 0 = (α + r + d + (S – r)) * E + (1 – E) * (-(S – α))
I simplified this equation as much as possible to save us some calculation work later or respecitvely to possibly notice how these variables are connected.
0 = (α + d + S) * E + (1 – E) * (α – S)
0 = E * (d + 2S) + α – S
What do we notice? The 3-betting size of the opponent is irrelevant! Whether he min raises or raises to four times of your raise is not of interest to us and doesn't affect our decision. We will never be able to make him fold anyways. Thats the reason why we don't have to think about the current pot size that we would win if the opponent folds. This will never happen without fold equity anyway.
On the basis of the equation we can now assign concrete numbers to questions like these: Which equity value forces me to always push preflop?
Hero(400$)
BU(100$)
Preflop: Hero is CO with K
, Q
UTG folds, MP3 folds, Hero raises to 14$, BU raises to 30$, 2 folds, Hero ???
All we have to do is solve the equation for equity and put in the variables. If you do this, you get the following result:
E = 0.41747
We therefore need around 42% equity against the 3-betting range of the BU to be able to profitably push in this situation. If we start the equilator, we can see that the range of the BU has to be like the following in order for us to be able to push here:
77+, A8s+, K9s+, QTs+, JTs, ATo+, KJo+ (if he 3-bets us with his top 13% of hands, a 4-bet would be a profitable move)
With a little mathematical skill and some effort you can check these situations on the basis of this equation and see where you are at against specific ranges, different stack sizes and different hands.
Something we definitely learn from this calculation is the following:
If the game theory suggests that we are forced to make a 4-bet all-in, an open raise push would have a higher expected value because we might even create some fold equity through the higher bet size.
However the described situation could very well happen at a cash game table. If a shortstack is situated on our left, we are in the CO and the blinds are deepstacked (like us), our open raise shouldn't be equal to the shorty's stack because the blinds could then exploit us.
The shortstack makes the whole situation more complicated, but we now know how to react to a 3-bet of the short stack, as long as we can reduce his range as good as possible. This mathematical model not only shows when we should 4-bet all-in but also when we should call a 3-bet all-in from the short stack.
4-Bet Push with fold equity
The next step I want to go through is the following: How does the situation change if there is a chance of our opponent folding?
We basically have a very similar situation except the fact that the 3-betting range and the 4-bet calling range is different for our opponent. Theoretically we gain the possibility to win the pot without a show down, which turns our hand into a semi bluff.
Our basic equation for this constellation looks like this:
EV = 0 = fold equity * pot size + (1 – fold equity) * (E * (d + 2S) + α – S)
folde quity : f
pot size = α + r + d
equity = our equity against his 4-bet calling range
0 = (α + r + d) * f + (1-f) * (E * (d + 2S) + α – S)
Rearranging the equation a little, the following results:
0 = f * (r +d – E * (d + 2S) + S) + E * (d +2S) + α – S
This equiation looks very theoretical. Therefore I want to show you how you can use this eqution to analyse real life situation.
Hero(400$)
BU(400$)
Preflop: Hero is CO with A
, 7 UTG folds, MP3 folds, Hero raises to 14$, BU raises to 48$, 2 folds, Hero ???
Should we push all-in straight away even though we are 100BB deep? Could this be any good?
Lets analyse the situation more closely. Which range would a really tight player call us with here?
QQ+, AKs, AKo
What is our equity against this range? It is 28.35!! The next step is to calculate the necessary fold equity by using the eqation above. Rearranging the equation for f we get:
f = -(E * (d +2S) + α – S) / (r + d – E * (d+2S) + S)
Once we have typed in our values, we get a result of 0.69844. He would therefore have to fold 69.84% of his 3-betting range so that we can make a +EV push in this situation.
How do we know what his 3-betting range should be like. There are two ways to get it:
Option 1: Using the equilator to get a range denominated in percent
1. We check what his calling range is using the equilator. In this case it is 2.6%.
2. Using the rule of three we can determine how large his 3-betting range has to be.
x = 2,6 / (100 – 69,84) * 100
x = 8.62
3. The x is equal to the 3-betting range in percent. We enter this into the equilator, always choosing the larger value in case the equilator can't be accurate.
8.62% equate a 3-betting range of 88+, ATs+, KTs+, QJs, AJo+, KQo. To simplify things I always chose the top range from the equilator. This doesn't always apply because some players polarise their 3-betting range.
Option 2: Counting the possible hand combinations by hand
1. We calculate the possible hand combinations of his calling range. In this case there are 27 possibilities (12x AK, 6x QQ, 6x KK, 3x AA). Needless to say that we can't include the ace we are holding. It is a dead card.
2. Making use of the rule of three again we can determine how many hand combinations have to be in his 3-betting range at least
x = 27 / (100 – 69,84) * 100
x = 89,5 (We always round up here to reach a +EV spot)
x = 90
3. We create an individual 3-betting range from 90 hand combinations and determine whether this is to tight or to loose for this player in this spot.
An example would be: (12x AK, 12x AQ, 16x KQ, 6x 88, 6x 99, 6x TT, 6x JJ, 6x QQ, 6x KK, 3x AA, 4x QJs, 4x JTs, 4x T9s)
We can create individual 3-betting ranges with either method and depending on the opponent find out, whether we think that the opponent is looser or tighter, whether a push would be +EV or not.
Normally you would use the equilator for these kinds of calculations. However if you don't have a computer available but still want to analyse a situations you could do this by following the steps described above and count the possible hand combinations by hand.
Lets go back to the analysis of the hand though. I want to give you some general thoughts about pushing straight away...
On the basis of the analysis we can now determine whether the 3-betting range of an opponent is larger or smaller than the needed one so that we could make a +EV 4-bet push with 100BB. We can therefore see that we could definitely push with a suited ace straight away.
When you follow through with this strategy and push a lot preflop, you have to be aware that you will be called by KK or QQ occasionally. This results in us having a maniac image on the table. However this could be beneficial to us in some other situations.
If you ever encounter an opponent who makes very strong 4-bet pushes that you call and he has a suited ace, you shouldn't be thinking that this guy doesn't know what he is doing because he might have actually made a +EV-push against you.
Using the description above you could actually anaylse your own call and 3-betting ranges to find out whether you are exploitable. It wouldn't harm you at all if you found out that you are, but you would have to be able to notice it while you are playing in order to adjust your ranges so that you can exploit your opponent instead of them exploiting you.
Basically it is just a question of which style you want to play and whether you really want to play this way preflop and whether you can actually deal with such a bad table image.
You should also consider that the effective stack sizes play a huge role in this calculation. For example, if we were playing with 66$-stacks we would have to create 78.21% fold equity in order to make the push +EV.
If you want to incorporate this strategy in your game, you should always consider all parameters, rather than randomly pushing any suited ace preflop. Otherwise you could make the mistake of making -EV-pushes and blame it on the higher variance that this style automatically has.
Lets now look at the most interest constellations which most of you are probably interested in.
Normal 4-bet size
Which 4-bet size should we choose if we don't want to push all-in straight away? Thinking about this issue we would assume that our opponent, if he does raise, would push all-in straight away.
We are not going to cover situations where the stack sizes are so large that your opponent could actually 5-bet without moving all-in straight away. You would have to consider how sense full a 4-bet would be with stacks that deep. A 3-bet or a call might actually have their advantages in these situations.
The prerequisite for the bet size is the following: We don't want to commit ourselves with the 4-bet. We do want to leave ourselves the option of folding to a 5-bet without actually making a -EV move.
Let's look at this first to try to derive a mathematical formula that calculates how much we want to bet at max.
In order to derive these formulae we make use of odds and pot odds which we would need in order to call. To simplify things, I am going to set up an inequality which will tell us the bet size that wouldn't commit us.
(1 – E) / E > (S + d + ß) / (S – ß)
ß < -E * (2S – d) + S
Explanation of the variables:
Equity vs. the 5-bet pushing range: E
Effective preflop stack: S
Dead money: d
Our 4-bet size: ß
Lets look at a concrete example:
Hero(400$)
BU(400$)
Preflop: Hero is CO with T
, 8 UTG folds, MP3 folds, Hero raises to 14$, BU raises to 48$, 2 folds, Hero ???
The BU would only 5-bet push against our 4-bet with QQ+, AQs+, AKo. We have around 30% equity.
How much could we 4-bet in order to not commit us?
ß < -0,3 * (2 * 400$ – 6$) + 400$
ß < -241,8$ + 400$
ß < 158,2$
If we were to 4-bet more than 158.2$ we would commit us against the pushing range of our opponent. We would have to call if he pushes because the equity of calling would be higher than folding.
So what was the point in that? We can now narrow down the bet size of our 4-bet. It can be anything between 82$ (a min 4-bet) and 158$ (a non-committing 4-bet).
The prerequisite of not committing us allowed us to determine the possible bet sizes, but we don't know which bet size is the best yet.
One thing we haven't looked at yet is whether our 4-bet preflop is +EV or not, or respectively when it turns into +EV. The same approach as when we are 4-bet pushing all-in applies here.
We have to create a lot of fold equity with our 4-bet so that our opponent folds most of the hands within his 3-betting range enabling us to take the pot before the flop. In contrary to the 4-bet push, which was a semi bluff (we can still win the hand if he calls), the 4-bet would be a pure bluff (If the opponent doesn't fold and 5-bets, we have to fold and therefore have no chance of winning something).
Another difference of these two strategies is the ranges that we consider as a reference. If we push all-in, we don't care what the calling range of our opponent would be.
If we 4-bet normally, the 5-betting range of our opponent is not of interest to us. These two ranges will be different most of the time. Especially if you push all-in straight away quite often, the calling ranges of your opponents could be larger than their own 5-bet push ranges because they might have seen you push all-in with A4s and therefore call you with ATs. They wouldn't 5-bet push ATs if you had a "normal" 4-betting image.
Both strategies are therefore dependent on your table image. One wouldn't be able to tell you which strategy is better because it generally has to suit your game. Surely you would be more familiar with integrating "normal" 4-bets because you would keep your solid image at the table.
The equation for calculating the necessary fold equity for a 4-bet is calculated like a bluff on the river. We have to find out what odds we are getting for a bluff to determine how many hands our opponent has to fold in order to make the bluff +EV.
As usual, I will use the same variables for our open raise, the dead money etc.
Therefore the following applies:
Pot size = α + r + d
Costs of the 4-bet = ß – α
For the necessary fold equity an equation, which puts the pot size and the costs into relation, applies.
f = [(ß – α) / (α + r +d)] / [1 + (ß – α)/( α + r +d)]
For those of you who don't like simplifying and rearranging equations I present you the equation in its simplest form.
f = (ß – α) / (ß + r +d)
If we put in the parameters, we get a result in percent. This numerical value shows us how much of the opponents 3-betting range we have to force to fold.
A min raise should therefore,
f(82) = (82 – 14) / (82 + 48 + 6) = 0.5
force the opponent to fold 50% of his range.
The maximum raise which doesn't commit us yet should therefore,
f(158) = (158 – 14) / (158 + 48 + 6) = 0.6792
force the opponent to fold 67.92% of his range.
Notice that an increase of 76$ increases the fold equity by 17.92%. Is this really that much? Are we really able to increase our fold equity?
Quite often, opponents don't pay attention to the size of the 4-bet because they usually think that they are in a push or fold phase. This means that the equity created is basically the same for a 105$ bet than it is for a 140$ bet. We therefore have to check one aspect a little further which I assumed in the beginning.
We want our opponent to either fold or push to our 4-bet. We don't want to be called because we don't like to play post flop with such a small relationship between the pot and the rest of our stack because we would become committed by betting very quickly.
We should therefore avoid min raising because it provokes too many calls if it is used too much.
I would tend to bet between 102$ and 115$ depending on the history and the opponent.
The more often we raise one opponent the more likely it is that he will play back at us. Knowing about how (call or push) gives us an advantage which we should incorporate in our decision about the 4-bet size.
You notice that I can't provide any charts that tell you the perfect bet size in consideration of the bet sizes, the effective stacks and hands even after having tried to solve the problem of the size of a 4-bet mathematically.
The equation only gives you the option of checking whether you can exploit your opponents' strategy, depending on whether you can actually put him on accurate ranges, because he:
a) he folds too much of his 3-betting range to a push
b) he folds too much of his 3-betting range to a normal 4-bet.
I hope, even without having provided you with charts, that this article showed you a couple of things about 4-bet sizes so that you can find your own "line" and style of play.
Kind regards and all the best at the tables,
Sammy
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